Methods and systems for explainable material-based determinations

Abstract

Systems, computer program products, and methods are described herein for explainable material-based determinations. The present invention is configured ingest, by a model, a first dataset including one or more first data entries associated with a material, generate, using the model, a second dataset including one or more second data entries associated with one or more properties of the material, generate an attribution dataset including one or more attribution data entries, where the attribution dataset is indicative of an influence or causal relationship associated with the model and / or the attribution dataset is indicative of an influence or causal relationship between the first dataset and the second dataset, output the second dataset, and / or output the attribution dataset.

Description

METHODS AND SYSTEMS FOR EXPLAINABLE MATERIAL-BASEDDETERMINATIONSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present international application claims priority' to U.S. Provisional Patent Application No. 63 / 670,047, filed July 11, 2024, the entire contents of which application is incorporated by reference in its entirety.TECHNOLOGICAL FIELD

[0002] Embodiments of the present disclosure relate generally to materials and, more particularly, to systems and methods for explainable material-based determinations.BACKGROUND

[0003] The properties, performance, composition, and similar characteristics of materials (e.g., cementitious mixes) may vary over time and under different contextual conditions. As such, these characteristics may be subject to modeling to inform vanous material-based determinations. Conventional material modeling is often viewed as a "black box,” where the model produces an output, but there is a lack in understanding of why a certain output was produced by a model (e g., a lack of explainability' and / or interpretability of an output of a model). Through applied effort, ingenuity, and innovation, many of the problems associated with explaining and / or interpreting material determinations have been solved by developing solutions that are included in embodiments of the present disclosure, many examples of which are described in detail herein.BRIEF SUMMARY

[0004] Embodiments of the present disclosure therefore provide for methods, systems, apparatuses, and computer program products for explainable material-based determinations.

[0005] In one aspect, a computer-implemented method for explainable material models may include ingesting, by a model, a first dataset including one or more first data entries associated with a material, generating, using the model, a second dataset including one or more second data entries associated with one or more properties of the material, and / or generating an attribution dataset including one or more attribution data entries, where the attribution dataset may be indicative of an influence or causal relationship associated with the model. Further, the attribution dataset may be indicative of an influence or causal relationship betweenthe first dataset and the second dataset. Additionally, or alternatively, the method may further include outputting the second dataset, and / or outputting the attribution dataset.

[0006] In some embodiments, the method may further include parsing, via a large language model (LLM), the attribution dataset to generate a trained LLM, providing, via a network interface, a graphical user interface (GUI) to a user, receiving, via user input into an interactable environment on the GUI and via the network interface, a user query associated with the one or more properties of the material, and / or providing, via the network interface and using the trained LLM, a response to the user query. Additionally, or alternatively, the method may further include ingesting a first weight set including one or more first weight entries associated with the first dataset, encoding the first dataset to generate a first transformed dataset, and / or generating, using the first weight set and the first transformed dataset, the second dataset.

[0007] In some embodiments, the method may further include generating, for each first weight entry7of the one or more first weight entries, a type associated with a degree of freedom associated with the first weight entry to generate a first typed weight set and / or storing the first typed weight set. Further, the method may include analyzing the second dataset and the first typed weight set to derive a first conclusion and / or generating the attribution dataset including the first conclusion. Additionally, or alternatively, the method may include analyzing a first entry of the typed weight set to determine an agentic model of a plurality of agentic models associated with a type of the first entry perturbing, via the agentic model, a weight of the first entry to generate a perturbed second data entry comparing, via the agentic model, an associated second data entry of the one or more second entries and the perturbed second data entry' to generate a second data entry' comparison, and / or generating the attribution dataset including the second data entry comparison.

[0008] In some embodiments, the method may include analyzing a data entry of the first dataset to determine an agentic model of a plurality7of agentic models associated with a type of the data entry7, perturbing, via the agentic model, a value of the data entry7to generate a perturbed second data entry7, comparing, via the agentic model, an associated second data entry of the one or more second data entries and the perturbed second data entry to generate a second data entry' comparison, and / or generating the attribution dataset including the second data entry comparison. Additionally, or alternatively, the method may include analyzing a data entry7of the first dataset and a first entry of the typed weight set to determine an agentic model of a plurality of agentic models associated with a type of the data entry7and a type of the first entry, perturbing, via the agentic model, a value of the data entry7and a weight of the first entry7togenerate a perturbed second data entry, comparing, via the agentic model, an associated second data entry and the perturbed second data entry to generate a second data entry comparison, and / or generating the attribution dataset including the second data entry comparison.

[0009] In some embodiments, the method may include identifying a data cluster within the first dataset, generating one or more causal features associated with the data cluster, and / or generating the attribution dataset including the one or more causal features. Additionally, or alternatively, the method may include ingesting a first subset of the first dataset to generate the second dataset and / or generating, using the second dataset and a second subset of the first dataset, an attribution data entry of the one or more attribution data entries including an interpretation of the second dataset in a context of the second subset, where the first subset and the second subset are absent shared first data entries.

[0010] In some embodiments, the method may include varying a first data entry of the one or more first data entries to generate a varied first dataset, generating, using the varied first dataset, a varied second dataset including the second dataset with a change in at least one second data entry of the one or more second data entries, and / or generating a continuous function mapping including the varied first data entry and the at least one second data entry. Additionally, or alternatively, the method may include perturbing, for each first weight entry of the one or more first weight entries, a first weight entry to generate a perturbed first weight set, generating, for each perturbed first weight entry of the perturbed first weight set, a perturbed second dataset including one or more perturbed second data entries, comparing the second dataset to each perturbed second data entry of the perturbed second dataset, identifying, via the comparison, a redundant weight of the one or first weights, and / or pruning the redundant weight from the first weight set.

[0011] In another aspect, a computer-implemented method for explainable material models may include ingesting, by a model including at least two modules, a first dataset including one or more first data entries associated with a material, generating, via ingestion of a first input including a first subset of the one or more first data entries in a first module of the at least two modules, a first output associated with a first property of the material, and / or generating, via ingestion of a second input including a second subset of the one or more first data entries in a second module of the at least two modules, a second output associated with a second property of the material, w here a modularity of the model may be associated w ith an influence or causal relationship. Additionally, or alternatively, the influence or causal relationship may be indicative of a relationship between the first dataset and the first output, the first dataset andthe second output, the first input and the second output, and / or the first output and the second output.

[0012] In some embodiments, the method may include generating an attribution dataset including one or more attribution data entries associated with the influence or causal relationship between the first property' and the second property. Additionally, or alternatively, the method may include ingesting a first weight set including one or more first weight entries associated with the first dataset, encoding the first dataset to generate a first transformed dataset, and / or generating, using the first weight set and the first transformed dataset, the first output.

[0013] In some embodiments, the method may include generating, for each first weight entry of the one or more first weight entries, a type associated with a degree of freedom associated with the first weight entry to generate a first typed weight set and / or storing the first typed weight set. Further, the method may include analyzing the second output and the first typed w eight set to derive a first conclusion and / or generating the attribution dataset including the first conclusion. Additionally, or alternatively, the method may include analyzing a first entry of the typed weight set to determine an agentic model of a plurality of agentic models associated with a type of the first entry, perturbing, via the agentic model, a weight of the first entry to generate a perturbed first output, comparing, via the agentic model, the first output and the perturbed first output to generate a first output comparison, and / or generating the attribution dataset including the first output comparison.

[0014] In some embodiments, the method may include analyzing a data entry of the first dataset to determine an agentic model of a plurality of agentic models associated with a type of the data entry, perturbing, via the agentic model, a value of the data entry' to generate a perturbed first output, comparing, via the agentic model, the first output and the perturbed first output to generate a first output companson, and / or generating the attribution dataset including the first output comparison. Additionally, or alternatively, the method may include analyzing a data entry of the first dataset and a first entry' of the ty ped weight set to determine an agentic model of a plurality of agentic models associated with a type of the data entry and a type of the first entry’, perturbing, via the agentic model, a value of the data entry and a weight of the first entry to generate a perturbed first output, comparing, via the agentic model, the first output and the perturbed first output to generate a first output comparison, and / or generating the attribution dataset including the first output comparison.

[0015] In some embodiments, the method may include identifying a data cluster within the first dataset, generating one or more causal features associated with the data cluster, and / orgenerating the attribution dataset including the one or more causal features. Additionally, or alternatively, the method may include, when generating the first output, ingesting an output of the first module in a first intermediate module, and generating, via an output of the first intermediate module, the first output. Further, the attribution dataset may include an uncertainty measurement associated with the output of the model, and the method may include identifying a module out of the first module, the first intermediate module, and the second module with a higher contribution to the uncertainty measurement and / or generating an attribution data entry of the one or more attribution data entries including data indicating the module identified with the higher contribution. Additionally, or alternatively, the first intermediate module may be a first module ofN intermediate modules and N may be a positive integer number. Further, an i- th intermediate modules of the N intermediate modules may be configured to receive an output of an (i - 1) intermediate module of the N intermediate modules, and an Nth intermediate module of the N intermediate modules may be configured to generate the first output.

[0016] In some embodiments, the method may include ingesting a first subset of the first dataset to generate the first output, generating, using the first output and using the second module, the second output, and / or generating, using the second output and a second subset of the first dataset, an attribution data entry of the one or more attribution data entries including an interpretation of the second output in a context of the second subset, where the first subset and the second subset may be absent shared first data entries. Additionally, or alternatively, the method may include varying a first data entry of the one or more first data entries to generate a varied first dataset, generating, using the varied first dataset, a varied first output, generating, using the varied first output and the second module, a varied second output, and / or generating a continuous function mapping including the varied first data entry and the varied second output.

[0017] In some embodiments, the method may include perturbing, for each first weight entry of the one or more first weight entries, a first weight entry to generate a perturbed first weight set, generating, for each perturbed first weight entry of the perturbed first weight set and using the first module, a first output set including one or more first output entries, comparing the first output to each first output entry of the first output set, identifying, via the comparison, a redundant weight of the one or first weights, and / or pruning the redundant weight from the first weight set. Additionally, or alternatively, the method may include generating a plurality of first weight groups each including at least two first weight entries of the one or more first weight entries, generating, for each first weight group of the plurality of first weight groups and using the first module, a first output set including one or more firstoutput entries, comparing the first output to each first output entry of the first output set, identifying, via the comparison, a redundant weight group of the plurality of first weight groups, and / or pruning the redundant weight group from the first weight set.

[0018] In some embodiments, the material may be a cementitious mixture. Further, the output may include a data visualization of data indicating a relationship between compressive strength of the cementitious mixture and a time to cure for the cementitious mixture. Additionally, or alternatively, the output may include a prediction of time required to reach a compressive strength value for the cementitious mixture Further, the prediction may be based on environmental conditions associated with a location and a time of year associated with the cementitious mixture.

[0019] The above summary is provided merely for purposes of summarizing some example embodiments to provide a basic understanding of some aspects of the present disclosure. Accordingly, it will be appreciated that the above-described embodiments are merely examples and should not be construed to narrow the scope or spirit of the disclosure in any way. It will be appreciated that the scope of the present disclosure encompasses many potential embodiments in addition to those here summarized, some of which will be further described below.BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Having thus described certain example embodiments of the present disclosure in general terms, reference will now be made to the accompanying drawings. The components illustrated in the figures may or may not be present in certain embodiments described herein. Some embodiments may include fewer (or more) components than those shown in the figures.

[0021] Figure 1 illustrates an example system for explainable material-based determinations in accordance with an example embodiment of the present disclosure;

[0022] Figure 2 illustrates a block diagram of example circuitry (e.g., server circuitry) that may be specifically configured in accordance with an example embodiment of the present disclosure;

[0023] Figure 3 illustrates an example model for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0024] Figure 4 illustrates an example prediction model for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0025] Figure 5 illustrates an example prediction model for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0026] Figure 6 illustrates an example generation model for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0027] Figure 7 illustrates an example physico-chemical and empirical model for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0028] Figure 8 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0029] Figure 9 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0030] Figure 10 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0031] Figure 11 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0032] Figure 12 illustrates a flow chart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0033] Figure 13 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0034] Figure 14 illustrates a flow chart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0035] Figure 15 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0036] Figure 16 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0037] Figure 17 illustrates a flow chart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0038] Figure 18 illustrates an example process flow- for agentic perturbations for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0039] Figure 19 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0040] Figure 20 illustrates a flow chart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0041] Figure 21 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0042] Figure 22 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0043] Figure 23 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0044] Figure 24 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0045] Figure 25 illustrates a flowchart for an example method for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0046] Figure 26 illustrates an example process flow for model compression for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0047] Figures 27A-27B illustrate example sensor types for data generation for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0048] Figure 28 illustrates an example of sensor data generation for explainable materialbased determinations in accordance with some embodiments of the present disclosure;

[0049] Figure 29 illustrates an example model output for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0050] Figure 30 illustrates an example explainable insight for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0051] Figure 31 illustrates an example explainable insight for explainable material-based determinations in accordance with some embodiments of the present disclosure:

[0052] Figure 32 illustrates an example explainable insight for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0053] Figure 33 illustrates an example explainable insight for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0054] Figure 34 illustrates an example explainable insight for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0055] Figure 35 illustrates an example explainable insight for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0056] Figure 36 illustrates an example explainable insight for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0057] Figure 37 illustrates an example explainable insight for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0058] Figure 38 illustrates an example explainable insight for explainable material -based determinations in accordance with some embodiments of the present disclosure;

[0059] Figure 39 illustrates an example explainable insight for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0060] Figure 40 illustrates an example model output for explainable material-based determinations in accordance with some embodiments of the present disclosure;

[0061] Figure 41 illustrates an example model output for explainable material-based determinations in accordance with some embodiments of the present disclosure; and

[0062] Figure 42 illustrates an example model output for explainable material-based determinations in accordance with some embodiments of the present disclosure.DETAILED DESCRIPTION

[0063] Various embodiments of the present disclosure will now be described more fully hereinafter with reference to the accompanying drawings in which some but not all embodiments are shown. Indeed, the present disclosure may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Like reference numerals refer to like elements throughout.Explainable Material-Based Determinations

[0064] Figure 1 illustrates an example system for explainable material-based determinations (e.g., system 100). It will be appreciated that the system 100 is provided as an example of an embodiment(s) and should not be construed to narrow the scope or spirit of the disclosure. The depicted system 100 of Figure 1 may include a server 200, as shown and described herein with respect to Figure 2, communicably coupled with one or more sensor devices 102a-n via a network 104. The server 200 may be configured to control or otherwise influence operations of the one or more sensors device 102a-n and as described hereafter and may be configured to receive from the one or more sensor devices 102a-n datasets comprising data entries associated with various measurements (e.g., measurement types) of a material. Still further, the server 200 may comprise or be communicably coupled with one or more databases 108. In some embodiments, the system 100 may further include various user devices 106 (e.g., mobile phones, laptop computers and / or the like) by which a user associated with the system 100 may interact with the system 100, such as via a user interface of the user device 106.

[0065] Although described hereinafter with reference to a server 200, the present disclosure contemplates that the operations described hereafter with reference to the server 200 may be performed by any computing device, system orchestrator, central processing unit (CPU), and / or the like. Furthermore, although illustrated as a single device (e.g., server 200), the present disclosure contemplates that any number of distributed components may collectively be used to form the server 200 and / or to perform the operations associated with the server 200. In some embodiments, the server 200 may comprise, in whole or in part, one or more of the sensor devices 102 and / or the user device(s) 106. In any embodiment, the server 200 may be configured to, based upon the data received from the various sensor devices 102a-n and / or databases 108, generate a material identifier associated with a material, generate sensor context awareness data, generate and / or modify a structural progress flow, generate a first dataset, generate a second dataset, generate an attribution dataset, and / or the like as described herein.

[0066] To facilitate or otherwise enable this connectivity between devices, the communication network 104 may be any means including hardware, software, devices, or circuitry that is configured to support the transmission of traffic (e.g.. data, signals, and / or the like) between components of the system 100. For example, the communication network 104 may be formed of components supporting wired transmission protocols, such as, digital subscriber line (DSL), Ethernet, fiber distributed data interface (FDDI), or any other wired transmission protocol obvious to a person of ordinary skill in the art. The communication network 104 may also be comprised of components supporting wireless transmission protocols, such as Bluetooth, IEEE 802. 11 (Wi-Fi), or other wireless protocols obvious to a person of ordinary skill in the art. In addition, the communication network 104 may be formed of components supporting a standard communication bus, such as, a Peripheral Component Interconnect (PCI), PCI Express (PCIe or PCI-e), PCI extended (PCI-X), Accelerated Graphics Port (AGP), or other similar high-speed communication connection. Further, the communication network 104 may be comprised of any combination of the above-mentioned protocols. In some embodiments, such as when one or more sensor devices 102a-n and the sen- er 200 are formed as part of the same physical device, the communication network 104 may include the on-board wiring providing the physical connection between the component devices.

[0067] In some embodiments, the system 100 may include one or more databases 108 configured to store data generated by the server 200, the one or more sensor device 102a-n, or the like. The database(s) 108 may be accessible by the server 200, such as to retrieve data for comparison with data generated by the one or more sensor devices 102a-n. In someembodiments, the database(s) may operate as a repository for attribution datasets (e.g., generated by the methods described herein or otherwise) associated with properties of materials (e.g., cementitious mixtures), environments associated with materials, and / or any other context associated with materials as described herein. Furthermore, the database(s) 108 may be configured to store data associated with performance of the machine learning models and / or artificial intelligence algorithms described herein. The present disclosure contemplates that the database(s) 108 described herein may be configured to store any of the data entries generated by the sensor devices 102a-n of the present disclosure, data associated with operations performed on the data entries generated by the sensor device 102a-n, and / or the like without limitation.

[0068] Although illustrated in Figure 1 as separate entities, the present disclosure contemplates that the sen’ er 200 and the one or more sensor device 102a-n may, in some embodiments, include common components and / or functionality. By way of example, the embodiments of the present disclosure are described hereinafter with reference to the server 200 performing the various material related operations and analyses based on data entries generated by the sensor devices 102a-n. The present disclosure, however, contemplates that, in some embodiments, the sensor devices 102a-n may be configured to, in whole or in part, perform the material operations described herein. Said differently, the present disclosure contemplates that each of the devices described herein may include the components necessary to perform one or more of the operations described hereinafter. Furthermore, although illustrated in Figure 1 with one or more sensors device 102a-n communicably coupled with the server 200 via the network 104, the present disclosure contemplates that the system 100 may include any number of intermediary7devices communicably coupled within the system 100. By way of a non-limiting example, the system 100 may include various host devices, gateway devices, etc. that receive data generated by the sensor devices 102a-n and provide this data to the server 200. In some embodiments, one or more intermediate networking devices, such as a hub 110 may be used. The hub 110 may operate to transmit and / or receive data over network 104 and / or directly with the sensor devices 102a-n. In some embodiments, the sensor devices 102a-n may include one or more communication interfaces configured for operation with nonterrestrial networks (NTN), terrestrial networks, or both (e.g., network 112). A non-terrestrial communication interface may include a radio module and antenna capable of direct communication with satellite networks 112, such as Low Earth Orbit (LEO) constellations (e.g., Starlink, Iridium, Swarm), and / or the like. Medium Earth Orbit (MEO) satellites, Geostationary Earth Orbit (GEO) satellites, or High Altitude Pseudo Satellites (HAPS).Example Server Circuitry

[0069] With reference to Figure 2, example circuitry components of the server 200 are illustrated that may, alone or in combination with any of the components described herein, be configured to perform the operations and / or produce the outputs described herein with reference to Figures 3-42. As shown, the server 200 may include, be associated with or be in communication with processor 202. a memory 206, and a communication interface 204. The processor 202 may be in communication with the memory 206 via a bus for passing information among components of the server 200. The memory' 206 may be non-transitory and may include, for example, one or more volatile and / or non-volatile memories. In other words, for example, the memory 206 may be an electronic storage device (e.g., a computer readable storage medium) comprising gates configured to store data (e.g., bits) that may be retrievable by a machine (e.g., a computing device like the processing circuitry). The memory 206 may be configured to store information, data, content, applications, instructions, or the like for enabling the apparatus to cany’ out various functions in accordance with an example embodiment of the present disclosure. For example, the memory 206 could be configured to buffer input data for processing by the processor 202. Additionally, and / or alternatively, the memory 206 could be configured to store instructions for execution by the processor 202.

[0070] The server 200 may. in some embodiments, be embodied in various computing devices as described above. However, in some embodiments, the apparatus may be embodied as a chip or chip set. In other words, the apparatus may comprise one or more physical packages (e.g., chips) including materials, components and / or wires on a structural assembly (e.g., a baseboard). The structural assembly may provide physical strength, conservation of size, and / or limitation of electrical interaction for component circuitry included thereon. The apparatus may therefore, in some cases, be configured to implement an embodiment of the present disclosure on a single chip or as a single “system on a chip.” As such, in some cases, a chip or chipset may constitute means for performing one or more operations for providing the functionalities described herein.

[0071] The processor 202 may be embodied in a number of different ways. For example, the processor 202 may be embodied as one or more of various hardware processing means such as a coprocessor, a microprocessor, a controller, a digital signal processor (DSP), a processing element with or without an accompanying DSP, or various other circuitry including integrated circuits such as, for example, an ASIC (application specific integrated circuit), an FPGA (field programmable gate array), a microcontroller unit (MCU), a hardware accelerator, a special-purpose computer chip, or the like. As such, in some embodiments, the processor 202 may include one or more processing cores configured to perform independently. A multi-core processing circuitry may enable multiprocessing within a single physical package. Additionally, and / or alternatively, the processing circuitry may include one or more processors configured in tandem via the bus to enable independent execution of instructions, pipelining and / or multithreading.

[0072] In an example embodiment, the processor 202 may be configured to execute instructions stored in the memory 206 or otherwise accessible to the processor 202. Alternatively, and / or additionally, the processing circuitry may be configured to execute hard coded functionality. As such, whether configured by hardware or software methods, or by a combination thereof, the processing circuitry may represent an entity (e.g., physically embodied in circuitry) capable of performing operations according to an embodiment of the present disclosure while configured accordingly. Thus, for example, when the processing circuitry7is embodied as an ASIC, FPGA or the like, the processing circuitry may be specifically configured hardware for conducting the operations described herein. Alternatively, as another example, when the processor 202 is embodied as an executor of instructions, the instructions may specifically configure the processor to perform the algorithms and / or operations described herein when the instructions are executed. However, in some cases, the processor 202 may be a processor of a specific device configured to employ an embodiment of the present disclosure by further configuration of the processing circuitry by instructions for performing the algorithms and / or operations described herein. The processor 202 may include, among other things, a clock, an arithmetic logic unit (ALU) and logic gates configured to support operation of the processing circuitry.

[0073] The communication interface 204 may be any means such as a device or circuitry embodied in either hardware or a combination of hardware and software that is configured to receive and / or transmit data, including media content in the form of video or image files, one or more audio tracks or the like. In this regard, the communication interface 204 may include, for example, an antenna (or multiple antennas) and supporting hardware and / or software for enabling communications with a wireless communication network. Additionally, and / or alternatively, the communication interface may include the circuitry for interacting with the antenna(s) to cause transmission of signals via the antenna(s) or to handle receipt of signals received via the antenna(s). In some environments, the communication interface may alternatively or also support wired communication. As such, for example, the communication interface may include a communication modem and / or other hardware / software for supportingcommunication via cable, digital subscriber line (DSL), universal serial bus (USB) or other mechanisms.

[0074] The communication interface 204 may provide for communications under various modes or protocols, such as the Internet Protocol (IP) suite (commonly known as TCP / IP). Protocols in the IP suite define end-to-end data handling methods for every thing from packetizing, addressing and routing, to receiving. Broken down into layers, the IP suite includes the link layer, containing communication methods for data that remains within a single network segment (link); the Internet layer, providing internetworking between independent networks; the transport layer, handling host-to-host communication; and the application layer, providing process-to-process data exchange for applications. Each layer contains a stack of protocols used for communications. In addition, the communication interface 204 may provide for communications under various telecommunications standards (e.g., 2G, 3G, 4G, 5G, and / or the like) using their respective layered protocol stacks. These communications may occur through a transceiver, such as radio-frequency transceiver. In addition, short-range communication may occur, such as using a Bluetooth, Wi-Fi, or other such transceiver (not shown).

[0075] In some embodiments, the server 200 may deploy one or more artificial intelligence (Al) models and / or modules to perform the operations described herein. To this end, the server 200 may include an artificial intelligence (Al) model 208 comprising circuitry configured to ingest data, such as a multivariate N-dimensional space of time-series data where N is the number of different measurement types (e.g., data of different types) and, via a various Al and / or artificial intelligence techniques described hereafter, output datasets (e.g., a first dataset, a second dataset, and / or the like) associated a material and / or one or more properties of a material, output attribution datasets indicative of an influence or causal relationship associated with a model, and / or one or more material properties of a material. The Al model 208 may leverage the processor 202 to perform its associated operations and may, for example store any results in the memon 206 and / or databases 108. Additionally, the Al model 208 may be formed by a set of interconnected, constituent modules that may each receive an input and produce an output that contributes to the output of the Al model 208 (e g., similar to an end-to-end model as described herein). Further, the Al model 208 may include and / or may be operably coupled to one or more explainability models and / or modules as described herein.

[0076] Of course, while the term “circuitry” should be understood broadly to include hardware, in some embodiments, the term “circuitry” may also include software for configuring the hardware. For example, although “circuitry” may include processing circuitry,storage media, network interfaces, input / output devices, and the like, other elements of the server 200 may provide or supplement the functionality of particular circuitry’.Example Sensor Hardware

[0077] As used herein, the terms “sensor,” “sensor device,” “transducer,” and “device” may be used interchangeably and / or collectively to refer to any hardware or circuitry component configured to generate data, such as first data entries, that is associated with material related data including material compositional data, material property data, material identifier data, material contextual data, material compositional arrangement data and / or the like without limitation. As described herein, a sensor device may include any relevant circuitry', components, etc. configured to generate data that is indicative of or associated with, for example, the material properties (e.g., static material properties, compositional material properties, contextual conditions, contextual material properties, etc.) of a material. The present disclosure contemplates that each of the techniques, models, etc. of the present disclosure may be implemented with any number of the sensor and / or sensor devices and / or transducers and / or devices described herein, alone or in any combination. Further, the one or more sensor devices 102a-102n as shown and described herein with respect to Figure 1 may include any one of or any combination of the sensor types described herein.

[0078] For example, the one or more sensors devices 102-102n may include any of a plurality of sensor types 2700 as shown in Figures 27A-27B. The plurality of sensor types 2700 may include a UPV sensor 2702, an EMI sensor 2704, a temperature / maturity sensor 2706, an ECI sensor 2708, and / or a spectroscopy sensor 2710. As will be understood by one of ordinary skill in the art in view of the present disclosure, each illustrated sensor of the plurality of sensor types 2700 is merely an example form of the sensor type. Embodiments of the present disclosure contemplate various forms of each sensor type of the plurality of sensor types 2700. Furthermore, the plurality' of sensor types 2700 is merely an exemplary list of sensors configured to perform any steps associated with sensors (e.g., generating data of a material) as described herein. The present disclosure contemplates the use of any sensor type necessary' to perform the steps disclosed herein as yvould be known to one of ordinary skill in the art. For a second example, with reference to Figure 28, one or more sensor devices 2800 may be embedded within a material making measurements and outputting the data for use in any of the models and / or modules as described herein.

[0079] In some embodiments, the present disclosure may make use of sensor systems configured to generate, collect, and transmit first data entries suitable for ingestion byexplainable material models, as described herein. These sensor systems may be deployed embedded or partially embedded in. surface mounted and / or directed at target materials such as concrete or cementitious mixes across various stages of the material lifecycle, including batching, transport, pouring, curing, or within finished structures. These systems may be used to construct multimodal measurement datasets that capture the evolving physical, chemical, and structural states of the material. These datasets may then be used directly by prediction, selection, optimization, or generation and / or attribution models or modules.

[0080] In some embodiments, the system may generate electromechanical impedance (EMI) data using piezoelectric transducers or equivalent electromechanical sensing elements (e.g., capacitive micromachined ultrasonic transducers, CMUTs, and / or the like), mechanically coupled to the host material. These sensors may apply time-varying electrical signals and measure the material’s response, yielding electromechanical impedance spectra that reflect material stiffness, microstructure, or curing progression. Data features such as resonance shifts, peak amplitudes, or bandwidths may be extracted and temporally tagged, providing high- resolution input data for model ingestion.

[0081] Additionally, or alternatively, the system may capture electrochemical impedance data using embedded electrodes excited with AC or DC signals. The resulting electrochemical impedance spectra, which may include magnitude and / or phase responses across frequencies, may reflect hydration kinetics, pore structure evolution, or ionic transport properties within the material. This spectral data, along with derived metrics (e.g.. Nyquist plot features or relaxation times), may serve as valuable first data entries for model-based strength or durability estimation.

[0082] Additionally, or alternatively, RF and electromagnetic wave impedance data maybe acquired using antenna-based sensors configured to emit and receive signals across a frequency range. The collected S-parameters or reflected / transmitted signal profiles provide information about the dielectric or conductive properties of the material, as well as internal features such as aggregate dispersion or voids. These datasets, particularly when acquired over time or under variable curing conditions, may enable fine-grained analysis and prediction of internal material performance.

[0083] In further embodiments, temperature and / or thermal data may be collected using thermocouples, RTDs, or digital temperature sensors. Time-series temperature data may be used directly or may be processed to generate maturity indices using classical or enhanced maturity methods (e.g., Nurse-Saul or combined maturity-impedance formulations). Thesetemperature-derived features may be particularly useful in performance prediction contexts, such as estimating set time or compressive strength at early ages.

[0084] Additionally, or alternatively, sensor systems may include optical or spectroscopic elements such as hyperspectral imagers, spectrometers, LEDs, or photodiodes. These systems may generate reflectance spectra, transmittance profiles, or spatially resolved images, enabling compositional analysis, surface defect detection, or phase identification. Such data may be structured and timestamped for ingestion into composition-prediction or anomaly-detection models.

[0085] Additionally, or alternatively, without loss of generality, these sensor systems may be used to generate multi-modal datasets that reflect material state and evolution over time. These data may be structured as time-aligned feature vectors, spectra, images, or summary statistics, and may be collected continuously or at defined intervals.

[0086] In some embodiments, the models and / or methods disclosed herein may employ sensor data in a variety of ways including those described herein. The following roles are illustrative and non-limiting. Sensor data may sene as direct input to one or more models and / or modules within a modular model architecture. For example, raw temperature values from thermocouples, impedance spectra from embedded electrodes configured for electrochemical impedance measurements, or strain measurements from embedded gauges may be directly ingested as inputs to models that predict material performance, curing progression and / or mechanical properties. In some embodiments, these inputs may be ingested in their raw form, or additionally and / or alternatively may be pre-processed or encoded into latent vectors, frequency -domain features, statistical summaries, maturity indices, or time- segmented representations prior to model ingestion.

[0087] Additionally, or alternatively, sensor data may be used to generate derived or engineered features, which may serve as input to downstream models or modules. For example, temperature data may be transformed into a maturity index using the Nurse-Saul or Arrhenius function for example, which may then be used as an input to a strength prediction model. Electrochemical impedance data may be reduced via Principal Component Analysis (PCA) and / or transformed into key descriptors (e.g., resistance at specific frequencies, phase lag trends), which may serve as model inputs. These derived features may retain physical interpretability and may be used in generating attribution datasets to trace model outputs and / or data generated by models and / or modules back to an influence and / or causal relationship with specific sensor readings and / or transformations thereof.

[0088] Additionally, or alternatively, sensor data may be used as training data of one or more models or modules, including as supervised training datasets. For instance, EMI-derived compressive strength profiles or ECI-derived porosity metrics may serve as ground truth values for training modules that predict mechanical or electrochemical properties based on mix composition and environmental data. In such cases, the sensor data is not directly ingested at inference time but rather contributes to training datasets that inform the internal representations and / or weights of the model. In such embodiments, attribution datasets may be generated that are for example indicative of biases, variances and / or other kinds of errors in sensor training datasets and / or in model outputs or weights as a result of sensor training datasets.

[0089] Additionally, or alternatively, sensor data may be used for model evaluation, performance monitoring, and self-improvement, wherein predictions made by the system are compared to real-world sensor observations. For example, a strength model’s output may be compared to sensor-derived strength estimates (e.g., via thermal maturity or EMI-based assessment), and any discrepancies may trigger loss calculations, flag performance drift, or initiate model retraining. These evaluations may also form the basis for attribution datasets that identify input variables most responsible for prediction errors or divergence from sensor measurements. The models and / or any submodule discrepancies and / or attribution datasets may be used, in whole or in part, to alter the model and / or improve model performance e.g. by incorporating data associated with the discrepancy into model training, or by adjusting the weights of the model to adjust the discrepancy.

[0090] Additionally, and / or alternatively, sensor data may be used in the generation of attribution datasets, for example in embodiments wherein the influence of specific sensorobserved phenomena on predicted outputs may be quantified. For example, a saliency map may show which segments of a temperature time series contributed most to a maturity index or strength prediction; a feature attribution table may show that core temperature values contributed more to predicted internal cracking risk than surface values; or a rule-based expression may indicate that “temperature drop > 5 °C between 12-24 hours, means that strength impact is -4.2 MPa." Attribution data may also be indicative of influence across sensor modalities (e.g., combined thermal and impedance readings) or sensor positions (e.g.. spatial attribution maps showing gradients within the pour).

[0091] Additionally, and / or alternatively, sensor data may support anomaly detection and diagnostic interpretation, wherein unexpected signals, such as thermal plateaus, impedance discontinuities, or out-of-range strain values, may be identified and explained. Attributiondatasets may be generated to be indicative of the influence of mix design choice and / or contextual conditions (e.g., ambient temperature) on these anomalies.

[0092] Additionally, and / or alternatively, sensor data may be used for model calibration, particularly in modules that simulate physical processes such as curing heat evolution, hydration rate, or temperature distribution. For example, embedded thermocouple data may be used to calibrate and / or alter the heat generation curve for a specific mix, aligning it with real- world observations. The calibrated model may then be reused for other predictions, and attribution datasets may record which variables were most responsible for calibration adjustments.

[0093] Additionally, and / or alternatively, sensor data may be used to condition or constrain optimization processes, particularly in generative or mix-optimization models and / or methods. For example, a model may be tasked with generating a mix that achieves a given strength curve under observed thermal conditions from embedded sensors measuring the material at a specific depth. In such cases, attribution data may reflect how specific sensor observations shaped the final mix design or constrained the search space. Additionally, or alternatively, a candidate material may be selected based on electromechanical impedance peak location, electrochemical conductivity, or measured thermal diffusivity. Additionally, or alternatively, optimization models may adjust a baseline mix formulation to satisfy one or more behavioral constraints derived from sensor measurements, such as ensuring a resonance peak shift of a certain magnitude within a specified time window, or limiting impedance growth beyond a threshold under given curing conditions. These sensor-informed constraints may be used as part of an objective function, loss function, or evaluation criterion within a material optimization or selection routine.

[0094] Additionally, or alternatively, sensor data may be used for spatial or geometric normalization, wherein sensor position, depth, or orientation is used to correct or align model inputs or outputs. For example, thermal delay between core and surface sensors may be used to infer embedded sensor depth, which in turn affects attribution w eights for those signals in downstream modules. Similarly, sensor readings from vertical elements (e.g., columns) may be weighted differently than those from horizontal ones (e.g.. slabs) in models sensitive to geometry-dependent thermal behavior.

[0095] Additionally, or alternatively, generative material models may be configured to produce new material formulations that satisfy behavioral requirements grounded in sensor- derived data. For instance, a model may generate a novel cementitious mix that achieves a specified range of thermal activation energy, impedance phase angle stability, or compressivestrength development as determined from sensor data in historical pours. Such constraints may be formulated as direct sensor-derived values (e.g., "‘impedance peak must increase by at least 8% over 24 hours”) or indirectly through derived features (e.g., ‘‘maturity index must exceed X within 12 hours under ambient conditions Y”). These constraints may be embedded within the generative process, and attribution datasets may be used to highlight which components of the generated mix most contributed to satisfying each behavioral criterion.

[0096] In some embodiments, sensor measurements associated with known mix formulations may be used to construct learned embedding spaces that position materials based on similarity in behavior or performance (e.g., construction of a mix space). For example, the models herein may leam a latent representation of mix space using electromechanical and thermal response data, such that mixes with similar impedance spectra or strength development curves occupy nearby regions in the embedding. These spaces may be labelled or annotated with metadata such as mix composition, identifier, or contextual performance scores. The system may then use this representation to interpolate between mixes, identify similar alternatives, or guide optimization procedures. Attribution datasets may be generated to show how different sensor features contributed to the mix's location within the space.

[0097] Additionally, or alternatively, where a material formulation is not directly present in the system’s database, the models may use sensor-informed interpolation techniques to estimate properties or performance characteristics based on nearby known mixes. For example, the system may use similarity metrics in a sensor-derived feature space such as temperature development curves or impedance spectra to interpolate strength, porosity, or hydration rate. In further embodiments, the system may use lookup-based retrieval for previously seen formulations and interpolate or extrapolate sensor-measured properties from those entries. This allows the system to provide estimates for novel or modified compositions using existing sensor-annotated datasets without requiring full retraining.

[0098] In some embodiments, the models may be configured to select or optimize a material mix based on calibration curve constraints derived from historical sensor data. For instance, a user may specify a target calibration response for compressive strength or maturity, and the system may adjust a given mix to better match the desired curve using regression, fitting functions, or optimization routines. These constraints may be expressed in terms of time- aligned performance targets (e.g., strength at 7 and 28 days) or more complex curve shape constraints (e.g., maximum slope or plateau behavior). Attribution datasets may be used to indicate which mix components or environmental assumptions most influenced the predicted calibration response.

[0099] In some embodiments, material generation models may employ genetic or evolutionary algorithms to search mix design space, using sensor-informed performance constraints as fitness functions. For example, a population of candidate mixes may be iteratively mutated and selected based on their predicted ability to meet EMI-derived stiffness values, thermal exothermicity limits, or hydration rate targets. Sensor-derived properties may be directly encoded into the fitness evaluation process, and attribution datasets may track which features contributed most to convergence. These evolutionary models may be particularly effective in generating non-obvious or novel formulations that meet strict real-world behavioral constraints.

[0100] Additionally, or alternatively, wherein the material is a cementitious mix, and especially when it is concrete, it is possible to characterize the compressive strength of the material using thermal data in conjunction with the maturity method, wherein concrete maturity refers to concrete maturity' as defined in ASTM Cl 074. This includes the use of temperature data captured through sensor measurements, maturity data comprising maturity function related information associated with the mix identifier, and calibration data comprising calibration and / or fitting function information associated with the mix identifier. A pre-existing database of thermal material measurements, alongside material identifiers, as well as maturity and calibration data for a plurality' of respective mixes and / or associated pours, may be used for training the models herein. This may enable the models to predict thermal properties of cementitious mixes given, for example, meteorological data and a mix identifier or mix library. If this data comprises temperature data collected from multiple points within a material, spatial thermal distribution may be predicted.

[0101] As used herein, the terms "material identifier," "material classification," and / or the like may be used to refer to any mechanism of identifying a material, mixture, a family / type of material or mixtures, or any characterizing feature of materials or mixtures. The material identifiers may be based on the composition (e.g. mix formulation, chemical composition, and / or the like), material properties, a unique designator or identifier, and / or any information that identifies a particular mix formulation. In some embodiments, the material identifier may include mathematical functions that represent particular volumes in mix space as defined herein. By way of a non-limiting example, a material identifier may include a strength-grading based identification methodology7in which particular mix formulations are identified by compressive strength (e.g., in megapascals or the like). In particular, aC40 mix may be defined as a concrete mixture that reaches a minimum of 40 MPa of compressive strength by 28 days, if cured as a standard cube (or cylinder) in standard conditions (in a temperature-controlledwater bath at a fixed temperature). A C60 mixture has a similar definition but instead must reach a minimum of 60 MPa. Although described herein with reference to compressive strength as an example mechanism by which material formulations may be identified (e.g., via mix identifiers), the present disclosure contemplates that any of the material properties (e.g., static material properties, compositional material properties, contextual conditions, and / or contextual material properties) described herein may be used to generate material identifiers.

[0102] Therefore, the material identifiers described herein provide information (e.g., data entries) regarding the particular mixtures (e.g., mix formulation) on which the models of the present disclosure are operating. By way of continued example, in the absence of additional information, the models described herein may determine that a material formulation identified as C40 within the applicable database(s) will reach a minimum of 40 MPa within the contextual conditions described above (e.g., standard conditions). As would be evident to one of ordinary skill in the art, this data associated with the material identifier for the material formulation may narrow a material's expected strength performance over time in any given context (e.g., target contextual material properties), where such performance may be determined by the models described herein. By way of a non-hmiting example, if a model of the present disclosure is used to estimate the material formulation of a material based on the concrete specifications to which it was designed, that strength specification may be used by the model to determine potential candidate material formulations in the mix space.

[0103] As used herein, the terms "‘contextual material condition,’" "contextual condition,” and “material context data” may be used interchangeably herein to refer to any imposed state or attribute that at least partially defines the instantiated context in which a material is used. The contextual condition may, for example, be associated with various characteristics, attributes, aspects, etc. of an external environment of the material and / or may be associated with characteristics, attributes, aspects, etc. of the material. With reference to an example building material, contextual material conditions may be associated with weather data, meteorological data, temperature data, insulation data, structural data, environmental data, structural burden data, batching plant data, pump contextual condition data, truck contextual condition data, kiln contextual condition data, temporal data, spatial data and / or the like associated with one or more building material. By way of continued example, insulation data may be indicative of a formwork type, a formwork coating, the presence or absence of blankets or other coverings. Example weather data and / or meteorological data may refer to ambient temperature data associated with the weather surrounding the building material, including but not limited to, temperature data, humidity data and the like, as well as meteorologicalconditions such as thunder, rain and the like. Example structural data as a contextual material condition may refer to data pertaining to the geometry, physical form, structure, layout, arrangement, configuration, and / or content (e.g., rebar or the like) of a pour. As such, the structural data may be indicative of or otherwise associated with element type data, geometry or dimensional data, exposure data (e.g., surface area of concrete exposed to air, surface area of concrete exposed to other materials, such as formwork, etc.), reinforcement geometry data (e.g.. data entries associated with rebar or the like), and / or data associated with the external environment of the same. Example spatial data as a contextual material condition may refer to data pertaining to the global location (e.g., latitude, longitude and altitude), or relative location of a building material at a construction site or related location (e.g.. location of a pour in relation to gridlines, or another pour, or location of a precast unit in a precast yard). Environmental data as an example contextual material condition may include meteorological data, such as ambient temperature data, humidity data, precipitation data, and / or other atmospheric effects (e.g., wind data, storm data, lightning data, etc.). Environmental data may further include electromagnetic radiation data, data indicative of mechanical vibration and / or other mechanical disturbances, geological data (e.g.. the type of soil surrounding foundations may impact its behavior), and / or oven data (e g., instance in which ovens are used for curing, particularly in precast implementations).

[0104] As used herein and as w ould be evident to one of ordinary' skill in the art, as concrete (e.g., a cementitious mixture) cures, its compressive strength increases. The rate of that increase varies during the curing process: beginning with an initial rapid strength gain, followed by a convergence towards some maximum (or “long-term”) strength and hardness. In some embodiments of the present disclosure, the materials that may be optimized by the methods described herein may be mixes or mix formulations. Mixes in the broadest sense of the term may be defined as materials that are either composite or mixtures in the physical, material senses of the words. Typically, these may be used for construction purposes (e.g., construct a building, construct a bridge, and / or the like). Further, these mixes may be materials that include cementitious materials or materials with cementitious properties as components. Mix optimization as described herein may mean the optimization of the ratios of these components to fit certain use case(s) and / or objective(s).

[0105] As used herein, the terms “mix,” “mixture,” “composite,” and similar terms may be used interchangeably to refer to a collection of materials (e.g., constituent components, constituent elements, constituent parts, and / or the like) that are combined together. In some embodiments, a mixture may be homogenous in which the composition of the constituent partsis substantially uniform throughout. Alternatively, in some embodiments, a mixture may be heterogenous in which the composition or proportion of the constituent parts may vary throughout. As described hereinafter, a mix or mixture of the present disclosure may refer to a cementitious mixture (e.g., a combination of constituent components that are combined to, following curing, form concrete) as an example building material. The present disclosure, however, contemplates that the devices, systems, methods, techniques, and / or the like described with reference to cementitious mixtures may be applicable to building materials, extracted materials, or industrial materials of any type without limitation.

[0106] As used herein, the terms “mix formulation”, “mix recipe”, “mix composition” and “mix design” may be used interchangeably to refer to a proportion of constituent components, parts, or elements that form a mix or mixture. In some embodiments, the mix formulation may refer to a chemical composition of constituent components, parts, or elements forming the mix or mixture. As described herein, for example, a cementitious mixture (e.g., an example building material) may be formed of a cementitious material (e.g., Portland cement), water, aggregates (e.g., sand, gravel, limestone, and / or the like), admixtures, and / or the like. The relative proportion of these constituent components may be defined by the mix formulations described herein. As described herein, the mix formulation may refer to a target set of constituent component proportions of w hich any particular instantiation of that mix formulation should be composed. In some embodiments, mix designs may refer to proportions of constituent component parts associated with one or more targets for contextual material properties. In another embodiment, mix designs may also include the steps (and associated timings) for mixing of a proportion of constituent components or raw materials. As would be evident to one of ordinary skill in the art, any particular instantiation of a mix formulation may include naturally variability’ in the proportions of constituent components for the same mix formulation.

[0107] An example, in accordance with some embodiments of the present disclosure, of a mix formulation may include the following recipe:

[0108] The constituent materials of a mix may be referred herein to as “raw materials”. As used herein, a “batch” may refer to a physical instantiation of a mix formulation. For example, a batch may include an associated volume and may often exist as a batch at the material manufacturer’s factory and throughout transit. Once a particular batch is pumped, the volume(s) associated with the batch may be referred to herein as one or more “pours.” A “pour” may refer to a defined volume (e.g., at least partially enclosed via a mold, formwork, or otherwise) into which at least a portion of one or more batches of a mix formulation are provided. A “pour” as described herein may be cured with the intent of forming an element of a structure (e.g., a building element).

[0109] In some embodiments, the systems and models described herein may be applied to materials including metals, polymers, ceramics, composites, cementitious mixtures, and / or the like. Material behavior across these domains may often be governed by complex, nonlinear interactions between composition, processing, environmental conditions, and / or geometry. Traditional modeling approaches rely on fixed empirical rules or isolated physical tests, limiting adaptability, generalization, and / or responsiveness to real-world variability. The present disclosure introduces a novel framework for representing material behavior using modular, interpretable, data-driven models that ingest heterogeneous inputs, including sensor readings and documentation, and generate both predictive outputs and attribution datasets. These attribution datasets enable the identification and quantification of causal relationships between variables and material properties, guiding material design, selection, and optimization across diverse applications.

[0110] This approach is particularly transformative in the context of building materials, such as cementitious mixes used in concrete construction, where explainability is often essential for adoption. The construction industry7, being risk-averse and highly regulated, requires transparency and traceability in decision-support systems such as Al systems. Conventional approaches, including black-box models (e.g.. typical neural networks), empirical charts, and prescriptive codes, offer limited adaptability to project-specificconditions and lack insight into the influence of individual inputs. Black-box models in particular are difficult to trust, as their opaque internal logic prevents users from understanding how predictions are made or diagnosing unexpected outputs. This lack of explainability and interpretability presents a major barrier in domains that demand reliability and compliance, making the explainable, attribution-aware architecture described herein a critical advancement.

[0111] Embodiments of the present disclosure address these limitations through modular, attribution-enabled models that incorporate real-world data such as embedded sensors, thermal and curing profiles, mix formulations, project context, and / or digital construction documentation. The models may not only generate predictive outputs and / or recommended mix formulations, but also attribution datasets that reveal which inputs most significantly influenced outcomes such as strength development, thermal risk, or durability’. This transparency builds user confidence and trust in the system, supporting informed decisions in environments where reliability’ and compliance are paramount. By’ making advanced modelling interpretable and context-aware, embodiments of the present disclosure enable broader adoption of data-driven technologies in material design, evaluation, and / or implementation workflows, particularly within the traditionally conservative building materials sector.

[0112] Without loss of generality, the data objects herein may in whole or in part be a part of any data associated with the methods and / or models described herein. In some embodiments, the data objects herein may in whole or in part be inputs and / or outputs to any models and / or modules herein. The data objects herein may also be used to construct training datasets which the models and / or modules herein may be trained upon.

[0113] As used herein, the terms “material composition”, “compositional material property ”, “compositional property ” and / or “composition data” may be used interchangeably to refer to any attribute, parameter, characteristic, state, and / or the like indicative of the proportions by which a material (e.g., a composite material as described herein) is composed of other materials (e.g., raw materials as defined herein), or any data indicative of such attribute, parameter, characteristic, state and / or the like. A compositional material property’ may, for example, provide an indication of the mix formulation or compositions as defined herein at various levels of granularity. By way of example, the proportional relationship of constituent components or composition may be provided as a percentage of volume, by particle number, by mass, and / or any other relevant metric, relationship, etc. In some embodiments, the compositional material property may, for example, be provided as an absolute mass, mass density, or other representation. The present disclosure contemplates that information associated with the compositional material properties of a particular material may be providedby any relationship, proportionality, metrics, and / or the like. By way of a non-limiting example, a cementitious mixture (e.g.. an example building material) may include compositional material properties that are representative of the atomic composition (e.g., by chemical element percentage or the like) of the building material, the compound composition (e.g., by chemical compound percentage or the like), the molecular composition (e.g., by chemical molecule percentage or the like), the mix recipe, by raw material composition (e.g., concrete raw materials, as defined herein, or the like). Additionally, or alternatively, the compositional material properties may be representative of a theoretical or idealized mix formulation as associated with various target contextual material properties as defined herein (e.g., C80 concrete, C60 concrete, C40 concrete, and / or the like).

[0114] As used herein, the term "‘material property" and / or “property'’ and / or “material performance” and / or “material behavior” may refer to any physical or chemical attribute, characteristic, parameter, feature, and / or the like of the materials described herein. The material properties of a material may include one or more of static material properties and / or contextual material properties. Although described herein with reference to an example framework for distinguishing between types or categories of material properties, for example static material properties or contextual material properties, the present disclosure contemplates that the devices, systems, methods, techniques, and / or the like of the present disclosure may be applicable to any determinable, measurable, and / or derivable attribute associated with building materials, formed of cementitious mixtures or otherwise. By way of example, a material property of a building material such as a cementitious mix may include, but is not limited to, the temperature of a building material, the curing rate of a cementitious mix, the compressive strength of a material at a single point in time or over a continuous period (which may be represented digitally by a timeseries). Additionally, or alternatively, a mix formulation, and the batches, pours, building elements, and / or the kike associated with the mix formulation, may further include various “material properties.” As used herein, “target material properties” may therefore refer to a set of material properties that are to be achieved (e.g., within applicable tolerances or the like) by the system, users, models, and / or the like described herein for the particular mixture (e.g.. as defined by mix identifier, mix classification, mix formulation, and / or the like). Additionally, or alternatively, material properties may in some embodiments include compositional properties.

[0115] In some embodiments, by w ay of example, material properties may include, but are not limited to any of the following properties: compressive strength; tensile strength; flexural strength; shear strength; elastic modulus; Poisson’s ratio; fracture toughness; permeability;porosity; capillary absorption; shrinkage potential; creep coefficient; thermal conductivity; thermal diffusivity; heat of hydration; specific heat capacity; maturity index; setting time; slump; air content; water-to-cement ratio; binder content; aggregate packing density ; paste volume fraction; hydration rate; degree of hydration; chloride diffusivity; sulfate resistance; carbonation depth; alkali-silica reactivity potential; resistivity; ultrasonic pulse velocity; electromechanical impedance; impedance amplitude shift; EMI resonance peak shift; drying rate; curing rate; surface moisture retention; surface finish quality; adhesion strength; abrasion resistance; freeze-thaw resistance; corrosion resistance; environmental degradation resistance; long-term durability index; embodied carbon; recyclability; early-age strength development; long-term strength gain; time-to-target strength; strength-to-weight ratio; and / or the like.

[0116] As used herein, the term "‘contextual material property" may be used to refer to any material property that is context-dependent and that may change with differing contextual conditions. By way of continued example with reference to a cementitious mix as the example building material, the compressive strength of the cementitious mixture may increase over time in a manner that is dependent upon temperature, geometric shape, humidity, wind, and / or exposure and / or the like. As would be evident to one of ordinary skill in the art in light of the present disclosure, data described herein related to contextual material properties may be time dependent, and may be composed of discrete, or continuous time series data. By way of a nonlimiting example, contextual material properties may refer data indicative of compressive strength (e.g., 7-day strength, 28-day strength. 42-day strength, full strength profile, and / or the like), shrinkage, workability, tensile strength, flexural strength, stress, strain, calibration data related thereof, structural health, reactivity, flow rate, specific surface area, and / or the like. The present disclosure contemplates that the contextual material properties described herein may include any determinable, measurable, derivable, and / or the like metric associated with the example building material based on the intended application of the devices and systems described herein. As used herein, “target contextual material properties” may therefore refer to a set of contextual material properties that are to be achieved (e.g., within applicable tolerances or the like) by the system, users, models, etc. described herein attempts to achieve for the particular mixture (e.g.. as defined by mix identifier, mix classification, mix formulation, and / or the like).

[0117] As used herein, the terms “static material property” and “static property” may be used interchangeably to refer to any attribute, parameters, characteristic, state, and / or the like of a material (e.g.. an example building material) that is independent of the context within which the material is used (e.g., an attribute that is context independent). By way of a non-limiting example, static material properties may include density (e.g., of water or other materials), particle size, homogeneity, fineness, specific gravity, natural variability, embodied carbon data, aggregate grading, porosity, and / or the like. Although described herein with reference to example static material properties for example cementitious mixtures, the present disclosure contemplates that static material properties may include any context independent attribute of any type for any material.

[0118] In some embodiments a data object may include a material space and / or an element from a material space. A non -exhaustive list of potential material spaces considered by the present disclosure may include N-dimensional space of compositions (e.g., raw material proportions, chemical composition (e.g., a material space of each combination of elements in periodic table), any other way of representing composition, and / or the like), N-dimensional space of material composition and structure (e.g., similar to the N-dimensional space of compositions, but space encodes information about the structure as well), N-dimensional space of properties, N-dimensional space of sensor signatures, N-dimensional space of compositional arrangements and / or the like. Example embodiments of material spaces may include materials being represented as N-dimensional vectors in matenal spaces.

[0119] Additionally, or alternatively, in some embodiments, the material space may be a mix space representing a material space of cementitious mixtures. As used herein, “mix space” and “mixture space” may refer to an N-dimensional vector space, such that all points in the domain of the N-dimensional space represent all possible mix formulations (where such space may be an infinite space). In the context of example building materials, mix space may refer to the space representing all possible cementitious mixtures used for construction, and whose N- dimensional coordinates include every material or non-material property' that uniquely defines a mix formulation (e g., composition) in the models and databases described herein. As would be evident to one of ordinary skill in the art, many N- dimensional spaces exist in which a mixture may be defined, and the number of dimensions may change depending, for example, upon the information available to a models or databases described herein, or upon the information deemed minimally sufficient to characterize a mixture uniquely (up to some tolerance or precision) with respect to other mix formulations. Additionally, or alternatively, a mix space may be defined through material properties, as an N-dimensional space of material properties, wherein mixes may exist at different regions in this space based on the different combinations of values of N chosen properties.

[0120] In some embodiments, data types of the present disclosure may include any of the discrete data and / or continuous data as described herein. In some embodiments, data sourcesof the present disclosure may include recorded values from measurement or sensors devices, documents (digital or handwritten which may include documents such as building material specifications, BIM models, and the like), human input (e.g., via forms, surveys, filling out data fields on digital platforms, and / or the like), insights derived from the execution of any models stored on a digital platform, data and insights accessed via external organizations or services (e.g., a weather forecasting service accessed via API), and / or the like. Data formats used by embodiments of the present disclosure may include PDF. Word, PNG, JPEG. BIM (e.g., IFC), CAD (e.g., STEP), Revit (e.g., RVT), Floorplan data (e.g., as pdf or image), and / or the like. Data methods used by embodiments of the present disclosure may include extracting data and / or inferring data (e.g., extracting I inferring constraints from BIM and / or schedule information), data manipulation, data storage (e.g., in a database), data linkage, data transmission (Bluetooth, Wi-Fi, 3G, 4G, 5G (or any future G’s), Bluetooth low energy (BLE), BLE long range, LoRa, Sigfox, Mesh networks, and / or the like), and / or the like.

[0121] Data for the models, methods and / or systems herein may be aggregated from a multitude of sources and through various means such as devices (e.g. sensor devices), documents, human-input, third party integrations, and / or other models. Techniques for sensor data collection and transmission, may be utilized to gather measurements from sensor devices. These devices may be strategically deployed at every stage of the concrete or material value chain, providing a continuous stream of data throughout the process. Documents may be obtained at both the inception and during the course of a project. Methods of retrieval may include document uploads, emailing documents to a server, photographing documents, and scraping servers. Once acquired, these documents may be processed through image processing and Optical Character Recognition (OCR) or interpreted using advanced language models, such as Large Language Models (LLMs). Additionally, documents may be parsed in specific cases, like BIM models, which may include the capability of auto-detecting unit naming conventions and / or pour / unit geometry data. Data may also be collected from human interactions, such as through forms or chat-like interfaces, with the assistance of LLMs and similar technologies. This human-input data provides valuable insights and complements the automated data collection methods. The system may also be integrated with external data systems via APIs (e g., meteorological data may be retrieved from climate and weather service APIs). This integration ensures that the system has access to real-time and relevant environmental data that might impact the concrete or material properties.

[0122] In some embodiments of the present disclosure, the models, methods and / or systems herein may make use of data extracted from digital documentation data associated withbuilding materials and / or construction projects. Such documents may originate from a variety of stages of the design, specification, testing, and construction workflow, and may contain structured, semi-structured, and / or unstructured data associated to one or more materials being modelled by the models herein, their properties, contextual conditions and / or any other kinds of data described herein associated with materials. By way of example, this may include data associated with concrete mixtures, raw materials, geometries, environmental conditions, material properties, constraints, or intended performance objectives. The system may be configured to extract, transform, and ingest such data in order to support operation of any model herein including but not limited to supporting operation of predictive modeling, model training, attribution dataset generation, anomaly detection and / or model self-modification or improvement.

[0123] Additionally and / or alternatively, in some embodiments, digital documentation may include one or more of: building information models (BIM), building codes, digital construction specifications, concrete mix submittals, quality assurance / quality control (QA / QC) reports, lab test reports, material safety data sheets (MSDS), compliance certifications, Revit models (RVT), industry foundation class files (IFC). CAD drawings, floorplans, construction schedules, photographic or scanned documents (e.g., PDFs), annotated markups, and embedded metadata fields. These documents may be uploaded, linked via API, shared via email, photographed on site, or retrieved from local or remote servers. The ingestion process may include natural language processing, structured parsing, computer vision, or combinations thereof.

[0124] Additionally, or alternatively, in some embodiments, the models and / or methods herein may include data extraction methods for example to extract data from a BIM model in IFC or RVT format. The BIM may include metadata associated with concrete elements such as slabs, beams, or columns. The system may parse the geometry, dimensions, and element types (e.g., slab, column, wall), along with embedded construction phase information and material tags. For example, a structural beam element tagged with "C35 / 45" concrete may be automatically mapped to a mix class (e g. mix identifier), while its geometry (e.g., 300x500 mm cross-section, 3.2 m span) may be used to infer surface-to-volume ratio, thermal behavior, or risk of differential curing. This data may be passed on to material models and / or modules herein such as curing rate determination, strength prediction, and / or durability estimation models or modules. The data may for example be used as inputs to the models, training datasets upon which the models may be trained, and / or the like.

[0125] Additionally, or alternatively, the models, methods, and / or systems herein may process digital construction specification documents, such as project mix specifications which may include performance-based requirements or criteria, and extract constraints and / or requirements in a variety of ways, including but not limited to using OCR or a Large Language Model (LLM). These may include requirements such as “Minimum compressive strength of 35 MPa at 28 days,’' “Sulfate resistance per ASTM C1012,'’ or “Maximum w / c ratio of 0.45.” The extracted data may be structured as constraint obj ects. which can be used to filter candidate mixes in selection modules, or to constrain generative modules in mix generation models, or to constrain optimization modules in mix optimization models. Attribution datasets generated by these models may reference these extracted constraints as causal contributors to the inclusion or exclusion of certain mix candidates and / or mix parameters (e.g. no mix with a water-to-cement ratio above 0.45 was selected due to the constraint).

[0126] Additionally, and / or alternatively, in some embodiments, concrete test data (e.g. from concrete crush tests) may be ingested to extract empirical measurements of mix performance for example under standardized and / or project-specific conditions. For example, a PDF report may contain tabular or free-form test data for slump, air content, strength (1, 3. 7, 28, 56 days), chloride migration, shrinkage, and / or creep. The system may parse these values using rule-based extraction, OCR, or natural language templates, and align them with corresponding mix identifiers. These outputs may serve as training labels for supervised learning models, as validation references for anomaly detection modules, or as calibration data for temperature-maturity -strength models. Attribution datasets may be generated to identify which extracted specification parameters or measured properties most strongly influenced a given model prediction or decision.

[0127] In further embodiments. QA / QC (quality assurance / quality control) reports for example produced during concrete delivery or construction (e.g., slump tests, cylinder breaks, batch tickets) may be extracted in real time or near-real time and used to validate predicted outcomes from strength or workability7models. Deviations between predicted and actual values for example as extracted from such QA / QC reports may trigger the generation of attribution datasets identifying whether discrepancies arose from contextual conditions (e.g., temperature drop during transport), compositional errors (e.g., unexpected admixture dosage), or test methodology anomalies (which may be an example of inferred attribution). Such attributions may be presented to users or used for automatic model retraining or feedback adjustment.

[0128] Additionally, or alternatively, document-based data extraction may serve as input to anomaly detection modules. For example, if a BIM model indicates a certain concrete grade(e.g., C50 / 60) for an outdoor column, but QA data reveals repeated strength failures, the system may automatically generate an attribution report linking the discrepancy to mismatched design assumptions or weather-exposed curing. The documentation-derived metadata enables the model to contextualize the anomaly and localize its likely causes.

[0129] Additionally, or alternatively, in some embodiments, extracted data may be encoded prior to ingestion by downstream models. For instance, specification documents may be encoded into vectorized embeddings using pre-trained transformer models fine-tuned for construction document language. Additionally, or alternatively, structured metadata (e g., date, location, responsible contractor) may be linked to extracted material values, which may be used as training data for the models herein. Attribution models may then incorporate both structured and encoded data to identify relationships between document-based data and model outputs.

[0130] In further embodiments, the extracted document data may be stored in a structured database and may for instance be associated with provenance information and ingestion confidence scores. This database may sen e as a centralized training data source for property prediction models, mix selection models, mix optimization models, and mix generation models herein. The attribution datasets produced by these models may themselves include document references and / or document-derived variables as part of their explanatory output. For instance, an attribution vector may indicate that a “Target strength from project specification document X” contributed +6.4 MPa to the selection of a high-cement mix, or that a “Sulfate resistance clause in spec PDF ' was the dominant factor in excluding fly ash as a component.

[0131] Additionally, or alternatively, in some embodiments, the models herein may use digital documentation as context for a project to generate inferred attribution datasets. For example, if data extracted from a construction schedule indicates that concrete pours are planned during winter months, the model may infer that cold-weather curing conditions are expected and attribute the inclusion of higher early-strength cement or thermal insulation measures to the need to meet strength development targets under low ambient temperatures.

[0132] In any such embodiments, document-derived data, whether parsed from BIM, specifications, test reports, or QA forms, may serve as input, label, constraint, contextual condition, attribution factors, and / or the like in the models of the present disclosure. The document ingestion pipeline may include optical character recognition-based pipelines, large language model parsing, template-based form recognition, CAD / BIM parsing, structured data mapping, and / or metadata alignment. The extracted data may be validated, stored, and / or optionally altered, encoded and / or otherwise modified before being passed to downstream modules.

[0133] By way of example, a concrete mix design may be digitally represented using a JSON object with the following structure: A field titled ’mix id" may store a unique identifier for the mix, such as '‘C-202507”. A nested '‘components’’ object may define the quantitative proportions of ingredients, such as “cement_opc”: 350, “fly_ash”: 100, '‘fine_aggregate”: 750, “coarse_aggregate’’: 1050, “water”: 200, “superplasticizer”: 5, and “air_entrainer”: 0.3, where all values are expressed in kilograms per cubic meter. A “unit” field may declare the measurement basis, e.g., “kg / m3”. Additional scalar values such as “water_cement_ratio”: 0.45 and “slump_target”: '‘75-100 mm” may also be included.

[0134] Another nested object under the key “curing” may specify conditions such as “temperature”: 23 (degrees Celsius), “humidity”: 95 (percent), and “duration_days”: 7. A separate “environment” object may contain data like “exposure”: “marine”, “chloride_class”: “C3”, and a “temperature_profile” array with values -5 and 30 representing expected minimum and maximum temperatures during service life. Finally, a “performance_targets” object may be provided, containing desired thresholds such as “compressive_strength_28d”: 45 (megapascals), “durability _index”: “high”, and “embodied_carbon_max”: 250 (kilograms of CO? per cubic meter).

[0135] Additionally, or alternatively, in some further embodiments, spatially resolved or visual data, such as thermal maps, microscopy images, or tomographic scans, may be stored in binary' formats (e.g., PNG or TIFF) and referenced within the digital input representation using file paths, hash pointers, or URIs. Accompanying metadata may include spatial resolution, magnification, acquisition parameters, and calibration coefficients. This may allow integration of high-dimensional data (e.g., input data) into the model pipeline and enables attribution datasets to refer back to spatial regions or features in the original input domain.

[0136] Additionally, or alternatively, in some further embodiments, data including input data, training data and the like, may be stored and organized in a relational database structure, with tables and / or entities corresponding to material designs, test conditions, experimental results, and process metadata. Each data entry' may be uniquely identified by a primary' key or timestamp, enabling joins across datasets and linkage to attribution outputs. Alternatively, in cases where causal or dependency relationships between inputs must be modeled explicitly (e.g., ingredient substitution rules, hierarchical process stages, or conditionally activated parameters), a graph-based digital representation may be used. In such cases, the digital input data may be stored in a graph database or serialized as an RDF schema, enabling dow nstream models to reason over input dependencies or perform structured queries during inference or attribution generation.

[0137] Additionally, or alternatively, in some embodiments, the data herein may include a target performance profile defined over time, such as a desired strength development curve or temperature exposure trajectory. For instance, a strength gain profile may specify that compressive strength should reach 10 MPa at 1 day, 25 MPa at 3 days, 40 MPa at 7 days, and 50 MPa at 28 days. Alternatively, a temperature profile may define that the material will be exposed to 20°C for the first 12 hours, ramp up to 40°C over the next 24 hours, and then gradually decrease to 25°C by 72 hours. These profiles may be expressed as arrays, key-value pairs, or continuous functions sampled at discrete time points tl,t2,...,tnt_l, t_2, ..., t n, tl ,t2 ,...,tn, and may be input to the system in structured digital formats such as JSON or CSV.

[0138] As used herein, attribution data entries, attribution datasets, and / or attribution data may include data indicative of an influence and / or causal relationship associated with the model. This may include any influence and / or causal relationship between any data objects and / or model data described herein, as well as any subset part of any material model and / or modules described herein including but not limited to material identifiers, material composition, material properties, and / or contextual conditions associated with one or more materials associated with the models herein. Additionally, or alternatively, this may also include any influence and / or causal relationship betw een models, modules, input data, output data, weights, encodings, objective functions, utility functions, constraints, training data, training loss function, latent representations and / or intermediary model representations, neurons, model features, tokens, and / or any data indicative of the above, and / or the like. Without loss of generality, the attribution datasets described herein may be associated with an influence and / or causal relationship between any of these aforementioned datasets and / or data objects and / or model data as well as any other influence and / or causal relationship associated with the model as would be evident to one skilled in the art.

[0139] The attnbution dataset and / or modularity of the one or more models may be indicative of a variety of types of explainability and / or influence or causal relationship associated with the model. In some embodiments, the explainability, attribution dataset, and / or influence or causal relationship may be associated with two direct pairs of model data (e.g., input and output, weight and output, and / or the like). Additionally, or alternatively, in some embodiments, the explainability, attribution dataset, and / or influence or causal relationship may be associated with a discrepancy between an output of a model or module and an expected or target baseline. Additionally, or alternatively, the discrepancy may include a difference between data indicative of a measured real behavior and / or performance and / or property associated with a material, and an output of a model or module (e.g., second data generated bythe model), or a physically simulated behavior and / or performance and / or property associated with a material, simulated based on physical laws, and an output of a model or module. For example, the discrepancy may include a difference between a baseline expected or measured thermal evolution of a concrete pour, and the predicted thermal evolution based generated or output by a model or module herein. The expected thermal evolution may be simulated by a physics-based simulation model (e.g. based on physical equations such as the heat diffusion equation) and may be compared with second data generated and / or output by any models herein (e.g. a prediction model empirically generated second data indicative of the thermal evolution of the material based on ingested first data). The models herein may then be used to generate an attribution dataset indicative of an influence and / or causal relationship between the discrepancy and another data associated with the model e.g. one or more inputs into the prediction model. Additionally, or alternatively, the baseline may include thermal evolution as measured for example through the use of temperature or thermal sensors embedded in, partially embedded in and / or in contact with the concrete. The discrepancy may then include the difference between the measured thermal evolution and the second data generated by a prediction model or module of the predicted thermal evolution. The generated attribution dataset may then be indicative of an influence or causal relationship between data indicative of the difference between measured and predicted properties, and any other data associated with the model, such as first data ingested by the model, intennediary or latent representations, data generated by intermediary models (e.g., intermediary module outputs), input data, weight data, encoding data and / or the like, including contextual condition data, environmental data, weather data, geometry data, insulation data, material properties, compositional properties, and / or the like. Additionally, or alternatively, in some embodiments the discrepancy may be attributed to an influence or causal relationship between first data ingested by the model, or first and second data ingested by the model or any number of data ingested by the model (e.g., one or more inputs), and data generated by the model (e.g., one or more outputs), where the models herein may include a single module or a plurality of modules interconnected in a variety of topologies (e.g. serialized or parallel or combination of both for more complex architectures), and / or neural networks and / or the like. Additionally, or alternatively, in some embodiments of the present disclosure, the models herein may be adjusted in whole or in part based on the discrepancy and / or the attribution dataset associated with the discrepancy. For example, an adjustment may be made to the one or more data ingested by the model or module, such as a change in data encoding, the addition of a target contextual condition, or the like. Additionally, or alternatively, a discrepancy may be attributed to an influence or causal relation between afirst or plurality of weights and the discrepancy or data generated from the model, in which case the weights may be adjusted based in whole or in part on the discrepancy and / or the attribution dataset. In some embodiments, adjustments may involve adjusting a parameter of the model, retraining the model and executing the model again (e.g., a first dataset comprising one or more first data entries associated with a material; generating, using the model, a second dataset comprising one or more second data entries associated with one or more properties of the material). The model execution method may also include generation of the discrepancy attribution dataset. In some embodiments, the model’s adjustment may be iteratively executed until the discrepancy is decreased to a predetermined threshold target and / or until it reaches a convergence criteria and / or until the discrepancy stops lowering or only marginally or asymptotically lowers with further iterations. Additionally, or alternatively, such embodiments may include the following: ingesting, by a model, a first dataset including one or more first data entries associated with a material; generating, using the model, a second dataset including one or more second data entries associated with one or more properties of the material; comparing the second dataset to a baseline dataset and / or generating a discrepancy between the second dataset and the baseline dataset; generating an attribution dataset compnsing one or more attribution data entries, where the attribution dataset is indicative of an influence or causal relationship associated with the discrepancy and one or more model data or parameters; adjusting the model data; optionally retraining the model; repeating the above steps based on the adjusted model data and / or optionally using the retrained model; generating a new dataset indicative of the discrepancy; generating new attribution datasets; repeating the above steps until a condition is met, where the condition may include reaching a maximum discrepancy threshold, reaching a convergence criterion, the discrepancy stopping to meaningfully decrease. Additionally, or alternatively, in some embodiments, the discrepancy data may be indicative of a discrepancy in model behavior compared to expected model behavior. For example, this may include discovering a bias in the model’s latent representations compared to expectations, which may be adjusted for example by retraining the model using a different loss function or retraining the model with altered training datasets.

[0140] Additionally, or alternatively, in some embodiments, attribution datasets may be generated based on inferred contextual reasoning by the models disclosed herein, even where the inferred context is not explicitly represented as a model input or output. In such embodiments, the model may interpret available inputs in light of latent or non-explicit project conditions, and / or general context information regarding building materials, construction projects and the like it may have been trained to reason about (e.g. LLM reasoning and / or otherreasoning model architectures) and generate attribution datasets that reflect inferred causal or influence-based relationships informed by those inferences. For example, where the input data includes a large pour geometry and elevated ambient temperatures, the model may internally infer a heightened thermal cracking risk, despite thermal cracking not being explicitly predicted or modelled. Based in whole or in part on this inferred context, the model may generate an attribution dataset indicating that variables such as binder composition, heat of hydration, supplementary cementitious material dosage, or cooling strategies exert greater influence on strength development or curing time predictions. Such inferred attribution datasets may be indicative of a model’s or module’s internal understanding of non-explicit project requirements or risks and may be used to surface explanations or explain model behavior in the absence of an explicit discrepancy or directly modelled target. In some embodiments, these explanations may be fed to users. Additionally or alternatively, inferred attributions may arise from digital documentation such as project documentation that encodes implicit expectations, such as schedule-driven strength targets and may be used by the models to adjust data generated by models such as predictions or material and / or mix formulations and / or explain such adjustments (e.g. one variable is made to influence the output to a greater extent by increasing its weight in the model in part based on the inferred attribution). These attributions may be generated independently or in conjunction with any other attribution associated with model data including input-based or discrepancy-based attributions.

[0141] In some embodiments, attribution datasets may include input-based attributions, which may be attributions indicative of an influence or causal relationship between input data and other data associated with the model and / or the material. By way of example, these may include influence and / or causal relationships between inputs and outputs; inputs and intermediate representations; or between one input and another. Such pairwise attributions may include: influence of an input on an output; influence of an input on an intermediate representation; influence of an input on a latent vector; influence of an input on attention weights; influence of an input on a hidden layer activation; influence of an input on an embedding dimension; influence of an input on a confidence interval; influence of an input on a prediction discrepancy; influence of an input on an evaluation score; influence of an input on a module output; influence of an input on internal model bias; influence of an input on the error in an output; influence of one input on another input; influence of an input on a reasoning module output; influence of an input on an explanation output.

[0142] In some embodiments, attribution datasets may include module-level attributions, which may be indicative of causal or influential relationships between elements of a modularmodel architecture, including separate portions of individual modules and / or relationships across modules, and / or including inputs, outputs, and / or intermediate layers or pathways. By way of example, these may include: influence of a first module input on a first module output; influence of a first module input on a second module output; influence of a module input on a final model output; influence of a module input on a module latent vector; influence of a module output on a final output; influence of a first module latent representation on a second module output; influence of a module latent representation on an attribution module output; influence of a module input on an explanation discrepancy.

[0143] In some embodiments, attribution datasets may include training-data-based attributions, which may be indicative of the influence or causal relationship between training data and model behavior, outputs, weights, and / or learned biases. By way of example, these may include: influence of a training data sample on a model output; influence of a training data distribution and / or clustering on output bias; influence of training data on one or more model weights; influence of training data on one or more latent representation; influence of training data on generated encoding; influence of training data on prediction variance; influence of training data on model confidence; influence of training data on output discrepancy (e.g. discrepancy between model output and expectations, which may by way of example be informed by physico-chemical laws and / or real sensor data); influence of a specific training data entry on a test result prediction (e.g. prediction of slump test result); influence of training data on the width of a confidence interval.

[0144] In some embodiments, attribution datasets may include weight-based attributions, which may be indicative of causal relationships between model weights and / or other aspects of the model or output behavior. By w ay of example, these may include influence of a model weight on an output; influence of one set of weights on another set of weights; influence of a model weight on a latent representation; influence of a model w eight on model bias; influence of a model weight on the model's error profile; and / or influence of a model weight on an output anomaly and / or discrepancy.

[0145] In some embodiments, attribution datasets may include objective-function-based attributions, which may be indicative of an influence and / or causal relation between loss functions, optimization terms, and the model’s learned behavior or biases. By way of example, these may include influence of a loss function on model bias; influence of an objective function on a model output; influence of a loss term on an internal latent structure; influence of a multiobjective function on a tradeoff outcome (e.g., an objective function which includes time-to- cure and embodied carbon influencing a model’s output to recommend a mix which takeslonger to cure but has lower embodied carbon); and / or influence of a loss function on a confidence interval and / or on model errors.

[0146] In some embodiments, attribution datasets may include latent and / or internal variable attributions, which may be indicative of relationships between hidden states within the model and its outputs and / or intermediate states. By way of example, these may include influence of a latent vector on an output; influence of a hidden neuron on an output property; influence of an embedding dimension on a predicted property; influence of a latent variable on a selection outcome; influence of a latent variable on a generated explanation or reason; influence of a latent variable on a prediction discrepancy; and / or influence of an internal variable on a confidence interval.

[0147] In some embodiments, attribution datasets may include contextual condition or environmental based attributions, which may be indicative of an influence or causal relationship between contextual conditions and / or material performance or model behavior and / or mode data. By way of example, these may include: influence of a contextual condition on an output; influence of a contextual condition on a model weight; influence of a contextual condition on a latent representation; influence of a contextual condition on an evaluation outcome; influence of an contextual condition on a property discrepancy compared to baseline expectation; influence of geometry on material performance; influence of climate on a predicted material property; and / or influence of a training data (e.g., sensor-based training data) on an output discrepancy.

[0148] In some embodiments, attribution datasets may include temporal attributions, which describe influence or causal relationships between variables observed or predicted at different points in time. By way of example, these may include influence of a model feature at an earlier time on an output at a later time; influence of an early-age material property on a later-age property (e.g. cementitious mix temperature at T = 6h and strength at T = 24h); influence of a material property at a particular time on the error in a prediction at a later time; influence of a timestamped sensor reading on a model prediction; and / or influence of a temporal condition on long-term durability.

[0149] In some embodiments, attribution datasets may include discrepancy-based attributions, which may be indicative of an influence or causal relationship between a discrepancy and / or anomaly in a model output and / or expected behavior, and the cause of this discrepancy (e.g., contextual conditions, model inputs, model training, and / or the like). By way of example, these may include influence of an input on a prediction discrepancy; influence of training data on a prediction discrepancy; influence of a model weight on a predictiondiscrepancy; influence of a loss function on a discrepancy; influence of a contextual condition on a discrepancy; influence of sensor data input on a discrepancy; influence of a latent state on a discrepancy; influence of human feedback on reduction of a discrepancy (e.g., in some embodiments the models herein may use human feedback to retrain and improve the model); influence of an unmodeled variable on a discrepancy (e.g., may be inferred by a reasoning module).

[0150] In some embodiments, attribution datasets may include inferred attributions, which may be indicative of an inferred influence and / or causal relationship between non-explicitly modelled variables and model data, for example through a reasoning and / or explainability module or model. By way of example, these may include influence of an unmodelled contextual condition that may be influencing a modelled material’s behaviors and / or properties; and / or influence of an unmodelled material property (e.g., material temperature) on an output material performance in a given set of contextual conditions.

[0151] In some embodiments, attribution datasets may include user or user-feedback-based attributions, which may be indicative of the influence and / or causal relationship between model behavior / data associated with the model, and user input (e.g.. a user providing feedback that a mix selected by a mix selection model is non-usable given workability requirements). By way of example, these may include influence of user feedback on model retraining effectiveness; influence of a user correction on a change in prediction; influence of a user input on model confidence; influence of a user input on an attribution score (e.g., a user may provide input to the model, the model may then retrain, and regenerate its output, the discrepancy between an attribution score give to a particular weight and an output pre- and post- retraining may be different, and may therefore be indicative of the influence of a user input on an attribution score).

[0152] In some embodiments, attribution datasets may include sensor data-based attributions, which may be indicative of an influence and / or causal relationship between measured sensor signals and / or model outputs (e.g., predictions), latent states, and / or inferred conditions. By way of example, these may include influence of a sensor input on a model output (e.g., the model is a model that predicts a material property based on sensor input data); influence of a sensor segment (e g., a segment of sensor time series data betw een t = T and t = T+ AT) on model output error or uncertainty; influence of a sensor data feature (e.g., peak, trough, mean value over time interval and the like) on a latent representation (e.g., in the case where sensor data is used as training data); influence of electromechanical impedance data on predicted dynamic modulus of elasticity; influence of a temperature curve on a strengthprediction; influence of a maturity index on a concrete performance prediction; influence of UPV time series data on stiffness prediction; and / or influence of sensor drift on a prediction discrepancy.

[0153] In some embodiments, attribution datasets may include multi-input and / or interaction-based attributions, which may be indicative of joint, nonlinear, and / or conditional influence or causal relationships of a plurality of variables on another set of variables. By way of example, these may include joint influence of two or more inputs on an output; influence of an input target material property and contextual condition on a material selection output; influence of an input and training bias on a model error; joint influence of an input and model weights on a latent representation of the model; influence of an input in combination with human feedback on an output change joint influence of sensor data and contextual condition data on an output; influence of both training data and weights on a final prediction; and / or influence of both the training data distribution and the objective function on a model bias.

[0154] In some embodiments, additional attributions may be indicative of an influence or causal relationship between data associated with the material. By way of example, these may include: influence of compositional data (e.g., fly ash content) on predicted compressive strength; influence of material structural data (e g., aggregate size distribution) on predicted shrinkage; influence of process parameters (e.g., mixing duration) on thermal profile predictions; influence of contextual environmental data (e.g., pour geometry) on predicted hydration rate; influence of input test results (e.g., slump test value) on predicted modulus of elasticity; influence of simulation-derived heat of hydration data on strength gain curves; influence of derived features such as binder intensity on sustainability classification; influence of user-specified performance targets (e.g., strength at 28 days) on generated recipe composition; influence of contextual conditions such as geographical location on predicted material selection; and / or influence of incomplete histoneal training datasets on output uncertainty.

[0155] In other embodiments, attribution datasets may include material identifier-based attributions, which may be attributions indicative of an influence or causal relationship between a material identifier and other model outputs and / or internal representations. By’ way of example, these may include influence of a strength-grade identifier (e.g., C40) on predicted strength; influence of a strength-grade identifier on generated mix; influence of exposure class (e.g., XD3) on durability predictions.

[0156] In some embodiments, attribution datasets may take a variety of formats including the formats described herein. These formats may be used alone or in combination, and areillustrative in nature, without limiting the scope of the disclosure. For example, an attribution dataset may include a feature attribution vector wherein each input variable used by the model may be associated with a corresponding score representing its influence on a particular output. This score may be positive or negative, indicating whether the input pushed the prediction higher or lower relative to some baseline. The attribution vector may include entries for all input variables or only for a subset of the most influential features. It may be used to support explanations such as, “fly ash content reduced strength by 3.2 MPa” or “curing temperature increased strength by 5.5 MPa.”

[0157] In related embodiments, the attribution dataset may be structured as a feature attribution table, where each row represents a feature and the columns may include the input’s value, attribution score, associated confidence level, and method of computation. An example of such a table may include:

[0158] This table is i lustrative and may vary in size, structure, or included fields. In some cases, the attribution dataset may consist only of a subset of such a table, showing, for instance, the top two contributing inputs or only those above a defined attribution threshold. Additionally, or alternatively, in some embodiments, the attribution dataset may include Shapley values, which reflect the contribution of each input variable based on principles from cooperative game theory. Shapley values may be represented numerically. Additionally, or alternatively, in some embodiments, including time-series or sensor-driven applications, attribution datasets may include time-aligned saliency maps, which may represent the influence of temporally varying inputs (e.g., curing temperature or relative humidity) on an output over varying segments of time. Each entry in such a dataset may correspond to a timestamp or time window or time segment, the associated input value at that time, and a score indicating its attribution to the final output. These scores may help identify specific time intervals (e.g., between 8 and 14 hours after casting) that had the highest impact on outcomes like cracking risk or early-age strength. For example:

[0159] In further embodiments, the attribution dataset may represent frequency -domain signal attributions, for example when inputs include sensor data captured in frequency space (e.g., acoustic or impedance spectroscopy data). Attribution values in this case may be mapped to specific frequency bands, such as 100 Hz or 500 Hz, and may indicate how much each band influenced an output like stiffness, reactivity, or degradation rate. The format may be expressed as a two-column table with frequency and attribution score, or as a visual spectrum with overlaid influence regions.

[0160] Additionally, or alternatively, the attribution dataset may also be structured as a graph, including but not limited to as a directed acyclic graph (DAG), symbolic causal graphs, and / or hypothesis trees that illustrate the causal or influence pathways between any data associated with the model and / or material, including inputs, intermediate variables, latent representations, and final outputs. Additionally, or alternatively, in such representation, nodes may correspond to model elements (e.g., “SCM dosage”, ‘"latent vector embedding”, “durability score”), and edges may represent influence, weighted by magnitude or strength of relationship. Such structures may enable tracing attribution across modules or reasoning layers within a hierarchical architecture. Additionally, or alternatively, in some embodiments the graphs herein may be used to represent inferred or reasoned explanations for model behavior, discrepancies, or anomalies. For example, each node in such a graph may represent a candidate cause (e.g., “insulation blanket present” or “sensor calibration drift”), and may be annotated with a confidence score or supporting rationale. These structures may be used in whole or in part by the methods and / or models and / or systems herein to generation explanations and / or attribution datasets, including for factors not directly included in the model inputs

[0161] Additionally, or alternatively, attribution may be encoded in the form of an attribution heatmap, for example in models with internal dimensional representations such as convolutional or transformer networks. The heatmap may present a matrix of values, with rows corresponding to neurons or embedding dimensions and columns corresponding to outputs or prediction classes. An illustrative example might include:

[0162] Additionally, or alternatively, in some embodiments, the attribution dataset may be defined by a set of interaction rules, which specify conditions under which multiple input features jointly affect an outcome in a nonlinear or non-additive way. These rules may include logical expressions (e g., “fly ash content > 100 AND curing temperature < 15”) and associated effects (e.g., “strength reduction of 5.5 MPa”), along with optional confidence metrics or rule weights. Such rules may be used for interpretability, constraint checking, or scenario analysis, and the dataset may contain one or more such rules, each encoded as a row in a structured format.

[0163] Additionally, or alternatively, in some embodiments including user-facing implementations, attribution may also be presented as natural language attribution summaries, which provide human-readable explanations of model behavior. For example: "Low curing temperature and high fly ash content jointly contributed to a predicted strength reduction of 5.5 MPa." These summaries may be generated from underlying structured attribution data and may be used in reports, dashboards, or interactive model inspection tools.

[0164] Additionally, or alternatively, in some embodiments, the attribution dataset may include an influence ranking list, which identifies and ranks the most influential features, latent factors, or training samples for a given prediction. The ranking may reflect absolute attribution magnitude, impact on prediction confidence, or contribution to observed discrepancy. This list may include the top-k most influential items and need not be exhaustive.

[0165] Additionally, or alternatively, in multi-objective or optimization-driven embodiments, attribution datasets may include Pareto trade-off attribution maps, which show how shifting objective function weights or constraints affects different output properties. These maps may consist of paired values (e.g., “carbon cost” vs. “strength”) and allow users to identify trade-offs between competing objectives, such as minimizing emissions while maintaining performance.

[0166] Additionally, or alternatively, in some embodiments, attribution datasets may include confidence-weighted attribution reports, where each attribution score is annotated with a confidence interval or statistical uncertainty. For example, a value of -6.8 MPa for water-to- cement ratio may be accompanied by an interval of [-8.2, -5.4], indicating the model s confidence in the effect range.

[0167] Additionally, or alternatively, in some embodiments, the systems and methods described herein may include generating an explainable insights report associated with one or more models, predictions, and / or outputs related to a cementitious material, such as a concrete mix. The explainable insights report may be generated automatically or upon user request and may comprise any data or representation derived from an attribution dataset as described herein. The report may include, for example, numerical attribution scores, ranked feature influences, confidence-weighted explanations, causal graphs, time-series impact maps, frequency-domain signal attribution, and / or natural language summaries indicative of one or more factors contributing to the prediction or model output.

[0168] Additionally, or alternatively, the report may include comparisons between predicted and measured material behaviors, indicators of confidence or uncertainty, and userfacing justifications for outputs such as predicted compressive strength, thermal evolution, cracking risk, or durability. In some embodiments, the report may include visualizations such as charts, saliency overlays, or trade-off diagrams (e.g., strength vs. carbon footprint), along with interpretability summaries and / or explanation narratives configured for consumption by users. In some embodiments, the explainable insights report may be embedded in dashboards, stored with model outputs, or transmitted as part of digital documentation associated with a project or mix.

[0169] The generation of such explainable insight reports may be critical in applications where trust, traceability, and compliance are required, such as in construction or infrastructure projects involving risk-averse or regulated stakeholders. In such cases, the report provides transparency into model behavior and decision-making processes, enabling users to evaluate, audit, and approve the use of Al-based recommendations or predictions. Accordingly, embodiments of the present disclosure may include generating, displaying, storing, transmitting, or otherwise making available explainable insights reports that summarize or surface attribution-based, interpretable, and traceable information associated with any model, output, input, intermediate representation, and / or discrepancy as described herein.

[0170] In any such embodiments, the attribution dataset may be generated automatically by the model, produced post hoc through interpretability algonthms, and / or generated fromhybrid sources including model-infused domain knowledge, training data analysis, or the use of reasoning modules, including multi-modal LLM based reasoning modules configured to inspect varying aspects of the models and / or modules herein, included but not limited to the model weights, the model inputs, outputs and / or intermediary module inputs and / or outputs, training datasets and biases, latent representations and the like. The formats described herein are merely illustrative of what such attribution datasets may look like and are not intended to be limiting. Any digital structure, whether full dataset tables, reduced subsets, logical expressions, ranked lists, or visual overlays, may serve as an attribution dataset.

[0171] In some embodiments, attribution datasets may convey explainable insights (e.g., attribution data entries) through a plurality of additional representations. A non-exhaustive list of additional forms of representations may include, as an example, a graphic representation of the different inputs and weights (or the correlation) that led to a conclusion (e.g., a graph with nodes for each weight connected by lines). In such an example, the representation may further have an ability to edit the weights and then recalculate. Further, statements about each weight and its impact may be generated and output. Additionally, or alternatively, the representation may include sliders for the different inputs and dynamic or button triggered recalculations. Additionally, or alternatively, the statement may also be recalculated or dynamically adjusted based on the sliders.

[0172] A non-exhaustive list of additional forms of representations may include, as another example, a graph of performances in different conditions with an ability to click and drag the graph and see suggestions on what input changes would change the model the way a user wants.

[0173] A non-exhaustive list of additional forms of representations may include, as another example, a comparison to other mixes and or ideals (e.g., graphic and / or numerical comparison to pours or mixes in similar situations with similarity based on a variety of categories.) A non- exhaustive hst of additional forms of representations may include, as another example, a color coding of outputs including, but not limited to, statements and graphs, color coding of overall outputs, color coding of inputs such that users may see what elements of the system are likely to be causing trouble, color coding that may dynamically adjust as users adjust parameters, color coding of suggested other models (e.g., show a graph with different options a user could change to and color code them such that the user may see which ones would perform 'better’ in different ways), color coding may be configured as a stoplight system (e.g., may see what inputs may impact, may compare to thresholds set by the user, and / or the like), color coding based on carbon saving, color coding based on cure time, color coding based on materials cost, and / or the like.

[0174] A non-exhaustive list of additional forms of representations may include, as another example, a prediction and alternatives (e.g., have ‘ghost lines’ alongside the actual which are alternatives to the current mix)

[0175] A non-exhaustive list of additional forms of representations may include, as another example, a drop down or "show more” button to allow for more detailed explanation of general happenings, (e.g., “This element is too thick for the chosen concrete recipe. All likely ambient conditions will lead to thermal cracking.” — Show More —> Additional Insights).

[0176] A non-exhaustive list of additional forms of representations may include, as another example, image representations (e.g., slides) of what the pour may look like at different stages with commentary' and labelling for what is happening.

[0177] A non-exhaustive list of additional forms of representations may include, as another example, animations of pour performance (e.g., 2D or 3D). Further, these may be continuous or a rolling version of the image representation. Additionally, or alternatively, these may have the ability7to pause and reconfigure or recalculate. Additionally, or alternatively, these may have the ability to reconfigure inputs and rerun. Additionally, or alternatively, these may include suggested sensor locations and predicted performance of those. Additionally, or alternatively, these may allow7the ability7to move them and observe how that changes the output. A non-exhaustive list of additional forms of representations may include, as another example, sounds to match different performances and characteristics.

[0178] In some embodiments, the attribution dataset may be generated by the model itself or a constituent module of the model. Additionally, or alternatively, a model and / or module may inspect and / or interrogate the model and / or any constituent submodule of the model to extract data to generate one or more attribution data entries of the attribution dataset. In some embodiments, sensor data may be used to identify discrepancy between one or more predictions and real-world outcomes. Further, an attribution dataset may be generated that includes attribution data entries with data associated with the identified discrepancy. Additionally, or alternatively, the identified discrepancy may be used to adjust an associated model to compensate for the identified discrepancy.

[0179] In some embodiments, generation of attribution datasets may be performed using gradient-based saliency methods, which may be indicative of the influence of one or more input features on one or more model outputs. The system may compute the partial derivative of the output with respect to each input variable (e.g., Output / f InputFeature). using automatic differentiation over the model’s computation graph. The resulting gradients may quantify the local sensitivity of the model to each input and may be captured as scalar attribution scores.These may be normalized, signed, or thresholded for clarity. For example, an attribution dataset may take the following form:

[0180] These values may be stored as arrays or embedded in attribution vectors and may support the identification of dominant input-output influence pathways.

[0181] Additionally, or alternatively, in some embodiments, attribution datasets may be generated using integrated gradients, which may be indicative of the influence of input variables on a model output, based on the path integral of gradient values between a reference (baseline) input and the actual input. The system may compute gradients at discrete points along a linear interpolation path and accumulate contributions to derive global attributions that reduce sensitivity to local noise. An example of such attribution dataset includes:

[0182] These cumulative attributions may reflect the total input-to-output effect across the input space.

[0183] Additionally, or alternatively, in some embodiments, attribution datasets may be generated using Shapley values, which may be indicative of the marginal contribution of an input variable to an output prediction, relative to all other variables. The system may compute the contribution of each feature to a model output by averaging its incremental effect across all permutations of feature subsets. For example, an attribution dataset generated using Shapley values may include:

[0184] Additionally, or alternatively, in some embodiments, attribution datasets may be generated using layer-wise relevance propagation, which may be indicative of the contribution of input features and intermediate hidden representations to the final model output. The method may involve backward redistribution of output relevance scores across the network layers, preserving the total prediction magnitude and tracing contributions through the full model architecture. Example attribution dataset may include:

[0185] Relevance scores may be visualized, structured into matrices, or aligned to input features and neuron activations.

[0186] Additionally, or alternatively, in some embodiments, attribution datasets may be generated using occlusion analysis, which may be indicative of the influence of specific input variables on a model output by systematically masking, replacing, or removing those inputs and measuring changes in the output. For each modified input, the model may be re-evaluated, and the output delta may be recorded. An example such attribution dataset includes:

[0187] Additionally, or alternatively, in some embodiments, attribution datasets may be generated through counterfactual perturbation, which may be indicative of the influence of one or more inputs on a prediction by exploring how deliberate, plausible changes to input values affect model outputs. For instance, inputs may be increased, decreased, or substituted within a defined domain. The resulting attribution may reflect real-world decision sensitivity. An example such attribution dataset may include:

[0188] Additionally, or alternatively, in some embodiments, attribution datasets may be generated by extracting attention weights from an attention-based model (e.g., transformers), which may be indicative of the degree to which each input token or time step contributes to a downstream output. Attention coefficients may be directly interpreted as influence scores and stored as matrices or time-aligned attribution records.

[0189] Additionally, or alternatively, in some embodiments, attribution datasets may be generated using influence functions, which may be indicative of the influence of individual training samples on model outputs. The system may estimate how the removal or modification of a specific training datapoint would affect the prediction of a test example, often using approximations to the Hessian or influence traces through the loss function. For example:

[0190] Wherein similarity scores may include similarity between training data samples and an input data (in this example the input that would have generated the crush test prediction).

[0191] Additionally, or alternatively, in some embodiments, attribution datasets may be generated using surrogate models trained to locally approximate the behavior of a complex model around a specific input region. The coefficients or structure of the surrogate model (e.g., linear regression, shallow tree) may then be used to infer input-to-output attributions. For example:

[0192] Additionally, or alternatively, in some embodiments, attribution datasets may be derived using symbolic rule extraction methods, which may be indicative of influence relationships between combinations of input variables and a model output. The system may convert nonlinear model behavior into a set of logical expressions using pattern mining or decision-tree approximation. For example, an extracted rule may include: if Fly Ash > 20% and Temp < 15 °C , then Strength Delay = +3.5 days with a confidence score of 0.89 (which may be indicative of the estimated probability that the model has of the rule holding true).

[0193] Additionally, or alternatively, in some embodiments, attribution datasets may be derived from Bayesian inference frameworks, which may be indicative of the contribution of different sources of uncertainty to the variability in model output. The posterior distribution may be decomposed into input-driven, model-driven, and parameter-driven components. For example:

[0194] Additionally, or alternatively, in some embodiments, attribution datasets may be generated by empirically probing the model over a structured grid or random sample of input values and fitting a regression surface. The resulting variance decomposition may be indicative of the influence of each input on output variability. For example:

[0195] These attributions may support interpretability in simulation-assisted models or multi-objective optimizers.

[0196] Additionally, or alternatively, in some embodiments, attribution datasets may be generated by tracing prediction responsibility across modules of a modular or hybrid model architecture. This may be indicative of the influence of one submodule’s output (e.g., a physicsbased simulation) on the final prediction output of the full pipeline. For example:

[0197] Such datasets may be derived using backpropagation, residual energy partitioning, or inter-module dependency analysis.

[0198] Additionally, or alternatively, in some embodiments, attribution datasets may be generated using temporal relevance mapping, which may be indicative of the influence of input values at specific time intervals on future predictions. This may involve applying masking, convolution-based saliency, or time-window ablation to identify windows of greatest effect.For example:

[0199] Such attributions may be used to link early-age conditions to strength or durability performance in time-series applications.

[0200] In some embodiments, encodings herein may include, but not are limited to, the following examples: direct scalar inputs (e.g., water-to-cement ratio as a float); categorical variables represented as integers (e.g., cement type = 1); one-hot encoding of discrete categories (e.g., mix ty pe, supplier, element ty pe); mean or median from time-series data (e.g., average curing temperature over 48 hours); min / max / standard deviation extracted from sensor signals (e.g.. max humidity during early curing); engineered features from mix recipes (e.g.,binder intensity, aggregate ratio); binary encoding for Boolean features (e.g., contains SCM = True); embedding vectors for categorical inputs (e.g., supplier ID embedded into a latent space); extracted slope or rate from time series (e.g., rate of temperature rise during hydration); input normalization or standardization (e.g., z-score scaling of ingredient mass); tokenized and / or embedded representations of text (e.g., specification requirements); manually constructed mix descriptors (e.g., "low-carbon" or "fast-setting" labels); simple ratios (e.g., fly ash to total binder); PCA-reduced components from multivariate sensor data; maximum observed property value (e.g., peak compressive strength); positional encoding in time or space (e.g., time since pour, distance from surface); feature counts or frequencies (e.g., number of admixtures used); rule-based features (e.g., satisfies regional standard = True); domain-derived scores (e.g., maturity index calculated from temp history); histogram or binned encodings (e.g., binned temperature profile over curing duration); FFT-transformed spectral components (e.g., impedance signal in frequency domain); polynomial or spline coefficients fitted to sensor curv es (e.g., hydration profile trend); embeddings from simulation outputs (e.g., simulation- derived porosity vector); learned latent representations from autoencoders (e.g., mix representation learned from strength curves); and / or attention-weighted contextual embeddings (e.g., geometry- or weather-aware mix embeddings).

[0201] In some embodiments, a data object may include an objective function and / or utility function, which may be used during model training, prediction, selection, optimization, or generation. Objective functions may define the desired output behavior of the model and may include, without limitation, loss functions such as cross-entropy, mean squared error, loglikelihood, hinge loss, reconstruction loss, Q-leaming objectives, or regularization terms (e.g., LI, L2, constraint parameters, or hyperparameters). Multi-objective functions may also be used, including Pareto-based methods or evolutionary algorithms, optionally weighted to reflect priority among competing objectives.

[0202] Additionally, or alternatively, in some embodiments, utility functions may be employed to encode user or system preferences over multiple possible outcomes into a single evaluative score. Utility functions may include cumulative reward, expected utility, payoff functions, risk-aware utilities, weighted sums, exponential or logarithmic forms, and other preference aggregation schemes.

[0203] Examples of obj ecti ves that may be encoded into such functions include minimizing cost, minimizing embodied carbon, maximizing strength, durability', thermal conductivity', recyclability, chemical resistance, fatigue life, or fire resistance; minimizing mixing time ormaterial weight; and maximizing lifecycle sustainability' or energy efficiency in raw material processing. Any combination of these may be used in multi-objective optimization settings.

[0204] In some embodiments, a data object may also include constraints. Constraints may take the form of quantitative thresholds (e.g., elastic modulus between 200-250 GPa, compressive strength > 40 MPa, thermal conductivity' > 50 W / m K, or embodied carbon < 10 kg CO2-eq / kg) or qualitative requirements (e.g., material must be non-toxic, chemically resistant to acids, or visually defect-free). These constraints may be directly input into the model or inferred from project context and used to bound the model’s domain or output space. For example, a material optimization model may be constrained to only converge to material solutions satisfying a modulus range or cost ceiling, thereby ensuring that final outputs respect performance or regulatory requirements.

[0205] In some embodiments, the systems, methods, and / or models of the present disclosure may be applied, in whole or in part, to any materials and / or material classes. Accordingly, in some embodiments, the systems and methods herein may be configured to operate with input, intermediate, and / or output data associated with any material class for which a model can be trained or used to infer one or more properties, selections, optimizations, or generations. Additionally, or alternatively, the methods herein may be used for explainable material discovery' use cases wherein discovered materials may include attribution datasets explaining material behavior

[0206] Additionally, or alternatively, in some embodiments, the systems and / or models herein may be applied to crystalline materials, including semiconductors, optoelectronic crystals, superconductors, ionic conductors, and piezoelectric compounds. Inputs for such materials may include lattice parameters, atomic composition, doping concentrations, symmetry’ groups, or band structure descriptors. Outputs may include bandgap energy, carrier mobility, refractive index, or electrical conductivity. Attribution datasets may indicate, for example, that a substitutional dopant (e.g., boron) decreased bandgap by 0.2 eV, or that crystal orientation influenced electron mobility'. Such attribution may be indicative of a causal or influential relationship between structural input parameters and predicted electronic performance.

[0207] Additionally, or alternatively, in some embodiments, the invention may be applied to metallic materials and metal alloys, such as steels, titanium alloys, aluminum alloys, superalloys, and high-entropy alloys. Input features may include chemical composition, grain size, thermomechanical history, phase fractions, or heat treatment parameters. Outputs may include tensile strength, yield stress, creep resistance, fatigue life, or corrosion resistance.Attribution datasets may include, for example, influence of nickel content on corrosion resistance, or combined effect of martensitic fraction and cooling rate on tensile strength. Attribution between input features and performance outputs may also be used to inform alloy design constraints or training-data-based influences (e.g., “alloys with prior thermal cycling histories contributed most to creep resistance predictions”).

[0208] Additionally, or alternatively, in some embodiments, the invention may be applied to polymeric materials, including thermoplastics, thermosets, elastomers, and polymer composites. Input data may include monomer ratios, degree of polymerization, crosslink density, plasticizer content, and molecular weight distribution. Outputs may include modulus, glass transition temperature, toughness, biodegradability, or permeability. Attribution datasets may show, for example, that increased crosslinker concentration raised modulus but decreased elongation, or that the presence of branching decreased optical clarity. Inferred attribution vectors may highlight the influence of processing temperature on internal phase segregation.

[0209] Additionally, or alternatively, in some embodiments, the invention may be applied to ceramic materials, including oxides, nitrides, carbides, perovskites, and electroceramics. Input features may include powder properties, sintering profile, dopant content, and grain boundary descriptors. Outputs may include dielectric constant, hardness, ionic conductivity, and fracture toughness. Attribution datasets may, for instance, indicate the influence of sintering temperature on density or the influence of dopant type on phase transformation pathway. Attribution may also be inferred between latent variables and observed macroscopic behavior.

[0210] Additionally, or alternatively, in some embodiments, the invention may be applied to glasses and amorphous materials, such as silicate glasses, polymeric glasses, metallic glasses, or sol-gels. Inputs may include precursor types, melt quenching rate, modifier ion concentration, or process temperature. Outputs may include glass transition temperature, chemical durability', thermal expansion coefficient, and optical clarity. Attribution datasets may indicate, for example, that rapid cooling suppressed phase separation, or that sodium content reduced glass transition temperature.

[0211] Additionally, or alternatively, in some embodiments, the invention may be applied to composite materials, such as fiber-reinforced polymers, metal matrix composites, and layered structures. Inputs may include fiber orientation, matrix properties, fiber-matrix interface strength, layup schedule, and void content. Outputs may include impact resistance, thermal conductivity’, interfacial shear strength, or fatigue crack growth rate. Attribution datasets may be indicative of an influence of ply angle on interlaminar failure, or jointattributions between porosity' and fiber volume fraction on strength. Attribution graphs may represent causal links between constituent-level variables and composite-level behaviors.

[0212] Additionally, or alternatively, in some embodiments, the invention may be applied to energy materials, including batten electrode materials, solid electrolytes, supercapacitor films, and fuel cell membranes. Inputs may include material composition, porosity, particle size, cycle history, binder chemistry, or interfacial resistance. Outputs may include capacity retention, Coulombic efficiency, voltage plateau behavior, and thermal stability. Attribution datasets may show, for example, that interfacial degradation caused voltage fade. Attribution to training data may identify specific prior electrode recipes that most strongly influenced model predictions for degradation risk.

[0213] Additionally, or alternatively, in some embodiments, the invention may be applied to biomaterials, including tissue scaffolds, biodegradable implants, hydrogel systems, or drugdelivery materials. Input variables may include crosslink density, swelling ratio, degradable ester group content, or protein composition. Outputs may include tensile modulus, biodegradation time, cell adhesion, or drug release kinetics. Attribution datasets may indicate, for example, that ester concentration contributed to faster degradation, or that pore size influenced infiltration depth. Attribution discrepancy modules may identify cases where expected biological response differs from prediction, prompting inferred attribution generation from contextual features (e.g., in vivo pH, ionic environment).

[0214] Additionally, or alternatively, in some embodiments, the invention may be applied to functional materials, including thermoelectrics, piezoelectrics, and stimuli-responsive polymers or alloys. Inputs may include phase boundaries, dopant gradients, domain orientation, and actuation stimuli. Outputs may include Seebeck coefficient, transformation temperature, strain under applied field, or hysteresis width. Attribution datasets may indicate that a specific grain boundary configuration affected actuation response or that a stress-temperature profile jointly influenced shape-memory recovery. These may be represented in time-resolved attribution heatmaps, vectorized attribution tables, or causal interaction rules.

[0215] Additionally, or alternatively, in some embodiments, the invention may be applied to electronic and photonic materials, such as LEDs, solar cells, transparent conductors, quantum dots, and laser crystals. Inputs may include layer thicknesses, trap density, energy level alignment, surface roughness, or photonic structure parameters. Outputs may include emission efficiency, reflectivity, absorption spectra, device lifetime, and power conversion efficiency. Attribution datasets may show, for example, that interfacial roughness reduced PCEby 2.1%, or that trap state density had a dominant influence on photoluminescence. Attribution format may include spectrally aligned saliency maps or feature-level attribution vectors.

[0216] Additionally, or alternatively, in some embodiments, the systems and methods described herein may apply material property, selection, optimization and / or generation models to any material herein.

[0217] For example, in some embodiments, a prediction model may receive as input a metal alloy composition and output a predicted fatigue strength; receive a polymer molecular structure and output a predicted permeability; or receive a photonic crystal geometry and predict a reflectivity spectrum. These models may be used for estimating mechanical, chemical, thermal, electrical, optical, biological, or functional properties, and may support attribution datasets that explain how particular input features (e.g., filler type, porosity, grain size) influenced the prediction.

[0218] Additionally, or alternatively, in some embodiments, a selection model may receive a target modulus and thermal conductivity range and return polymer blend candidates; or receive exposure class constraints and recommend corrosion-resistant alloys.

[0219] Additionally, or alternatively, in some embodiments, an optimization model may optimize a polymer formulation to reduce processing temperature while maintaining mechanical performance; a battery' electrode composition may be optimized for cycle life and conductivity; or a glass composition may be optimized for lower thermal expansion.

[0220] Additionally, or alternatively, in some embodiments, the systems and methods described herein may include material generation models, which may be configured to generate entirely new material compositions, structures, or design candidates that satisfy one or more input constraints or objectives. These may include generative models based on variational autoencoders (VAEs), generative adversarial networks (GANs), diffusion models, reinforcement learning agents, or rule-based generation systems. Generated outputs may include new crystalline structures, polymer backbones, alloy compositions, composite layups, or porous architectures. In such embodiments, attribution datasets may provide insight into how input constraints, learned priors, or latent representations influenced the generation of a particular material candidate.

[0221] Additionally, or alternatively, in some embodiments, the systems, methods, and / or models described herein may be configured to automatically or semi-automatically and / or iteratively generate novel material compositions, structures, formulations, or processing pathways that may satisfy one or more defined objectives. Such objectives may include mechanical, chemical, thermal, electrical, optical, magnetic, biological, environmental, ormulti-functional performance targets. In some embodiments, the system may generate new candidates within unexplored or underexplored regions of the material design space, or discover previously unobserved combinations of constituents or structural motifs. Generative models herein may be configured for example to receive as input one or more of: user-defined target properties, desired application conditions, digital representations of existing materials, domain-specific constraints, or optimization criteria. Based on such inputs, the system may output candidate material representations, such as polymer chains, alloy compositions, atomic or molecular graphs, crystalline lattices, morphologies, porous structures, or digital encodings of manufacturing routes.

[0222] Additionally, or alternatively, in some embodiments, the systems and methods herein may support explainable material discovery’, wherein the behavior, structure, composition, processability, or predicted performance of a generated material candidate is made interpretable through the generation of one or more attribution datasets. In such embodiments, the attribution dataset may be indicative of an influence or causal relationship between input features and the generated novel material, between prior training data and generation outcomes, between optimization terms and resulting trade-offs, or between internal model components and predicted property values. For instance, the attribution dataset may indicate that a generated semiconducting material’s bandgap was primarily influenced by a latent representation associated with p-orbital overlap, that a particular alloy composition was shaped by multi -objective optimization between strength and corrosion resistance, or that the inclusion of a sulfonic acid functional group in a generated polymer was causally linked to an input requirement for high proton conductivity.

[0223] Additionally, or alternatively, in some embodiments, the system may include or be functionally coupled with one or more material property prediction models configured to simulate the expected behavior and performance of a discovered or generated material to ensure it meets target properties, performance and / or behaviors.

[0224] In some embodiments, the prediction model may be integrated into an iterative discovery' loop wherein candidate materials are generated, simulated, evaluated, and optionally modified or discarded based on their predicted performance and compliance with user-defined targets. Additionally, or alternatively, in such embodiments, attribution datasets may be generated in connection with the operation of the prediction model, providing causal or influence-based explanations for why a given material is predicted to perform in a certain way. For example, a prediction model may simulate a novel composite’s resistance to fatigue and generate an attribution dataset showing that the predicted high performance is primarily due tofiber orientation, matrix stiffness, and interfacial bonding properties. These attribution datasets may be structured as feature importance vectors, intermediate activation maps, symbolic influence trees, or natural language explanations, and may be used to trace which aspects of the material representation are causally responsible for predicted outcomes.

[0225] In some embodiments, the attribution datasets generated by the prediction model may be used to confirm that the generated material behaves as expected for valid and explainable reasons, thereby supporting user trust and design confidence. For example, if a generative model proposes a new alloy composition predicted to resist high-temperature oxidation, the attribution dataset produced by the prediction model may show that this performance is causally linked to the chromium and aluminum content, supporting known passivation mechanisms. Such causal understanding may be critical in safety-critical, regulated, or cost-sensitive applications, and may be used to produce validation reports, compliance documentation, or interpretability dashboards.

[0226] Additionally, or alternatively, in some embodiments, attribution datasets may be generated not only for the predicted outputs but also for internal representations of the prediction model (e.g.. latent vectors or embeddings), showing how learned internal states map onto physical concepts. For example, a latent feature in the prediction model may be attributed to stiffness variation and linked to nanoscale structural motifs in a polymer blend. In this way, explainability methods may uncover structure-property relationships, enable hypothesis generation, and improve generalization across different material classes.

[0227] In any such embodiments, the systems and methods of the present disclosure may support explainable material discovery by combining generative and predictive capabilities with attribution-based interpretability tools. The overall system may therefore not only propose novel materials but also provide traceable, explainable, and auditable pathways from design objectives to material structure to expected performance, including causal rationales at each step.

[0228] The models herein may include computer-implemented methods for explainable material models, configured to ingest, by a model, a first dataset including one or more first data entries associated with a material; generate, using the model, a second dataset comprising one or more second data entries associated with one or more properties of the material; and additionally generate an attribution dataset comprising one or more attribution data entries, wherein the attribution dataset is indicative of an influence or causal relationship associated with the model. Such steps may be applicable to any of the model types and / or classes described herein.

[0229] Additionally, or alternatively, in some embodiments, the models herein may execute additional and / or alternative steps beyond the ones listed herein. Such steps, unless stated otherwise, may generally be executed in any order as well as in relation to the steps mentioned above (e.g., before the second step including generating, using the model, a second dataset comprising one or more second data entries). Additionally or alternatively, example steps may include outputting the second dataset; outputting the attribution dataset; altering a feature of the model based on one or more of first data, second data and / or attribution data; retraining the model in whole or in part based on attribution datasets; determining an anomaly and / or discrepancy in whole or in part based on the generated second dataset and / or a baseline dataset; additionally or alternatively, wherein the baseline dataset may include physics- informed expectation data (e.g., heat diffuses from hot to cold, therefore heat diffusion in material X should behave in way Y) generated by one or more physics based models, and / or the baseline dataset may include measurement data such as sensor data associated with the material, or test crush data extracted from a testing record; additionally or alternatively, wherein the models include two or more sub-modules; additionally or alternatively, in some embodiments, the model may be configured to generate discrepancy data comprising one or more data entries indicative of a deviation, delta, or difference between the first dataset, second dataset, and / or third dataset, and a baseline or reference dataset; additionally or alternatively, the discrepancy data may include error metrics (e.g., RMSE between measured and predicted strength). Additionally, or alternatively, the methods herein may also include generating attribution datasets associated with such discrepancies, indicating which input or internal model component most influenced the deviation.

[0230] Additionally, or alternatively, in some embodiments, the methods herein may include steps for updating or altering a portion of the model architecture, model weights, or internal module parameters. Additionally, or alternatively, the updating may be based in whole or in part on an attribution dataset, a discrepancy data, and / or a combination thereof. For example, if attribution data reveals that a non-physical variable disproportionately influenced the output, the model may suppress that attribution via regularization or retraining. Alternatively, a submodule generating low-confidence outputs may be replaced, fine-tuned, or gated off entirely.

[0231] Additionally, or alternatively, the model may be configured to generate confidence scores or uncertainty metrics associated with the second or third data, such as probabilistic intervals, variance estimates, or confidence thresholds.

[0232] Additionally, or alternatively, in some embodiments, the model may execute one or more reasoning steps based on the attribution dataset, including generating natural language explanations, symbolic expressions, or visual overlays to communicate influential variables or causal factors to end-users. These explanations may be included in user-facing reports, dashboards, or automated notifications.

[0233] Additionally, or alternatively, the methods herein may include steps to generate optimized data entries based on the outputs of one or more prediction models. For example, using attribution-informed optimization loops, the model may adjust one or more input variables (e.g., composition, curing condition) to generate fourth data indicative of an improved material formulation or process setting that better satisfies a defined performance objective or constraint.

[0234] Additionally, or alternatively, in some embodiments, the model may identify temporal or spatial segments within the first dataset (e.g., time windows, sensor zones), and generate attribution scores or impact measures per segment.

[0235] Without loss of generality any methods described in the current disclosure may be executed using a variety of model types, including but not limited to lookup tables, which may include ingesting material identifiers, searching for said material identifiers in a database, and generating associated material property and associated attribution dataset. For example, this may include ingesting mix name “Mix A’", searching for that mix in a database, finding and / or inferring a match, extracting and / or generating associated time to strength milestone data from database, and extracting and / or generating an associated attribution dataset from the database. In some embodiments, a perfect match may not be found, in which case a similarity criterion may be used to select one or a plurality of materials (e.g. set of concrete mixes) which may be similar enough to the input material. Additionally, or alternatively, the models herein may include physical simulation models. Neural Networks, functional mappings, PINNs (Physics- infused neural networks) and the like.

[0236] In some embodiments, the input and / or output data may include process-related parameters, such as the mixing duration, temperature of mixing water, curing temperature and humidity, compaction method, or transportation and casting protocol. For example, a record may specify that the concrete mix was prepared with 2 minutes of dry mixing, followed by 4 minutes of wet mixing at 25°C, cast into molds, and cured for 3 days at 20°C and 95% relative humidity. These parameters are often temporally or sequentially ordered and may be encoded as time series or structured event sequences.

[0237] As would be clear to one skilled in the art, any of the examples listed herein are illustrative and any model herein may employ any input data and / or output data and / or attribution datasets mentioned herein as well as any data associated and / or indicative of said input, output and / or attribution datasets in any combination, including combinations of pluralities of input and / or output data and / or attribution datasets.Example General Modeling Paradigm

[0238] In some embodiments, a model, f, may be an arbitrary function of arbitrary complexity that may receive continuous and / or discrete quantities in a generally mixed ensemble. In such embodiments, the model f may be generally evaluated using one or more of three categories of input: I) data, [2)}, 2) encodings. {$}. and 3) weights, my. When f is evaluated for a given set of data, encodings, and / or weights, the output of the model f may be a set of quantities, {0}K= { ok| k e {1,2,such that {O]K= f({2)}, {cb}, wf), where the vector okdenotes the / z-th output value discretized over some physical space, time, physical spacetime, and / or some other conceptual space (e.g., over the values of some other know n or hypothesized quantities). For example, a model f may have a form of a model 300 as shown in Figure 3, where the data, {2)}, may include percentages of constituent materials (e.g., water, sand, cement, rebar, and / or the like) of the material being modeled by f. Further, as shown in Figure 3, the model may ingest this data and analyze the data in a plurality' of interconnected steps (e.g., in series, in parallel, or in a combination of both), layers, and / or in modules (e.g., a first module, a second module, and / or the like) with the associated weights and encodings. Finally, the model may then generate and / or output the set of quantities {(2}K(e.g., a second dataset, a second output, and / or the like). For example, the set of quantities {O}Kmay include a plurality of predicted properties such as slump and strength values at various time thresholds as shown in Figure 3.

[0239] In general, data may be represented as a set of information, {2)}N= { dj | i e {1,2, ... , N] }, where d may denote a vector of values that may have been measured and / or may have been otherwise hypothesized. Further, the values may be representative of attributes of some system. In some embodiments, the z-th value may represent the z-th distinct measurable or hypothesized quantity in a set, such that 2)^ denotes the N distinct quantities in the set. Additionally, or alternatively, the vector d, may be a discretized sampling of the z-th quantity over an arbitrary conceptual and / or physical space.

[0240] An encoding may be the output of some function, 4>, that may map a set of data, {®}N- into another representation of arbitrary dimensionalities. The valuemay therefore be another set {<5 }M= { Vj | j G [1,2, ... , M] ], where the vector Vj may represent a j- th distinct representation in some arbitrary' conceptual and / or physical space. Additionally, or alternatively, the vectors, Vj, may denote any types of encodings, with any dimensionality and / or meaning. A non-exhaustive list of encoding types may include sums, means, and / or median values; convolutional and filter transformations; joint and / or marginal probability distributions; matrix-transformed vector-space mappings; hash-type encodings and tokenization; ordinal counts of sets and subsets of data; and upper and lower bounds (e.g., characterizing the extremes of data domains).

[0241] Mixed encoding types may, in some embodiments, be output by the mapping c[> such that {T’JM may contain vectors of different dimensionality and / or meanings. Thus, the set of all encoded values may be given by the function evaluation {<h}M=

[0242] In some embodiments, weights may be a vector of values, wf, that may define transformations within the model, f, that may map the encodings, {<b]M, to the outputs, {O]K.

[0243] In general, an end-to-end model may be comprised of an ensemble of R constituent models, fF]R= { frI r G 1,2, ... , R], such that all models may be connected by a series of dependent inputs and outputs. Additionally, or alternatively, the connections may be of mixed serial and parallel nature in the chain of logic of the end-to-end model. Additionally, or alternatively, the set of K outputs, {0}K, of the r-th model may be data, encodings, and / or weights. Dependencies between models may therefore be constructed by chaining the output of one function to the associated inputs of other functions, whereby the output of a constituent model, fr, may be the calculation of data, encodings, and / or weights.

[0244] The process of constructing an end-to-end model by chaining together subsets of outputs and inputs of an ensemble, {^{R, of models may be referred to as modularity, where the r-th model. fr, may be equivalently referred to as the r-th module. In such embodiments, when building an end-to-end model to represent some physical system and / or some other known conceptual system, known causal dependencies may be incorporated into the chain of logic by enforcing boundaries within the end-to-end model architecture, such that those boundaries may be delineated by the modules that are defined. Further, a module may be defined by the choice of data, encodings, and / or outputs that the module may model.

[0245] As used herein, a “module” may refer to any model, component, unit, subsystem, construct, and / or the like, whether physical, logical, virtual, algorithmic, and / or the like, that performs one or more functions individually, in parallel, and / or in series with other modules, models, components, systems, layers, and / or the like. A module may include, but is not limited to (i) an entire artificial intelligence (Al) model, (ii) a sub-model or subcomponent thereof, (iii) a computational unit within a model (e.g., an encoding function, a neural network layer, attention mechanism, transformer block, activation function, and / or the like), (iv) a preprocessing or post-processing component (e.g., a model configured to generate an attribution dataset associated with explainability and / or interpretability' of an output of an end-to-end model), (v) a constituent model of a chained set of models invoked in a series, parallel, and / or series-parallel sequence to produce a final output, (vi) a software-implemented logic block that performs an algorithmic operation or transformation on data, and / or the like.

[0246] In some embodiments, a module may be stateless or stateful, may operate independently or dependently, and / or may be implemented using software, firmware, hardware, or any combination thereof. Additionally, a module may also reside on a single computing node or be distributed across multiple computing resources. Further, a module may be trained or untrained, deterministic or stochastic, and / or may be configured to operate within supervised, unsupervised, self-supervised, reinforcement learning, and / or other machine learning paradigms.In some embodiments, a module may be implemented as an agentic Al model, meaning it may be configured not only to process inputs and generate outputs, but also to autonomously initiate actions directed toward other modules, models, systems, and / or external entities. Such a module may include functionality for monitoring, controlling, invoking, modifying, or interacting with one or more other components in a larger system architecture.

[0247] In some embodiments, an end-to-end model may be configured as a prediction model associated with a material. As shown in Figure 4, a prediction model 400 may receive an ensemble of data 402 (e.g., a first dataset) associated with a material that may include data entries d^ through d5. For example, the ensemble of data 402 may include data of an element type (e.g., slab), a recipe (e.g., materials, sources, and quantities), a pour start time (e.g., a date with a timestamp), a location, and a strength (e.g., 25 megapascals) associated with the material. While not pictured, the ensemble of data 402 may include fewer data entries or more data entries as required by the prediction model 400. The ensemble of data 402 may be subject to an encoding function 404 prior to analysis by the prediction model 400. Continuing theabove example, the encoding function 404 may be a weather model encoder configured to generate an encoding, 4>W(D). This encoding produced by the encoding function 404 may be fed (e.g., as a first input) to a first module 406 (e.g., a weather module) configured to map predicted values to a predicted encoding such that the first module 406 produces an output, 4>c, (e.g., a first output). For instance, the first module 406 may map predicted weather values (e.g., ambient weather temperature, humidity, windspeed, and / or the like) to a predicted concrete encoding to generate an output of a predicted encoding of concrete temperature. The output of the first module may then be fed (e.g., as a second input) to a second module 408 (e.g., a concrete module) configured to use the output of the first module and a set of weights, c, to generate a prediction (e.g.. a second output, a second dataset, and / or the like) associated with the material. For example, the second module 408 may be configured to predict a curing time of concrete for a specific strength. Although Figure 4 shows example elements of the prediction model 400, in some embodiments, the prediction model 400 may include additional or fewer modules, encodings, and / or data entries than those depicted in Figure 4.

[0248] In some embodiments, an end-to-end model may be configured as a generation model configured to output a composition (e.g., a recipe) for a preferred set of characteristics of a material. As shown in Figure 6, a generation model 600 may receive an ensemble of data 602 (e.g., a first dataset) associated with a material that may include data entries d^ through d5. For example, the ensemble of data 602 may be input specification data that may include data of a strength, a pour start time, a location, an element geometry, a cost (e.g., maximum price per meter squared), and CO2 (e.g., maximum amount of CO2 per meter squared) associated with the material and / or preferred characteristics of the material. While not pictured, the ensemble of data 602 may include fewer data entries or more data entries as required by the generation model 600. The ensemble of data 602 may be subject to an encoding function 604 prior to analysis by a subsequent module of the generation model 600. Continuing the above example, the encoding function 604 may be a specification data encoder configured to generate an encoding, (^SPECC^)- The output of the encoding function 604 may be passed to two separate modules (e.g., a first and a second module) modules that may work in parallel to produce two outputs. For instance, a first module 606 may function as a weather module configured to generate a first output (e.g., a predicted heat encoding) and / or a second module 608 may function as a geometry module configured to generate a second output (e.g., a predicted thermal mass encoding). The output of the encoding function 604, the first module 606, and / or the second module 608 may be input into a third module 610 configured to generateand / or output a composition of the material that best fits the preferred set of characteristics (e.g., an optimal recipe for the material).

[0249] Although Figure 6 shows example elements of the generation model 600, in some embodiments, the generation model 600 may include additional or fewer modules, encodings, and / or data entries than those depicted in Figure 6. Furthermore, although each of the modules and / or functions associated with modules are shown with example inputs and / or outputs in Figure 6. in some embodiments, the modules and / or functions of the generation model may include additional inputs and / or outputs.Explainability and Interpretability

[0250] As used herein, explainability may refer to an influence or causal relationships between two or more components of a system. For example, explainability may refer to understanding a model’s learned representation of a system associated with the model via the model’s weights. The weights may encode patterns in the training data and, if these weights carry human-interpretable meaning, they may reveal domain-level causal relationships. For example, if a weight is known to represent thermal conductance, its learned value reflects how the model has understood the thermal properties of the system.

[0251] As used herein, interpretability may refer to understanding causal relationships between specific inputs and outputs during individual model evaluations. Stated differently, interpretability may focus on input-output pairs within specific scenarios and / or simulations in contrast to explainability that generalize over the whole domain. Embodiments of the present disclosure may use both explainability and interpretability to generate automated insights regarding the underlying system. Said insights may be used to guide real-world action, optimizing for a plurality of outcomes (e.g., reduced cost, programmed time, embodied CO2, and / or the like). Due to these insights being backed by an influence or causal reasoning, users may interrogate the basis for each recommendation and / or may easily identity incorrect assumptions. Additionally, or alternatively, such insights may help correct and / or mitigate system drift when predictions indicate deviations from expected outcomes.

[0252] For example, explainability and / or interpretability of a model may be generated, in some embodiments, using steps of flowchart 800 of Figure 8. Figure 8 illustrates a flowchart 800 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 8 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as descnbed above. Inthis regard, performance of the operations may invoke one or more of processor 202, memory 206, communication interface 204. and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0253] As shown in block 802, the flowchart 800 may include the step of ingesting, by a model, a first dataset including one or more first data entries associated with a material. In some embodiments, the one or more first data entries may include one or more material identifiers, a plurality of material composition data, a plurality of material properties, preferred characteristics of the material, and / or material properties in a plurality of contextual conditions associated with the material. Further, the first dataset may be generated by one or more sensor devices, data aggregated from one or more databases, and / or the like. Additionally, or alternatively, the one or more first data entries of the first dataset, upon ingestion by the model, may undergo encoding as described herein prior to further analysis by the model. The model may be configured as a prediction model, an optimization model, a generative model, a selection model, and / or any other type of model contemplated by the present disclosure.

[0254] As shown in block 804. the flowchart 800 may include the step of generating, using the model, a second dataset including one or more second data entries associated with one or more properties of the material. In some embodiments, the one or more second data entries may include one or more material identifiers, a plurality of material composition data, a plurality of material properties, a recipe for a material with preferred characteristics, and / or material properties in a plurality of contextual conditions associated with the material. Further, the second dataset may be generated via simulations performed by the model using the one or more first data entries of the first dataset and / or data retrieved using the one or more first data entries of the first dataset.

[0255] As shown in block 806, the flowchart 800 may include the step of generating an attribution dataset including one or more attribution data entries, where the attribution dataset is indicative of an influence or causal relationship associated with the model. In such embodiments, the one or more attribution data entries of the attribution dataset may be generated via any of the explainability and / or interpretability methods as described herein and as shown in subsequent figures. Additionally, or alternatively, the attribution dataset may be indicative of an influence or causal relationship betw een the first dataset and the second dataset. As such, the attribution dataset may inform any user and / or system as to why the model generated a set of data (e.g., the one or more second data entries). Further, knowledge of such influence or causal relationships associated with the model may enhance downstream processing of the first and / or second dataset and / or future analysis of other datasets.

[0256] The flowchart 800 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 8 shows example blocks of the flowchart 800, in some embodiments, the flowchart 800 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 8. Additionally, or alternatively, two or more of the blocks of the flowchart 800 may be performed in parallel.

[0257] Figure 9 illustrates a flowchart 900 for an example method for explainable materialbased determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 9 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2). as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0258] As shown in block 902, the flowchart 900 may include the step of outputting a second dataset. In some embodiments, the second dataset may be output to a memory device for short-term and / or long-term storage. Further, the memory device may include one or more databases including data on the material and / or additional materials. Additionally, or alternatively, the second dataset may be received as input into a processing device, and / or an Al model for use in further processing, simulating, data manipulation, and / or the like. In some embodiments, the step of the block 902 of the flowchart 900 may be performed following the step and / or in conjunction with the step of the block 804 of the flowchart 800 as shown and described herein with respect to Figure 8.

[0259] As shown in block 904, the flowchart 900 may include the step of outputting an attribution dataset. In some embodiments, the attribution dataset may be output to a memory device for short-term and / or long-term storage. Further, the memory device may include one or more databases including data on the material, additional materials, and / or additional explainable and / or interpretable insights. Additionally, or alternatively, the attribution dataset may be received as input into a processing device, a model, and / or a module for use in further processing, simulating, data manipulation, and / or the like. For instance, the attribution dataset may be transmitted to an explainability module to develop further insights into any influence or causal relationship associated with the material and / or the model. Additionally, or alternatively, the attribution dataset may be ingested by an LLM for analysis and further processing. In some embodiments, the step of the block 904 of the flowchart 900 may beperformed following the step and / or in conjunction with the step of the block 806 of the flowchart 800 as shown and described herein with respect to Figure 8.

[0260] The flowchart 900 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 9 shows example blocks of the flowchart 900, in some embodiments, the flowchart 900 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 9. Additionally, or alternatively, two or more of the blocks of the flowchart 900 may be performed in parallel.

[0261] In some embodiments, explainability may be enabled via causal modularity. By way of example, consider a dataset of three measurable variables, £0} = {dp d2, d3, In such embodiments, d3may be modeled using inputs {d, , d2}, yielding {0}t= ot= d3= f(< di, d2), wf), where c[> encodes the inputsare the model weights. This end-to-end model, / , may be monolithic, where all inputs may be independent. Additionally, or alternatively, if there is domain knowledge that d2is causally dependent on dt, the model may be restructured into modular components, such that d2 = j (cty3(c 1), aj^l) and £>i = d3 =

[0262] This modular form encodes known causal relationships into the architecture itself, enabling more explainable behavior. Some examples of explainable behavior enabled by the modular form include, but are not limited to, the weights u>fiexplaining the transformation from dj to d2, the w eights Wf2explaining how d2contributes to d3, and each module being independently interrogable, allowing clearer attribution of causal influence and traceability within the system.

[0263] As an example of modularity, Figure 10 illustrates a flowchart 1000 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 10 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory7206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0264] As shown in block 1002, the flowchart 1000 may include the step of ingesting, by a model including at least two modules, a first dataset including one or more first data entries associated with a material. In some embodiments, the one or more first data entries may includeone or more material identifiers, a plurality of material composition data, a plurality of material properties, preferred characteristics of the material, and / or material properties in a plurality of contextual conditions associated with the material. Further, the first dataset may be generated by one or more sensor devices, data aggregated from one or more databases, and / or the like. Additionally, or alternatively, the one or more first data entries of the first dataset, upon ingestion by the model, may undergo encoding as described herein prior to further analysis by the model. The model may be configured as a prediction model, an optimization model, a generative model, and / or any other type of model contemplated by the present disclosure.

[0265] In some embodiments, the at least two modules may each be configured to perform a type of analysis on the first dataset or a subset of the first dataset. For example, one module may be configured as a physico-chemical module as described herein, while another module may be configured as an empirical module as described herein. Alternatively, both modules may be empirical modules or both modules may be physico-chemical modules. As will be understood by one of ordinary skill in the art in view of the present disclosure, the number of modules and type of modules included by the model may vary dependent on the type and / or purpose of the model. Additionally, the number and type of modules of the model may vary due to the number of explainability and / or interpretability techniques applied to the model as described herein.

[0266] As shown in block 1004, the flowchart 1000 may include the step of generating, via ingestion of a first input including a first subset of the one or more first data entries in a first module of the at least two modules, a first output associated with a first property of the material. In some embodiments, the first subset of the one or more first data entries may include data required by the first module to perform its associated analysis. The first subset may include all of the one or more first data entries, half of the first data entries, a quarter of the first data entries, and / or any other percentage of the one or more first data entries. Further, the first module may act as an encoding function, where, after ingestion of the first subset, the first module applies a specific encoding to the first subset as needed for downstream processing by the model. Alternatively, the first subset may have been subject to an encoding module prior to ingestion by the first module, and, in some embodiments, the first module may be configured to analyze the first subset with an associated set of weights (e.g., similar to the steps of the flowchart 1200 as shown and described herein with respect to Figure 12).

[0267] In some embodiments, after the first module performs its designated function on the first subset, the first module may generate the first output that may be indicative of any property of the material as described herein. In series configuration embodiments, the firstoutput may then be fed to the second module as the input and / or as a partial input to the second module. In parallel configuration embodiments, the first output may be fed to another module, system, user, and / or the like as a stand-alone output or in combination with an output of a module of the model acting in parallel (e.g., the second module). In some embodiments, the first output may be fed to an explainability' module and / or an interpretability' module for subsequent insight generation on the model and / or the material.

[0268] As shown in block 1006, the flowchart 1000 may include the step of generating, via ingestion of a second input including a second subset of the one or more first data entries in a second module of the at least two modules, a second output associated with a second property7of the material, where a modularity of the model is associated with an influence or causal relationship. In some embodiments, the second subset of the one or more first data entries may include data required by the second module to perform its associated analysis. The second subset may7include all of the one or more first data entries, half of the first data entries, a quarter of the first data entries, and / or any other percentage of the one or more first data entries. Further, the second module may act as an encoding function, where, after ingestion of the second subset, the second module applies a specific encoding to the second subset as needed for downstream processing by the model. Alternatively, the second subset may have been subject to an encoding module prior to ingestion by the second module (e.g., in a series configuration, the first module or another module encoded the second subset of data), and, in some embodiments, the second module may be configured to analyze the second subset with an associated set of weights (e.g., act as an empirical module, a physico-chemical module, and / or the like).

[0269] In some embodiments, after the second module performs its designated function on the first subset, the second module may generate the second output that may be indicative of any property of the material as described herein. In series configuration embodiments, the second output may then be fed to another module of the at least two modules as the input and / or as a partial input to the other modules. In parallel configuration embodiments, the second output may be fed to another module, system, user, and / or the like as a stand-alone output or in combination with an output of a module of the model acting in parallel (e.g., the first module). In some embodiments, the second output may be fed to an explainability module and / or an interpretability' module for subsequent insight generation on the model and / or the material. Additionally, or alternatively, the modularity of the model (e.g., having at least two modules) may serve to inform of potential influence or causal relationships as described above. For example, it may inform of an influence or causal relationship via causal chaining of the modules. The ordenng of the modules may be reflective of causal relationships and influence(e.g., weather influences the temperature of concrete, the temperature of concrete influences strength gain, so the modularity of the model informs influence or causal relationships between these elements). Further, the influence or causal relationship may, in some embodiments, be indicative of a relationship between the first dataset and the first output, the first dataset and the second output, the first input and the second output, the first output and the second output, and / or any other input-output pair in the end-to-end model.

[0270] The flowchart 1000 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 10 shows example blocks of the flowchart 1000, in some embodiments, the flowchart 1000 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 10. Additionally, or alternatively, two or more of the blocks of the flowchart 1000 may be performed in parallel.

[0271] Figure 11 illustrates a flowchart 1100 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 11 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory7206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0272] As shown in block 1102, the flowchart 1 100 may include the step of generating an attribution dataset including one or more attribution data entries associated with an influence or causal relationship between a first property7and a second property7. In such embodiments, the one or more attribution data entries of the attribution dataset may be generated via any of the explainability and / or interpretability methods as described herein and as shown in subsequent figures. As such, the attribution dataset may inform any user and / or system as to why the model generated a set of data (e.g., the one or more second data entries) and as to how the second output may be influenced by the first output. Further, knowledge of such influence or causal relationships associated with the model may enhance downstream processing of any of the inputs and outputs of the end-to-end model and / or future analysis of other datasets. In some embodiments, the step of the block 1102 of the flowchart 1100 may be performed following and / or in conjunction the step of the block 1006 of the flowchart 1000 as shown and described herein with respect to Figure 10.

[0273] The flowchart 1100 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 11 shows example blocks of the flowchart 1100, in some embodiments, the flowchart 1 100 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 11. Additionally, or alternatively, two or more of the blocks of the flowchart 1100 may be performed in parallel.

[0274] Figure 12 illustrates a flowchart 1200 for an example method for explainable material -based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 12 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0275] As shown in block 1202, the flowchart 1200 may include the step of ingesting a first weight set including one or more first weight entries associated with a first dataset. In some embodiments, the first weight set may correspond to a collection of parameter values, scores, coefficients, and / or other weight values that may be linked to or derived from the first dataset and / or may be linked to or derived from a module (e.g., a first module). Further, the one or more first weight entries may represent the relative importance, reliability, contribution, confidence level, and / or the like associated with one or more first data entries in the first dataset. In such embodiments, the ingestion of the first weight set may be performed by a module and / or a model and may involve reading from a local or remote data store, database, and / or, in some embodiments, be stored in the module itself.

[0276] In some embodiments, the step of the block 1202 of the flowchart 1200 may be performed prior to the step of the block 1004 of the flowchart 1000 as shown and described herein with respect to Figure 10. Additionally, or alternatively, the step of the block 1202 of the flowchart 1200 may be performed prior to the step of the block 804 of the flowchart 800 as shown and described herein with respect to Figure 8.

[0277] As shown in block 1204, the flowchart 1200 may include the step of encoding the first dataset to generate a first transformed dataset. In some embodiments, the encoding process may involve applying one or more transformations, mappings, and / or any other encoding techniques as described herein to the one or more first data entries of the first dataset into a different representational format. In such embodiments, the encoding may be performed usinga module of a model configured to perform the required algorithm required to encode the one or more first data entries of the first dataset as needed. Further, the first transformed dataset may retain essential data from the first dataset while being adapted for subsequent processing.

[0278] As shown in block 1206, the flow chart 1200 may include the step of generating, using the first w eight set and the first transformed dataset, a first output. In such embodiments, a module (e.g., the first module) of a model may be configured to use the first weight set and the first transformed dataset to produce the first output. In some embodiments, the steps of the flowchart 1200 may be performed for one or more additional modules (e.g., a second module) of the model as required by the analysis being conducted.

[0279] The flowchart 1200 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 12 shows example blocks of the flowchart 1200, in some embodiments, the flowchart 1200 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 12. Additionally, or alternatively, two or more of the blocks of the flowchart 1200 may be performed in parallel.

[0280] In some embodiments, explainability may be enabled by using a novel typing system for weights, where each weight may be assigned a type representing the physical or conceptual degree of freedom it encodes. For example, if it is known that represents thermal conductance (e g., a value with units of W / K) and oof2represents a thermal time constant (e.g., a value with units of seconds), this semantic information may be explicitly encoded as types in the source code. In contrast to standard models, where weights are just floats or doubles, embodiments of the present disclosure retain these numerical formats alongside domain-specific meaning defined at the type level in the associated programming language.

[0281] By assigning domain-specific types at compile time, automated reasoning may be enabled based on the weight semantics. Both human beings and / or automated reasoning models may ‘‘read'’ the typed weights of a given model, and, because the model’s inputs and outputs are also typed, derive logical conclusions grounded in physical and / or conceptual understanding. Further, the automated reasoning systems may assess the model's scope and / or real-world utility by analyzing weight values together with their defined types. For example, consider a finite element model (FEM), ft, which takes as input environmental variables and / or weather values (e.g., ambient temperature, windspeed, humidity, and / or the like), concrete mix constituents, grid coordinates and dimensions for 3D FEM cells, and / or a timestampindicating time since pour. If the model includes logic mapping, such as ambient temperature to internal temperature, then a subset of weights, one per FEM cell, may represent heat capacity (e.g., a value with units of J / K). As explained above, these meanings and units are encoded at the type level.

[0282] This ty ped structure allows standard optimization of the model to obtain desired outputs, while preserving the ability to interrogate trained weights for human-interpretable insight, based on their type-level meaning. For example, suppose it is determined that ^contains heat capacities tied to spatial coordinates. An insight-discovery system may check for an inference model that accepts weights of type “heat capacity” with positional data. If such a model exists, it may receive the typed weights and coordinates and may perform analysis. For instance, it may compute 3D gradients of heat capacity and. if the gradient exceeds a threshold, return the insight: '‘This element is too thick for the chosen concrete recipe. All likely ambient conditions will lead to thermal cracking. ” In this way, by encoding human domain knowledge in type-level constructs, automated systems are enabled to detect structural issues and / or generate interpretable insights that may generalize across the model’s input space.

[0283] For example, as shown in Figure 5, a model 500 configured as a prediction model associated with a material may have explainable and / or interpretable insights generated associated with its outputs. In some embodiments, one or more elements of the model 500 may be similar to the prediction model 400 as shown and described herein with respect to Figure 4. For instance, the model 500 may receive an ensemble of data (e.g., a first dataset) associated with a material that may include a plurality of data entries associated with a material. The ensemble of data may be subject to an encoding function 502 prior to analysis by the model 500. In some embodiments, the encoding function 502 may be a weather model encoder configured to generate an encoding, 4>W(D). This encoding produced by the encoding function 502 may be fed (e.g., as a first input) to a first module 504 (e.g., a weather module) configured to map predicted values to a predicted encoding such that the first module 504 produces an output, (ty. (e.g., a first output). For instance, the first module 504 may map predicted weather values to a predicted concrete encoding to generate an output of a predicted encoding of concrete temperature. The output of the first module may then be fed to subsequent modules (e.g., similar to the second module 408 as shown and described herein with respect to Figure 4) for further processing.

[0284] Furthermore, a dataset 506 including typed weights may be fed to an explainability module 508 to generate insights in association with the dataset 506 and the outputs of the model500 and / or outputs of any module of the model 500 (e.g.. the first module 504). The explainability module 508 may extract one or more weights of a specific and / or different type for analysis to generate one or more insights into the material and / or the model 500. For instance, the explainability module 508 may extract weights of type “thermal conductance” and, using those typed weights, generate an insight of “The chosen recipe is insensitive to changes in weather. " The insights generated by the explainability module 508 may be included in an attribution dataset as one or more attribution data entries of the attribution dataset. Although Figure 5 shows example elements of the prediction model 400, in some embodiments, the model 500 may include additional or fewer modules, encodings, and / or data entries than those depicted in Figure 5.

[0285] Additionally, referring back to Figure 6, explainability may also be demonstrated via an explainability module 614 of the generation model 600. A dataset 612 of typed weights of the generation model 600 may be fed into the explainability module 614. The explainability module 614 may extract weights of a specific type (e.g., thermal conductance) or of different types and use these weights in its analysis of the output of the generation model 600 and / or any of the constituent modules of the generation model 600. This analysis performed by the explainability module 614 may produce an explainability insight. For example, an insight generated by the explainability' module 614 may be “The optimal recipe required higher GGBS content because of low thermal conductance to protect against cracking. " Although described with reference to Figure 6 as a textual output, the present disclosure contemplates that explainable insights may be conveyed through a variety of output modalities or representational formats (e.g., textual, numerical, audio, visual, and / or the like). The insights generated by the explainability module 614 may be included in an attribution dataset as one or more attribution data entries of the attribution dataset.

[0286] Figure 13 illustrates a flowchart 1300 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 13 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0287] As shown in block 1302, the flowchart 1300 may include the step of generating, for each first weight entry of one or more first weight entries, a type associated with a degree offreedom associated with the first weight entry to generate a first typed weight set. In some embodiments, the first weight set may include a plurality of first weight entries, each of which may be associated with a different degree of freedom of the material and / or an associated module. In such embodiments, to enhance the explainability of a model and / or the modules of the model, rather than using a weight set of simply values, each weight of the weight set may have a type (e.g.. thermal conductance) stored alongside the value for use in the model and / or a module of the model. In some embodiments, the step of the block 1302 of the flowchart 1300 may be performed following and / or in conjunction with the step of the block 1202 of the flowchart 1200 as shown and described herein with respect to Figure 12.

[0288] As show n in block 1304, the flow chart 1300 may include the step of storing the first typed weight set. In some embodiments, storing may include writing, saving, or otherwise committing the first typed weight set to a memory location or data storage medium (e.g., the memory 206 as shown and described herein with respect to Figure 2). In such embodiments, storing may further include formatting the data according to a predetermined schema and / or associating the stored data with metadata tags or identifiers to facilitate indexing and / or retrieval.

[0289] The flowchart 1300 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 13 show s example blocks of the flow-chart 1300, in some embodiments, the flowchart 1300 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 13. Additionally, or alternatively, two or more of the blocks of the flowchart 1300 may be performed in parallel.

[0290] Figure 14 illustrates a flowchart 1400 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 14 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206. communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0291] As showTi in block 1402, the flowchart 1400 may include the step of analyzing a second output and a first typed w eight set to derive a first conclusion. In some embodiments, a module and / or a model may ingest the second output in combination with the first typed weight set to generate an insight as to why a model and / or module may have generated the secondoutput by using the first typed weight set. For example, the first ty ped weight set may include one or more weights of type “heat capacity.” The typed weights of such a type may be used in an explainability and / or interpretability module to generate the first conclusion (e.g., an insight of an influence or causal relationship between the type and the second output that informs explainability and / or interpretability') that may, in such examples, include “ambient temperatures may lead to thermal cracking of the material '’ as detailed above. In some embodiments, the step of the block 1402 of the flowchart 1400 may be performed following and / or in conjunction with the step of the block 1302 of the flowchart 1300 as shown and described herein with respect to Figure 13.

[0292] As shown in block 1404, the flowchart 1400 may include the step of generating an attribution dataset including the first conclusion. In some embodiments, the attribution dataset may include one or more attribution data entries, each of which may be associated with various forms of explainability and / or interpretability' of the associated model. In such embodiments, an attribution data entry' of the one or more attribution data entries may be the first conclusion and / or may include data associated with the first conclusion.

[0293] The flowchart 1400 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 14 shows example blocks of the flowchart 1400, in some embodiments, the flowchart 1400 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 14. Additionally, or alternatively, two or more of the blocks of the flowchart 1400 may be performed in parallel.

[0294] In some embodiments, explainability' may be enabled by weight-based agentic perturbations, where use of ty ped weights may enable self-referential agentic models that intentionally perturb the weights of a trained model to assess sensitivity and robustness. In such embodiments, these agentic models may be built for specific weight types (e.g., a model that perturbs weights typed as “thermal conductance”). Perturbing a thermal conductance weight may reveal how output variables (e.g., temperatures) respond to changes in thermal coupling. The agentic model may include logic to determine whether perturbations of a certain magnitude cause meaningful shifts in specific output types. If. for instance, the temperature output changes by more than a threshold, the system may conclude: “Temperature is highly sensitive to variations in thermal conductance. This suggests your chosen recipe has low tolerance to batching variation. Consider a mix design with greater thermal robustness. ”

[0295] In some embodiments, explainability’ may be enabled by data-based agentic perturbations, where self-referential agentic models may perturb and / or simulate input data toprobe causal dependencies between inputs and outputs (e.g., for fixed and unperturbed weights), thereby illuminating a model’s internal representations. These models may interpret the typed meaning of both inputs and outputs, allowing them to reason about causal relationships within a specific domain context. For known input types (e.g., time, temperature, compressive strength, sound velocity, density, and / or the like), corresponding agentic models may exist to evaluate how perturbations in those inputs affect outputs. Since any data type may appear as either an input or output, the perturbation models may operate across a shared domain of typed variables. In some embodiments, an agentic model may implement counterfactual reasoning to uncover causal structures learned by the model. For example, an agentic model may perturb a concrete pour start time to assess its influence on a time-to-milestone output such that the agentic model may return an insight such as ‘‘This recipe, when used in this element, is insensitive to variations in pour time within the same calendar day. Whether poured at the start or end of the workday, the outcome remains unchanged. ”

[0296] It will be understood that, although the above description refers to perturbations being conducted by agentic models, the present disclosure contemplates all possible means to perturb values of weights, data, and / or the like associated with the models and / or modules described herein.

[0297] Figure 15 illustrates a flowchart 1500 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 15 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0298] As shown in block 1502, the flowchart 1500 may include the step of analyzing a first entry of a typed weight set to determine an agentic model of a plurality of agentic models associated with a type of the first entry. In some embodiments, the typed weight set may include a plurality of different types (e.g.. thermal conductance, thermal time constant, effective density, rate of heat generation, and / or the like). Further, each agentic model may be associated with a specific type of weight. As such, the type of the first entry may be extracted and used to identify the agentic model associated with that type. In some embodiments, an agentic model may be configured to analyze more than one weight type. As used herein, an agentic model may refer to a model configured to initiate or direct actions that affect external models, systems.or modules. Such a model may include logic or policies that enable it to interact with, control, or modify the behavior of other models or modules outside of itself. In some embodiments, the step of the block 1502 of the flowchart 1500 may be performed following and / or in conjunction with the step of the block 1302 of the flowchart 1300 as shown and described herein with respect to Figure 13.

[0299] As shown in block 1504, the flow chart 1500 may include the step of perturbing, via the agentic model, a weight of the first entry to generate a perturbed first output. In some embodiments, the agentic model may slightly increase or decrease the value associated with the typed weight (e.g., perturb the weight). After the adjustment to the weight, the perturbed weight may be incorporated into the w eight set and the weight set may be fed into the module that generated a first output (e.g., a first module) to generate a new output (i. e. , the perturbed first output). The perturbed first output may, in some embodiments, be an output of the same type as the first output, but with a different value or, in certain embodiments, the same value (e.g., changes to the weight of the first entry did not yield changes in the first output). Additionally, or alternatively, the perturbed weight may be stored alongside the perturbed first output in an operably coupled database for future processing.

[0300] As shown in block 1506, the flow chart 1500 may include the step of comparing, via the agentic model, a first output and the perturbed first output to generate a first output comparison. In some embodiments, the perturbed first output may be compared to the first output using a variety of comparison techniques (e.g.. absolute difference, relative difference, percentage error, symmetric mean, absolute percentage error, root mean square error, log ratio, and / or the like) to determine the effect perturbing the weight of the first entry had on the first output.

[0301] As shown in block 1508, the flowchart 1500 may include the step of generating an attribution dataset including the first output comparison. In some embodiments, the first output comparison may yield an influence or causal relationship associated with the model and / or material. For example, perturbing the w eight of the first entry7may yield little to no change in the first output (e.g., the first output comparison illustrates there was no change between the first output and the perturbed first output) which may generate an explainable insight that weights of that type have smaller impact on the material and / or model. As such, one or more attribution data entries of the attribution dataset may be the first output comparison and / or data associated with the first output comparison. In some embodiments, the steps of the flowchart 1500 may be performed for additional weights of the same type and / or of different types untileach weight of the typed weight set or a subset of the typed weight set has been perturbed and analyzed.

[0302] The flowchart 1500 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 1 shows example blocks of the flowchart 1500, in some embodiments, the flowchart 1500 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 15. Additionally, or alternatively, two or more of the blocks of the flowchart 1500 may be performed in parallel.

[0303] Figure 16 illustrates a flowchart 1600 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 16 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0304] As shown in block 1602, the flowchart 1600 may include the step of analyzing a data entry of a first dataset to determine an agentic model of a plurality of agentic models associated with a type of the data entry. In some embodiments, the first dataset may include a plurality of different types (e.g., thermal conductance, thermal time constant, effective density, rate of heat generation, and / or the like). Further, each agentic model may be associated with a specific type of data entry7. As such, the type of the data entry may be extracted and used to identify the agentic model associated with that type. In some embodiments, an agentic model may be configured to analyze more than one type. In some embodiments, the step of the block 1602 of the flowchart 1600 may be performed following and / or in conjunction with the step of the block 1302 of the flowchart 1300 as shown and described herein with respect to Figure 13.

[0305] As show n in block 1604, the flowchart 1600 may include the step of perturb, via the agentic model, a value of the data entry to generate a perturbed first output. In some embodiments, the agentic model may slightly increase or decrease the value associated with the data entry (e.g., perturb the value of the data entry'). After the adjustment to the value, the perturbed value of the data entry7may be incorporated into the first dataset and the first dataset may be fed into the module that generated a first output (e.g., a first module) to generate a new output (i.e., the perturbed first output). The perturbed first output may, in some embodiments, be an output of the same type as the first output, but with a different value or, in certainembodiments, the same value (e.g., changes to the value of the data entry did not yield changes in the first output). Additionally, or alternatively, the perturbed data entry may be stored alongside the perturbed first output in an operably coupled database for future processing.

[0306] As shown in block 1606, the flowchart 1600 may include the step of compare, via the agentic model, a first output and the perturbed first output to generate a first output comparison. In some embodiments, the perturbed first output may be compared to the first output using a variety of comparison techniques (e.g.. absolute difference, relative difference, percentage error, symmetric mean, absolute percentage error, root mean square error, log ratio, and / or the like) to determine the effect perturbing the data entry' had on the first output.

[0307] As shown in block 1608, the flowchart 1600 may include the step of generate an attribution dataset including the first output comparison. In some embodiments, the first output comparison may yield an influence or causal relationship associated with the model and / or material. For example, perturbing the value of the data entry may yield little to no change in the first output (e.g., the first output comparison illustrates there was no change between the first output and the perturbed first output) which may generate an explainable insight that the data entry or data entries of that type have smaller impact on the material and / or model. As such, one or more attribution data entries of the attribution dataset may be the first output comparison and / or data associated with the first output comparison. In some embodiments, the steps of the flow chart 1600 may be performed for additional data entries of the same ty pe and / or of different types until each data entry of the first dataset or a subset of the first dataset has been perturbed and analyzed.

[0308] The flowchart 1600 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 16 show s example blocks of the flowchart 1600. in some embodiments, the flowchart 1600 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 16. Additionally, or alternatively, two or more of the blocks of the flowchart 1600 may be performed in parallel.

[0309] Figure 17 illustrates a flowchart 1700 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 17 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206. communicationinterface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0310] As shown in block 1702, the flowchart 1700 may include the step of analyzing a data entry of a first dataset and a first entry of a typed weight set to determine an agentic model of a plurality7of agentic models associated w ith a ty pe of the data entry and a type of the first entry. In some embodiments, the first typed weight set and the first dataset may include a plurality of different types (e.g., thermal conductance, thermal time constant, effective density, rate of heat generation, and / or the like). Further, each agentic model may be associated with a specific type of data entry . Additionally, or alternatively, the type of the data entry and the type of the first entry' may be equivalent or may be different. As such, the type of the data entry' and the type of the first entry’ may be extracted and used to identify the agentic model or agentic models associated with that type or types. In some embodiments, an agentic model may be configured to analyze more than one type. In some embodiments, the step of the block 1702 of the flowchart 1700 may be performed following and / or in conjunction with the step of the block 1302 of the flowchart 1300 as shown and described herein with respect to Figure 13.

[0311] As shown in block 1704, the flowchart 1700 may include the step of perturbing, via the agentic model, a value of the data entry and a weight of the first entry to generate a perturbed first output. In some embodiments, the agentic model and / or agentic models may slightly increase or decrease the values associated with the data entry' (e.g., perturb the value of the data entry) and / or the first entry (e.g., perturb the value of the first entry). After the adjustment to the values, the perturbed values of the data entry and the first entry may be incorporated into their respective sets (e.g., the first dataset and the ty ped weight set) and these sets may be fed into the module that generated a first output (e.g., a first module) to generate a new' output (i.e., the perturbed first output). The perturbed first output may, in some embodiments, be an output of the same type as the first output, but with a different value or, in certain embodiments, the same value (e.g., changes to the value of the data entry and the first entry did not yield changes in the first output). Additionally, or alternatively, the perturbed data entry' and the perturbed first entry may be stored alongside the perturbed first output in an operably coupled database for future processing.

[0312] As shown in block 1706, the flow chart 1700 may include the step of comparing, via the agentic model, a first output and the perturbed first output to generate a first output comparison. In some embodiments, the perturbed first output may be compared to the first output using a variety of comparison techniques (e.g.. absolute difference, relative difference,percentage error, symmetric mean, absolute percentage error, root mean square error, log ratio, and / or the like) to determine the effect perturbing the data entry had on the first output.

[0313] As shown in block 1708, the flowchart 1700 may include the step of generating an attribution dataset including the first output comparison. In some embodiments, the first output comparison may yield an influence or causal relationship associated with the model and / or material. For example, perturbing the value of the data entry and / or the first entry may yield little to no change in the first output (e.g.. the first output comparison illustrates there was no change between the first output and the perturbed first output) which may generate an explainable insight that the data entry or data entries and / or the first weight or weights of that type have smaller impact on the material and / or model. As such, one or more attribution data entries of the attribution dataset may be the first output comparison and / or data associated with the first output comparison. In some embodiments, the steps of the flowchart 1600 may be performed for additional data entries of the same type and / or of different types and / or additional weights of the same ri pe and / or of different types and / or different combinations of weights and data entries until each data entry of the first dataset or a subset of the first dataset and each weight of the typed weight set or a subset of the typed weight set has been perturbed and analyzed.

[0314] The flowchart 1700 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 17 shows example blocks of the flowchart 1700. in some embodiments, the flowchart 1700 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 17. Additionally, or alternatively, two or more of the blocks of the flowchart 1700 may be performed in parallel.

[0315] As an example, agentic perturbations for explainable material-based determinations may be performed via a process flow 1800 as shown with respect to Figure 18. In some embodiments, the process flow 1800 may begin with the step 1802, where input data, d. and a function, (ri), u>), are ingested by a perturbation module (e g., a first module, a second module, and / or any other module configured to perturb weights and / or data entries as described herein). In such embodiments, the perturbation module may, after ingestion, output a perturbed function,where the set of typed weights have had a single entry, a plurality of entries, or all of the entries of the weight set modified (e.g., by A<z>). While, the step 1802 of Figure 18 illustrates the weights being perturbed, in some embodiments, the data entries of the input data may alternatively or additionally be perturbed in the perturbed function.

[0316] In some embodiments, the process flow 1800 continues with the step 1804 where a module performing the perturbed function (i.e., the function with perturbed weights) may ingest the input data. Upon ingestion of the input data, the module may analyze, in accordance with the perturbed function, the input data and produce a perturbed output, y + Ay, where Ay represents the change in the original output y. Additionally, or alternatively, although illustrated as the original input data, the input data may be a perturbed dataset in the step 1804.

[0317] In some embodiments, as shown in step 1806 of the process flow 1800, the value of the perturbation of the weight set, Au>, may be stored with and / or linked to the associated change in output Ay in a database operably coupled to the module. Additionally, or alternatively, in embodiments where the input data is perturbed, the perturbation of the input data may also be stored with the aforementioned values. Furthermore, the steps of 1802, 1804, and 1806 may be repeated for multiple iterations to evaluate multiple different perturbations of the weight set, the input data, and / or different combinations of both.

[0318] As shown in step 1808 of the process flow 1800, once all weights and / or a subset of the weights have been perturbed, the weight perturbation and output change differential may, in some embodiments, be formatted into a matrix representation for ingestion into an explainability module. Additionally, or alternatively, in embodiments with input data perturbations, said data perturbations may be ingested by the explainability module. In suchAy; embodiments, the data may be stored in the matrix as =. Upon ingestion by the explainability module, the data may be analyzed and one or more insights associated with an influence and / or causal relationships associated with a material and / or the model or module may be generated. For example, a generated insight may include “Recipe A is prone to high levels of heat generation for small increases in opc; ensure low batch variability to prevent thermal cracking. ” The generated insight may then be included as an attribution data entry of one or more attribution data entries of an attribution dataset.

[0319] The process flow 1800 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 18 shows example steps of the process flow 1800, in some embodiments, the process flow 1780 may include additional steps, fewer steps, different steps, or differently arranged steps than those depicted in Figure 18. Additionally, or alternatively, two or more of the steps of the process flow 1800 may be performed in parallel.

[0320] In some embodiments, explainability may be enabled using measures of data dependence during model and / or module creation, where a module frencodes an internal latent representation of the data, defined by its weights o)fr, that may capture the model’s internal degrees of freedom. For instance, in neural networks, each layer may progressively transform the input data using different subsets of weights such that different latent features are encoded. During training, as weights are optimized over input-output pairs, the model may naturally form latent clusters within the data space, where each may represent an emergent categorization learned by the model at a specific logical depth. For example, a neural network trained to map atemperature timeseries to aBoolean output (e.g., whether cracking occurred during the curing of a concrete element) may learn internal representations that cluster data by peak temperature due to concrete exceeding a threshold temperature tending to crack. By inspecting the model’s internal logic, the clusters may be identified, and causal features may be uncovered that drive them. Additionally, or alternatively, latent clusters (e.g., data clusters) may be identified in the training data for the models and / or modules described herein.

[0321] Figure 19 illustrates a flowchart 1900 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 19 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0322] As shown in block 1902. the flowchart 1900 may include the step of identifying a data cluster within a first dataset. In some embodiments, a model and / or module may ingest the first dataset and, due to prior training and optimization over pluralities of inputs and associated outputs, may identify the data cluster within the first dataset. In such embodiments, the data cluster may reflect an implicit or emergent categorization learned by the model and / or module, where data associated with the data cluster exhibit similar features. In some embodiments, the step of the block 1902 of the flowchart 1900 may be performed following and / or in conjunction with the step of the block 1202 of the flow-chart 1200 as shown and described herein with respect to Figure 12.

[0323] As shown in block 1904, the flowchart 1900 may include the step of generating one or more causal features associated with the data cluster. In some embodiments, generation ofthe one or more causal features associated with the data cluster may be facilitated by understanding of the internal logic of the model and / or module (e.g., via automated clustering algorithms). For example, a module or module that maps a temperature timeseries to a Boolean output may have a data cluster of peak temperature and a causal feature that may be uncovered may include an indication that a material exceeding a threshold temperature may crack.

[0324] As shown in block 1906, the flowchart 1900 may include the step of generating an attribution dataset including the one or more causal features. In some embodiments, the one or more causal features may be associated with an influence and / or causal relationship of the model and / or the associated material. In such embodiments, one or more attribution data entries may be generated that include the one or more causal feature and / or additional data associated with the data cluster for the attribution dataset.

[0325] The flowchart 1900 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 19 shows example blocks of the flowchart 1900, in some embodiments, the flowchart 1900 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 19. Additionally, or alternatively, two or more of the blocks of the flowchart 1900 may be performed in parallel.

[0326] In some embodiments, this form of explainability derives from analyzing and / or interpreting latent structures within the model, aiming to relate these emergent representations to causally meaningful patterns in the outputs. Further, characterization of latent representations is performed both manually (e.g., post-training analysis) and via automated clustering algorithms that may identify distinct data partitions in latent space. Once clusters are identified, human experts may interpret their semantic meaning, which may then be encoded into automated text explanations triggered when similar clustering conditions are met in future inputs. Continuing the above example, the model may output “This recipe, when poured into a column, is prone to cracking due to high heat generation during curing. Consider using an alternative mix design with less Ordinary Portland Cement. ”

[0327] In some embodiments, explainability may be enabled by uncertainty propagation. In such embodiments, all trained modules may exhibit some degree of prediction error, representing the statistical uncertainty of their outputs compared to measured data. In an end- to-end model, uncertainty of the final output arises from propagated errors through the entire sequence of constituent modules. Embodiments of the present disclosure that are modularized along causal lines, may enable tracing and / or quantifying of which modules contribute most to the overall uncertainty such that more targeted interpretation and intervention may be enabled.For example, a model may forecast a concrete temperature timeseries from a mix design and element geometry. The model may include a first module that maps element shape to finite- element thermal conductance weights and a second module that uses these weights and a pour date to predict the concrete temperature. If the full model exhibits high output uncertainty, it may be found that the thermal conductance prediction module (e.g., the first module) contributes little uncertainty, while the temperature forecasting module (based on pour date and conductance) contributes significantly more. This insight may localize the source of uncertainty to a specific module, enabling two pathways, model refinement (e.g., investigate whether the poorly performing module suffers from inadequate data or structural limitations) and user-facing insight (e.g., automatically inform the user using a type-aware inference system that maps the uncertain weights to human-interpretable concepts). In this example, the system may output "It is unclear how this mix and element combination performs across different times of year. This may reflect a weak dependence on pour time or a lack of data for this specific mix design. ”

[0328] Figure 20 illustrates a flowchart 2000 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 20 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206. communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0329] As shown in block 2002. the flowchart 2000 may include the step of ingesting an output of a first module in a first intermediate module. In some embodiments, an end-to-end model may include a plurality- of modules (e.g., a first module, a second module, an intermediate module, an explainability' module, an encoding module, and / or any other module as described herein). In such embodiments, each module may be used and / or a step in the process of producing an output of the end-to-end model. Furthermore, the constituent modules of the end-to-end model may be in a series configuration (e.g., where an output of a module is an input to another module), a parallel configuration (e.g., where two or more modules are configured to operate independently of one another (e.g., the output of one is not ingested by the other)), and / or in a combination of both configurations.

[0330] In some embodiments, the first intermediate module may be a first module of N intermediate modules, where N may be a positive integer number. In other words, the end-to-end model may include at least N constituent modules in generating its output. Additionally, or alternatively, an i-th intermediate module of the N intermediate modules may be configured to receive an output of an (i - 1) intermediate module of the N intermediate module, where an N-th intermediate module of the N intermediate modules may be configured to generate the first output. Said differently, the end-to-end model may be configured with at least N constituent modules in a fully series configuration such that the output of the first module is ingested by the second module and the process is repeated until the final module generates an output. In some embodiments, the step of the block 2002 of the flowchart 2000 may be performed following and / or in conjunction with the step of the block 1206 of the flowchart 1200 as shown and described herein with respect to Figure 12.

[0331] As shown in block 2004, the flowchart 2000 may include the step of generating, via an output of the first intermediate module, a first output. In some embodiments, prior to ingestion by a later module in the end-to-end model (e.g., a second module), the first module may generate an output that may be ingested by the first intermediate module for additional processing in order to generate the first output.

[0332] The flowchart 2000 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 20 shows example blocks of the flowchart 2000, in some embodiments, the flowchart 2000 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 20. Additionally, or alternatively, two or more of the blocks of the flowchart 2000 may be performed in parallel.

[0333] Figure 21 illustrates a flowchart 2100 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 21 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory7206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0334] As shown in block 2102, the flowchart 2100 may include the step of identifying a module out of a first module, a first intermediate module, and a second module with a higher contribution to an uncertainty7measurement. In some embodiments, outputs of each module of an end-to-end model (e.g., the first module, the first intermediate module, the second module, and / or the like) may have vary ing degrees of uncertainty associated with the outputs. In suchembodiments, the degree of uncertainty associated with an output of a module may be propagated throughout the end-to-end model as subsequent modules may use the output of the module or use an output of a module that used the output in their analyses. As such, an uncertainty of an output of the end-to-end model may be heavily influenced by one module with a high degree of uncertainty .

[0335] In some embodiments, the outputs of each module may be analyzed (e.g.. by another module, by an explainability module, and / or the like) to determine degrees of uncertainty associated with each module’s output and to determine which module contributes the most to the overall uncertainty of the end-to-end model. Additionally, or alternatively, the step of the block 2102 of the flowchart 2100 may be performed following and / or in conjunction with the step 2004 of the flowchart 2000 as shown and described herein with respect to Figure 20.

[0336] As shown in block 2104, the flowchart 2100 may include the step of generating an attribution data entry of one or more attribution data entries including data indicating the module identified with the higher contribution. In some embodiments, the uncertainty measurement of the end-to-end model may be stored as an attribution data entry in an attribution dataset. Additionally, or alternatively, the module identified as contributing the highest uncertainty to the uncertainty measurement of the end-to-end model may be indictive of an influence and / or causal relationship in the module, model, and / or an associated material and, as such, data associated with the uncertainty of the module may be stored as one or more attribution data entries in the attribution dataset.

[0337] The flowchart 2100 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 21 shows example blocks of the flowchart 2100, in some embodiments, the flowchart 2100 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 21. Additionally, or alternatively, two or more of the blocks of the flowchart 2100 may be performed in parallel.

[0338] In some embodiments, interpretability may be enabled using interpretable input, where input data to a model contains more information than is strictly required to generate outputs. Formally, while the model may only require n input features, the model may often be fed n + m features, where m represents additional contextual data not directly used in the trained function. This additional context, though unused in the core prediction, may enable post hoc interpretation of the model's outputs via separate insight inference models or modules. These models or modules may identify causal or correlational patterns that may otherwise remain hidden. For example, a model may ingest a concrete temperature timeseries and a pourstart time and may output a forecasted date for when a target compressive strength may be reached. The model may also receive geographical location of the pour but may not use this location in the core computation. A separate insight inference model or nodule may then analyze how outputs vary with location, identifying regional trends (e.g., consistent delays in colder climates) and / or anomalies (e.g., performance variations due to supplier practices or elevation). In this example, the system may generate the following automated insight “This mix, in the chosen element, when poured in London, performs similarly year-round as for those projects your organization has worked on in Cardiff. ”

[0339] These insight models or modules may take various forms, including, but not limited to clustering models, applied to model outputs conditioned on additional inputs; Bayesian inference models, used to identify posterior beliefs about which context variables influence output variance; mutual information estimators, quantifying dependency between extra inputs and outputs; SHAP value attribution, extending to auxiliary features not in the core model; decision trees or rule-extraction models, trained on residuals or secondary' features; and / or the like. These models or modules provide interpretable explanations of why the output was what it was. not by interrogating the trained model directly, but by leveraging the contextual metadata alongside the predictions. This approach enhances interpretability by bridging the gap between black-box predictions and real-world understanding, especially when rich, structured input data is available.

[0340] Figure 22 illustrates a flowchart 2200 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 22 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory- 206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein yvith respect to Figure 2.

[0341] As shown in block 2202, the flowchart 2200 may include the step of ingesting a first subset of a first dataset to generate a first output. In some embodiments, a model may ingest the first dataset that may include one or more first data entries associated with a material. In such embodiments, a module of the model (e.g., a first module) may only use the first subset of the one or more first data entries of the first dataset in its analysis. Further, the first subset may not include each first data entry of the one or more first data entries. The first subset may be ingested by the module of the model and used to generate the first output. In someembodiments, the step of the block 2202 of the flowchart 2200 may be performed following and / or in conjunction with one or more steps of the flowchart 1200 as shown and described herein with respect to Figure 12.

[0342] As shown in block 2204, the flowchart 2200 may include the step of generating, using the first output and using a second module, a second output. In some embodiments, the model may include the second module, where a first module may generate the first output, and the first output may be ingested by the second module. In such embodiments, the second module may use the first output and, in some embodiments additional data, to generate the second output associated with the material.

[0343] As shown in block 2206, the flowchart 2200 may include the step of generating, using the second output and a second subset of the first dataset, an attribution data entry of one or more attribution data entries including an interpretation of the second output in a context of the second subset, where the first subset and the second subset are absent shared first data entries. In some embodiments, the first dataset may include additional features not used in the analysis performed by the model and / or any of the constituent modules of the model, (i.e., the second subset). In such embodiments, the second subset may include additional contextual data that, when used to interpret the second output, generate one or more influence or causal relationships associated with the model and / or the material. Further, one or more attribution data entries of the attribution dataset may then be generated that include data associated with the one or more influence or causal relationships that inform the explainability of the model.

[0344] The flowchart 2200 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 22 show s example blocks of the flow chart 2200, in some embodiments, the flowchart 2200 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 22. Additionally, or alternatively, two or more of the blocks of the flowchart 2200 may be performed in parallel.

[0345] In some embodiments, explainability7may be enabled by local-domain, low7dimensional- continuous representations, where, with models with many weights and / or discretized outputs (e.g.. milestone values of a continuous variable), an automated search for locally continuous representations within bounded regions of the input space may be conducted. This process may identify local functions that approximate the model’s output behavior in specific regions, using low-degree basis function regressions. The goal may include minimizing both the prediction error and the basis degree (e.g., the order of polynomial terms required to explain the data). In such embodiments, high-dimensional, discretized outputs maybe effectively compressed into smooth, continuous approximations, enabling more interpretable functional forms. These local models act as interpretable module, analogous to local linearization of a nonlinear function, capturing nuanced, continuous dependencies over constrained subspaces of the input domain.

[0346] For example, a model may receive a mix design, element geometry, and pour time, and may predict the time-to-strength for 10 MPa, 20 MPa, and 40 MPa milestones. These discrete predictions represent samples of a continuous variable: strength. In such embodiments, a single input (e.g. water / binder ratio) may be locally varied and changes may be observed in all three output values. Further, a basis function regression may then be fit to this data, producing a continuous function mapping (e.g., strength, water / binder ratio to time-to- strength). In some embodiments, the selected model may be the lowest-degree basis satisfying a specified error threshold such that interpretability may be ensured without overfitting. Additionally, or alternatively, this process may enable uncovering of functional relationships that may otherwise be hidden within the discretized outputs of a complex model. For instance, it may be discovered that early strength milestones are less sensitive to water / binder ratios than later ones. Such discoveries may tngger an automated insight such as "Early strength curing times are insensitive to water / binder ratio content for the chosen specification, when this mix is poured into a column. ” Additionally, or alternatively, locally regressed continuous models may improve explainability by identifying low-dimensional, context-specific relationships that would be difficult to extract from the full model directly.

[0347] Figure 23 illustrates a flowchart 2300 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 23 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein w ith respect to Figure 2.

[0348] As shown in block 2302, the flowchart 2300 may include the step of varying a first data entry of one or more first data entries to generate a varied first dataset. In some embodiments, a value associated with the first data entry7may be adjusted to generate the varied first dataset for analysis in a plurality of modules of a model. Additionally, or alternatively, values of other data entries of the one or more first data entries may be varied to generate the first varied dataset. In some embodiments, the step of the block 2202 of the flowchart 2300may be performed following and / or in conjunction with one or more steps of the flowchart 1200 as shown and described herein with respect to Figure 12.

[0349] As shown in block 2304, the flowchart 2300 may include the step of generating, using the varied first dataset, a varied first output. In some embodiments, the varied first dataset may be ingested by a first module of the model. Further, after ingestion, the first module may produce a varied first output in accordance with its underlying logic.

[0350] As shown in block 2306, the flowchart 2300 may include the step of generating, using the varied first output and a second module, a varied second output. In some embodiments, the second module may ingest the varied first output and / or the varied first dataset. Further, after ingestion, the second module may output the varied second output in accordance with its underlying logic.

[0351] As shown in block 2308, the flowchart 2300 may include the step of generating a continuous function mapping including the varied first data entry and the varied second output. In some embodiments, the continuous function mapping may serve as a means to approximate the model's output in specific regions. As such, high dimension, discretized outputs may be compressed into functional approximations. Such local models may illuminate various influences and / or causal relationships in the model and / or modules by capturing nuanced dependencies over various subregions (e.g., similar to local linearizations of a non-linear function). These may be used to enhance explainability and / or interpretability of the model and data associated with these local models may be stored as one or more attribution data entries in an attribution dataset. Additionally, or alternatively, other data entries of the one or more first dataset may be varied and ingested by the modules to probe for continuous function mappings over various subregions.

[0352] The flowchart 2300 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 23 show s example blocks of the flowchart 2300, in some embodiments, the flowchart 2300 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 23. Additionally, or alternatively, two or more of the blocks of the flowchart 2300 may be performed in parallel.

[0353] In some embodiments, explainability may be enabled by compression of a model, where the number of weights may be reduced, and the functional representation of the domain space may be simplified. In such embodiments, each module within an end-to-end model maybe analyzed by automatically perturbing its weights and observing the effects on its outputs. If perturbing different weights (e.g., individually or in groups) yields identical or highly similaroutput patterns, those weights may be classified as redundant. This process may extend beyond single weights to include pairs and / or higher-order groupings, enabling the discovery of both independent and correlated redundancies in weight-space. Additionally, or alternatively, the search may combine random subsampling of weight sets with automated pattern-matching of the resulting output behaviors. Once a group of weights (or groupings) is shown to yield functionally equivalent results, an automated pruning system may remove the redundant weights from the module. Such a process leads to a more efficient representation of the transformation performed by the module and, by extension, the full end-to-end model.

[0354] By converging on the minimal necessary set of transformations, the compressed model surfaces essential causal mappings between inputs and outputs. In this context, "meaningful" may refer to transformations that are required to achieve the output behavior. The resulting simplified model is not only more interpretable, but also becomes a clearer subject for both manual inspection and the automated explainability techniques described herein.

[0355] In some embodiments, explainability may be enabled by compression of the data. When training a model over an ensemble of data {2)}, the model typically learns both pertinent causal relationships and spurious correlations that may arise from incidental features in the data. To minimize these unnecessary' degrees of freedom, data compression techniques may be applied prior to training. These may be seen as specific instantiations of the generalised encoding function ({£’})■ In such embodiments, by designing compressions that downplay less relevant data attributes, the model may focus on causally meaningful signals.

[0356] For example, for a model that classifies Boolean outcomes based on input images, M versions of the model may be built, each trained on a different image resolution, reduced using a method such as mean down sampling. Each of the M models, trained on the same task but with differing data resolution, may yield distinct sets of weights. The model compression procedure described above may be used to prune redundant weights from each model and to compare both the efficiency and prediction accuracy across resolutions.

[0357] In some embodiments, if lower-resolution models yield comparable accuracy to higher-resolution ones, this may suggest that finer image detail is not causally relevant to the task. In such embodiments, identifying the minimum sufficient resolution may allow construction of models that encode only the essential causal transformations, reducing susceptibility to noise or overfitting caused by high-resolution artifacts. Additionally, once this optimal data compression is found the model may be further interrogated using the full suite ofexplainability methods described herein. This process enables extraction of core latent representations that characterize the system, stripped of non-essential detail. Further, these insights, derived from training on compressed data, are often inaccessible when working with raw, high-dimensional data alone.

[0358] Figure 24 illustrates a flowchart 2400 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 24 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0359] As shown in block 2402, the flowchart 2400 may include the step of perturbing, for each first weight entry of one or more first weight entries, a first weight entry7to generate a perturbed first weight set. In some embodiments, value of a weight entry may be slightly increased or decreased (e.g., perturb the weight). After the adjustment to the weight, the perturbed weight may be incorporated into the perturbed first weight set and the perturbed first weight set may be fed into a module (e.g., a first module) that generates a first output to generate a new output. Additionally, or alternatively, each first weight entry of the one or more first weight entry may be a typed weight as described herein. In some embodiments, In some embodiments, the step of the block 2402 of the flowchart 2400 may be performed following and / or in conjunction with one or more steps of the flowchart 1200 as shown and described herein with respect to Figure 12.

[0360] As shown in block 2404, the flowchart 2400 may include the step of generating, for each perturbed first weight entry' of the perturbed first weight set and using a first module, a first output set including one or more first output entries. In some embodiments, the first module may ingest a perturbed weight entry7of the perturbed first weight set and generate a perturbed output associated with that weight entry. In such embodiments, the step of the block 2404 may be repeated for each perturbed first weight entry of the perturbed first weight set until each perturbed first weight entry has a corresponding perturbed output of the first module. Further, the first output set may be generated including each perturbed output of the first module. Additionally , or alternatively, the perturbed weights may be stored with the first output set in an operably coupled database for future processing.

[0361] As shown in block 2406, the flowchart 2400 may include the step of comparing a first output to each first output entry of the first output set. In some embodiments, each perturbed output of the first output set may be compared to the first output using a variety of comparison techniques (e.g., absolute difference, relative difference, percentage error, symmetric mean, absolute percentage error, root mean square error, log ratio, and / or the like) to determine the effect perturbing the weight of the first entry had on the first output.

[0362] As shown in block 2408, the flowchart 2400 may include the step of identifying, via the comparison, a redundant weight of the one or first weights. In some embodiments, the comparison may reveal that certain weights do not impact the output of the first module and / or certain sets of weights impact the output of the first module similarly (e.g., the weights are redundant and not needed by the first module). Additionally, or alternatively, a plurality of weights may be identified as redundant.

[0363] As shown in block 2410, the flowchart 2400 may include the step of pruning the redundant weight from the first weight set. In some embodiments, the identified redundant weights and / or plurality of redundant weights may be removed from the first weight such that the model is compressed. Furthermore, data associated with the redundant weights may be stored as an attribution data entry of an attribution dataset to inform explainability of the model and / or the first module.

[0364] The flowchart 2400 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 24 shows example blocks of the flowchart 2400, in some embodiments, the flowchart 2400 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 24. Additionally, or alternatively, two or more of the blocks of the flowchart 2400 may be performed in parallel.

[0365] Figure 25 illustrates a flowchart 2500 for an example method for explainable material-based determinations, in accordance with some embodiments of the present disclosure. The operations illustrated in Figure 25 may, for example, be performed by, with the assistance of, and / or under the control of an apparatus (e.g., the server 200 as shown and described herein with respect to Figure 2), as described above. In this regard, performance of the operations may invoke one or more of processor 202, memory 206, communication interface 204, and / or artificial intelligence (Al) module 208 as shown and described herein with respect to Figure 2.

[0366] As shown in block 2502. the flowchart 2500 may include the step of generating a plurality of first weight groups each including at least two first w eight entries of one or morefirst weight entries. In some embodiments, a first weight group of the plurality of first weight groups may include at least two first weight entries. Further, the at least two first weight entries of a first weight group may be typed weights, where each weight entry of a first weight group may have the same type. In such embodiments, each weight of a first weight group may have its value slightly increase or slightly decreased (e.g., perturbed). Additionally, or alternatively, each value may be shifted by the same amount or by different amount. After the adjustment to the at least two weights, the perturbed grouping may be combined with any remaining weights to generate a perturbed first weight set including a first weight group and the perturbed first weight set may be fed into a module (e.g., a first module) that generates a first output to generate a new output. In some embodiments, the step of the block 2502 of the flowchart 2500 may be performed following and / or in conjunction with one or more steps of the flowchart 1200 as shown and described herein with respect to Figure 12. Additionally, or alternatively, one or more steps of the process flow 2500 may be performed via one or more steps of the process flow 2400 as shown and described herein with respect to Figure 24 with first weight groups.

[0367] As shown in block 2504, the flowchart 2500 may include the step of generating, for each first weight group of the plurality of first weight groups and using a first module, a first output set including one or more first output entries. In some embodiments, the first module may ingest a perturbed first weight set that includes a first weight group of the plurality of first weight groups and may produce an output entry. In such embodiments, the step of the block 2404 may be repeated for each set including a first weight group of the pl ural ity of first weight groups until each first weight group has a corresponding first output of the first module. Further, the first output set may be generated including each output of the first module. Additionally, or alternatively, the plurality of first weight groups may be stored with the first output set in an operably coupled database for future processing.

[0368] As shown in block 2506, the flowchart 2500 may include the step of comparing a first output to each first output entry of the first output set. In some embodiments, each first entry output of the first output set may be compared to the first output using a variety of comparison techniques (e.g.. absolute difference, relative difference, percentage error, symmetric mean, absolute percentage error, root mean square error, log ratio, and / or the like) to determine the effect each first weight group had on the first output.

[0369] As shown in block 2508, the flowchart 2500 may include the step of identifying, via the comparison, a redundant weight group of the plurality of first weight groups. In some embodiments, the comparison may reveal that certain groups of first weights do not impact theoutput of the first module and / or different groupings of first weights impact the output of the first module similarly. In such embodiments, the revealed groups of first weights may be identified as redundant weight groups.

[0370] As shown in block 2510, the flowchart 2500 may include the step of pruning the redundant weight group from the first weight set. In some embodiments, the identified redundant weight group and / or a plurality of redundant weight groups may be removed from the first weight such that the model is compressed. Furthermore, data associated with the redundant weight groups may be stored as an attribution data entry of an attribution dataset to inform explainability of the model and / or the first module. Additionally, or alternatively, analyzing how shifting values of grouped weights may reveal further explainable insights associated an influence or causal relationships of the model, the first module, an associated material, the weights, and / or the like.

[0371] The flow-chart 2500 may include additional embodiments, such as any single embodiment or any combination of embodiments described herein. Although Figure 25 show s example blocks of the flowchart 2500. in some embodiments, the flowchart 2500 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in Figure 25. Additionally, or alternatively, two or more of the blocks of the flowchart 2500 may be performed in parallel.

[0372] As an example, model compression for explainable material-based determinations may be performed via a process flow 2600 as shown with respect to Figure 26. In some embodiments, the process flow 2600 may begin with the step 2602, where input data, d. and a weight set, &>, are received by a pretrained module,suc'qembodiments, the pretrained model may produce an output, y, that module may be ingested by a perturbation module (e g-, a first module, a second module, and / or any other moduleconfigured to perturb w-eights and / or data entries as described herein). The perturbation module may be configured to perturb a weight value and / or values of a group of weights (e.g., similar to the steps of the flowcharts 2400 and 2500 as shown and described herein with respect to Figures 24 and 25) by producing a weight adjustment, Au>. Said weight adjustment may then be ingested by the pretrained module such that it has the formThe pretrained module may then produce another output, y , that may be ingested by the perturbation module. This process may be repeated for each weight in the weight set and / or each potential grouping of weights. As the output to weight perturbation process is occurring, the perturbationmodule stores the output and the associated weight adjustment in an operably coupled database. Further, to avoid repeating adjustments to the same weight or groupings of weight, the perturbation module may ingest historic weight adjustment and associated outputs from the database as the perturbation process is occurring. While illustrated and described with respect to weight perturbations, the above process may be performed for perturbations to the input data and / or perturbations to both the weights and the input data.

[0373] In some embodiments, once all weights of the weight set and / or all groupings of weights have been perturbed and stored in the database with the associated outputs, the process flow 2600 may continue with the step 2604. In such embodiments, the weight adjustments and output entries of the database may be ingested by a pruning module, / PRUNE10prune the pretrained module. The pruning module may search to find sufficient similarity between sets of outputs and, if sufficiently similar, will deem the corresponding weights as encoding equal logic and that the corresponding weights should be pruned. For example, the pruning module may find two outputs, y and yn, that satisfy jyq — yn| < e, where E is the magnitude below which outputs are considered identical. The pruning module may then remove ytand ynand the associated weights and any additional associated logic to generate a pruned module,

[0374] In some embodiments, the explainability and / or interpretability techniques described herein may be used by manually defined text-based automations and / or LLMs to produce a structured set of automated, text-based insights for each model module, for entire end-to-end models, and / or for individual prediction instances (e.g., specific input data points). In such embodiments, these insights may be collated into an itemized document (e.g., a master explanation log) containing causally grounded statements derived from typed weights, local functional approximations, uncertainty analysis, and / or other techniques. Additionally, or alternatively, a separate insight model may be responsible for generating and / or structuring the document, which becomes the ground truth for a downstream interface powered by a large language model (LLM). Further, the LLM may ingest the document and may be deployed within a user-facing chat interface, enabling users to ask natural-language questions about the model’s predictions and receive causally grounded, context-specific answers.

[0375] For example, a user may request predictions for how long two mix designs, Recipe A and Recipe B, will take to reach 25 MPa when poured into a column on July 16th. The model predicts 6 hours for Recipe A and 12 hours for Recipe B. The user may then ask, via the interface. "Why does Recipe B take longer than Recipe A?" and the LLM may respond withan explanation such as “Recipe B is less sensitive to weather variations due to its lower thermal conductance values. Recipe A has higher thermal conductance, which, in combination with the forecasted 3-day average temperature of 30 °C, results in faster curing. The higher sensitivity in Recipe A is caused by its GGBS / Binder ratio of 50%, compared to 25% in Recipe B. ” In such embodiments, this answer is not hallucinated or inferred freely by the LLM; rather, it is constructed entirely from statements in the ground-truth insight document generated at prediction time. For example, the document may include “Recipe A has a high ambient weather dependence due to low thermal conductance, based on the weights of module Al .”, “Recipe B has a low ambient weather dependence due to high thermal conductance, based on the weights of module Bl.”, “The 3-day forecasted temperature is 30°C, which significantly accelerates curing for Recipe A but has minimal effect on Recipe B ”. “Recipe A has a GGBS / Binder ratio of 50%, influencing its thermal behavior in a column.”, “Recipe B has an OPC / Binder ratio of 75%, reducing its thermal conductance in the same geometry.”, and / or the like. Many additional insights will be present in the document, but the LLM selects only those relevant to the user's query, ensuring focused, transparent responses grounded in physically and causally valid model explanations.

[0376] Figures 29-39 illustrate various example explainable insights that may be included as an attribution data entry in an attribution dataset as described herein. For example, with reference to Figure 29, an attribution data entry of an attribution dataset may include data of and / or visualization of a pour schedule 2900 associated with a material. Additionally, or alternatively, with reference to Figure 30, an attribution data entry of an attribution dataset may include data of a pour geometry 3000. In such embodiments, Figure 30 illustrates an explainable insight in the form of a counterfactual analysis, where a causal relationship between geometry and output strength is demonstrated (e.g.. what happens if the pour has a different geometry).

[0377] Additionally, or alternatively, with reference to Figure 31, an attribution data entry of an attribution dataset may include data of a pour geometry 3100. In such embodiments, a slider associated with a plot of concrete strength versus time during curing may generate commentary such as “You are likely to reach this strength at time T. ”, “You are likely to reach peak temperature at time T” , and / or the like as an explainable insight for an attribution dataset.

[0378] Additionally, or alternatively, with reference to Figure 32, an attribution data entry of an attribution dataset may include outputs 3200 of a model associated with a material. In such embodiments, Figure 32 illustrates a causal relationship between inputs and outputs that may inform the explainability of a model. Furthermore, an attribution dataset may include anequation that a model uses to model a material (e.g., f = a * log(cement) - b * (w / c) + c * sqrt(age): Meaning: f = a * log(cement content) - b * (water-to-cement ratio) + c * sqrt(concrete age since pour was poured), where f is a desired material property being modeled)

[0379] Additionally, or alternatively, with reference to Figure 33, an attribution data entry of an attribution dataset may include a graph 3300 that represents the importance of a plurality of features (e g., cement content, water-cement ratio, curing time, and / or the like) of a material. Additionally, or alternatively, with reference to Figure 34, an attribution data entry of an attribution dataset may include a graph 3400 that includes a plurality of thresholds that may be used to generate explainability inferences (e.g., “if a value is in this threshold, then your mix is X”). Further, the graph 3400 may be used to show confidence intervals around the associated data that may be included as an attribution data entry.

[0380] Additionally, or alternatively, with reference to Figure 35, an attribution data entry of an attribution dataset may include an output 3500 of a mix prediction model as described herein. In such embodiments, with respect to the top visualization, a pour schedule of a material is illustrated, where each line in the Gantt chart may a different pour that may be performed. Further, using the model, the time it requires for multiple pours to reach strength milestone and overall, how much time it should take in planning may be simulated for various mixes. From the simulation, the one that yields the optimal combination of time, cost, carbon, and / or the like may be chosen. With respect to the bottom visualization, an example weather forecast is illustrated, where the pour schedule prediction may be performed incorporating weather forecast data. As such, the output 3500 may be used to generate attribution data entries and / or explainable insights related to pour schedules (e.g., “This pour takes longer than the other pours to cure even though they 're all the same mix due to an expected weather drop on that day").

[0381] Additionally, or alternatively, with reference to Figure 36, an attribution data entry of an attribution dataset may' include a graph 3600. In such embodiments, the graph 3600 may be representative of clustering data associated with explainability of a model and / or module. Additionally, or alternatively, with reference to Figure 37, an attribution data entry' of an attribution dataset may include a graph 3700 of a plurality of mixes. In such embodiments, the graph 3700 may be of property one of a mix versus property two of a mix to compare the behavior of different mixes of a material with respect to these properties. Further, such a graph may be an output of a module and may be used to generate explainable insights associated with another output of another module. Additionally, or alternatively, with reference to Figure 38, an attribution data entry of an attribution dataset may include a graph 3800. In suchembodiments, the graph 3800 may illustrate how an output of a model fits to data (e.g., data generated by a sensor). Further, such a graph may be an output of a module and may be used to generate explainable insights associated with another output of another module. Additionally, or alternatively, with reference to Figure 39, an attribution data entry of an attribution dataset may include a graph 3900. In such embodiments, the graph 3900 may illustrate a variation of an output of a model output or module based on a variation of the weights (e.g., a causal relationship between weights and output) generating an explainable insight into the model.Explainable and Interpretable Mix Al Models

[0382] Embodiments of the present disclosure may include a plurality of categories of Mix artificial intelligence (Al) models. Broadly, there are at least four categories of Mix Al models, classified by the meaning and utility7of their outputs considered herein. The categories of Mix Al models may include mix prediction models (e.g., a model configured to predict material attributes of a concrete mix design when poured into a specific element geometry7under specified environmental conditions), mix selection models (e.g. a model configured to use outputs from mix prediction models, evaluated across a range of predefined mix recipes, to identify the most appropriate recipe for a given real-world use case), mix optimization models (e.g., a model configured to modify the constituents of existing mix designs to optimize for user-defined constraints on material attributes, such as curing time, cost, strength, and / or the like), and / or recipe generation models (e.g., a model configured to generate entirely new mix recipes (without using an existing baseline) to satisfy input constraints such as cost, environmental impact, required performance, and / or the like). Further, each of the aforementioned Mix Al model categories may be implemented using empirical, physics-based, or hybrid approaches.Material Prediction Models

[0383] Material prediction models and / or associated methods herein may include any model that generates data and / or datasets indicative of and / or associated with one or more properties of a material including material identifiers material properties, contextual material properties, static material properties, compositional properties and / or the like. Prediction modules may include any subcomponent of any such model, including subcomponents that may be used in whole or in part in the dataset generation step. Without loss of generality, the prediction models herein may take in as input and / or outputs any combination of data objectsand / or types herein and generate first datasets, second datasets, and / or attribution datasets associated with any of these examples. Additionally, or alternatively, the models herein may also generate an attribution dataset

[0384] Additionally, or alternatively, in some embodiments, a material prediction model may ingest data indicative of material composition (e.g., proportions of cement, water, aggregates, and admixtures), generate data indicative of one or more material properties (e.g., compressive strength, slump, setting time), and output an attribution dataset. The attribution dataset may include, for example, that increasing the fly ash content by 10% reduced the predicted strength by 3 MPa relative to a baseline mix composition defined by average values from the training data.

[0385] Additionally, or alternatively, in some embodiments, the model may ingest material composition along with contextual conditions, such as ambient temperature, element geometry, and wind speed, and generate data indicative of early-age thermal evolution. The attribution dataset may include a time-aligned saliency map highlighting that ambient temperature during the first 12 hours after casting most strongly influenced predicted maximum internal temperature.

[0386] Additionally, or alternatively, in some embodiments, the model may ingest first data indicative of a material’s composition, such as proportions of cement, water, aggregates, supplementary cementitious materials (SCMs), admixtures, and fibers, along with data indicative of one or more production or processing parameters associated with the material’s preparation. In the context of cementitious mixes, such processes may include batching, mixing, transport, placement, and early curing procedures. Process or production parameters may include, but are not limited to, mixing time, mixing speed, sequence of material addition, water addition method, mixing temperature, ambient conditions during mixing, truck rotation speed, delay time before placement, and duration of rest penods in staged mixing. The model may generate second data indicative of one or more material properties or behaviors, such as initial slump, temperature evolution, setting time, hydration rate, or segregation risk. The attribution dataset may include, for example, an influence ranking table showing that mixing temperature and sequence of admixture addition were the most significant contributors to predicted workability loss, or that excessive delay before placement had a strong negative effect on setting behavior.

[0387] Additionally, or alternatively, in some embodiments, the model may ingest a material identifier, such as a predefined mix code or class label (e.g., "‘Mix C40-F”) and generate an associated property, such as air content or modulus of elasticity. The attributiondataset may include a table indicating the internal embedding dimensions most responsible for driving the prediction, with interpretation tied to specific encoded features (e.g., SCM dosage or w / c ratio).

[0388] Additionally, or alternatively, in some embodiments, the model may ingest a mix identifier and contextual data (e.g., slab geometry', curing method, ambient weather), and predict performance outcomes such as thermal cracking risk or rate of strength development. The attribution dataset may take the form of a directed acyclic graph tracing the influence of specific input variables, such as "slab thickness" and "wind speed", through intermediate latent variables to the final risk score.

[0389] Additionally, or alternatively, in some embodiments, the model may ingest a material identifier and generate predicted composition parameters such as binder proportions or additive content. The attribution dataset may include a symbolic rule set, e.g., ‘'if strength class is > C50 and slump class is S5, then fly ash content is likely > 15%”, with associated confidence scores.

[0390] Additionally, or alternatively, in some embodiments, the model may ingest a property like thermal conductivity along with contextual inputs such as cunng setup and element orientation, and output performance data such as drying rate or internal temperature peak. The attribution dataset may include interaction effects, indicating that high thermal conductivity only significantly affects drying time when insulation is absent.

[0391] Additionally, or alternatively, in some embodiments, the model may ingest a property such as 7-day compressive strength and predict another property such as long-term shrinkage risk. The attribution dataset may be a compact attribution vector, showing relative sensitivities of the prediction to changes in the input property, e.g., "a 1 MPa increase in 7-day strength increases shrinkage risk score by 0.2".

[0392] Additionally, or alternatively, in some embodiments, the model may ingest material measurement data such as time series of in-situ temperature data and predict future strength evolution. The attribution dataset may include a segment-wise attribution table indicating that the temperature profile between 10-16 hours after casting contributed most significantly to the predicted rate of strength gain.

[0393] Additionally, or alternatively, in some embodiments, the model may ingest material measurement data such as sensor data, e.g. real-time impedance measurements, and generate predictions for a property such as current strength. The attribution dataset may include saliency over the impedance spectrum, indicating that signal variation in the 1-5 kHz range had the greatest impact on predicted strength.

[0394] Additionally, or alternatively, in some embodiments, the model may ingest material measurement data such as test result data (e.g., measured slump, compressive strength, and set time), and output a likely material identifier identifying the material under measurement (e.g., “Mix Type B with low-carbon binder"). In some embodiments the material measurement data may be multi-modal e.g. may include datastreams from EMI, electrochemical impedance spectroscopy, temperature and / or other such sensing techniques. The attribution dataset may include a latent space proximity map showing which reference mixes in the training data were closest in the learned representation, enabling similarity-based explanations.

[0395] As an example, an output of a prediction model (e.g., a first data entry of a first dataset, a second data entry of a second dataset, and / or the like) may be a data visualization such as a graph. As shown in Figure 40, an output 4000 may be a graph of a predicted concrete temperature versus time during curing. In such embodiments, the output 4000 illustrates the evolution of temperature of a concrete pour as the concrete cures. Additionally, as shown in Figure 41, an output 4100 may be a graph of predicted time taken to reach a specific strength (e.g., 35 MPa) versus time (e.g., over a year) for a material mix. In such embodiments, the output 4000 illustrates predictions of the variance in the amount of time required to reach a specific strength milestone at specific times during a year. Additionally, as shown in Figure 42, an output 4200 may be a graph of impedance versus frequency. In such embodiments, the output 4200 may illustrate a prediction of impedance associated with any of the devices as described herein.Material...

Claims

1. CLAIMS:

1. A computer-implemented method for explainable material models, the method comprising: ingesting, by a model, a first dataset comprising one or more first data entries associated with a material; generating, using the model, a second dataset comprising one or more second data entries associated with one or more properties of the material: and generating an attribution dataset comprising one or more attribution data entries, wherein the attribution dataset is indicative of an influence or causal relationship associated with the model.

2. The method of claim 1, wherein the attribution dataset is indicative of an influence or causal relationship between the first dataset and the second dataset.

3. The method of claim 1, further comprising: outputting the second dataset; and / or outputting the attribution dataset.

4. The method of claim 1, further comprising: parsing, via a large language model (LLM), the attribution dataset to generate a trained LLM; providing, via a network interface, a graphical user interface (GUI) to a user; receiving, via user input into an interactable environment on the GUI and via the network interface, a user query associated with the one or more properties of the material; and providing, via the network interface and using the trained LLM, a response to the user query'.

5. The method of claim 1, further comprising: ingesting a first weight set comprising one or more first weight entries associated with the first dataset; encoding the first dataset to generate a first transformed dataset; andgenerating, using the first weight set and the first transformed dataset, the second dataset.

6. The method of claim 5, further comprising: generating, for each first weight entry of the one or more first weight entries, a ty pe associated with a degree of freedom associated with the first weight entry to generate a first typed weight set; and storing the first typed weight set.

7. The method of claim 6, further comprising: analyzing the second dataset and the first typed weight set to derive a first conclusion; and generating the attribution dataset comprising the first conclusion.

8. The method of claim 6, the method further comprising: analyzing a first entry of the typed weight set to determine an agentic model of a plurality of agentic models associated with a type of the first entry; perturbing, via the agentic model, a weight of the first entry7to generate a perturbed second data entry7; comparing, via the agentic model, an associated second data entry of the one or more second entries and the perturbed second data entry7to generate a second data entry comparison; and generating the attribution dataset comprising the second data entry7comparison.

9. The method of claim 6, further comprising analyzing a data entry of the first dataset to determine an agentic model of a plurality^ of agentic models associated with a ty pe of the data entry7; perturbing, via the agentic model, a value of the data entry7to generate a perturbed second data entry7; comparing, via the agentic model, an associated second data entry7of the one or more second data entries and the perturbed second data entry to generate a second data entry7comparison; and generating the attribution dataset comprising the second data entry comparison.

10. The method of claim 6. further comprising analyzing a data entry of the first dataset and a first entry of the typed weight set to determine an agentic model of a plurality of agentic models associated with a type of the data entry and a type of the first entry: perturbing, via the agentic model, a value of the data entry' and a weight of the first entry to generate a perturbed second data entry; comparing, via the agentic model, an associated second data entry and the perturbed second data entry' to generate a second data entry comparison; and generating the attribution dataset comprising the second data entry' comparison.

11. The method of claim 5, further comprising: identifying a data cluster within the first dataset; generating one or more causal features associated with the data cluster; and generating the attribution dataset comprising the one or more causal features.

12. The method of claim 5. further comprising: ingesting a first subset of the first dataset to generate the second dataset; and generating, using the second dataset and a second subset of the first dataset, an attribution data entry of the one or more attribution data entries comprising an interpretation of the second dataset in a context of the second subset, wherein the first subset and the second subset are absent shared first data entries.

13. The method of claim 5. further comprising: varying a first data entry of the one or more first data entries to generate a varied first dataset; generating, using the varied first dataset, a varied second dataset comprising the second dataset with a change in at least one second data entry' of the one or more second data entries; and generating a continuous function mapping comprising the varied first data entry and the at least one second data entry'.

14. The method of claim 5, further comprising: perturbing, for each first weight entry of the one or more first weight entries, a first weight entry to generate a perturbed first weight set;generating, for each perturbed first weight entry of the perturbed first weight set, a perturbed second dataset comprising one or more perturbed second data entries; comparing the second dataset to each perturbed second data entry of the perturbed second dataset; identifying, via the comparison, a redundant weight of the one or first weights; and pruning the redundant weight from the first weight set.

15. A computer-implemented method for explainable material models, the method comprising: ingesting, by a model comprising at least two modules, a first dataset comprising one or more first data entries associated with a material; generating, via ingestion of a first input comprising a first subset of the one or more first data entries in a first module of the at least two modules, a first output associated with a first property of the material; and generating, via ingestion of a second input comprising a second subset of the one or more first data entries in a second module of the at least two modules, a second output associated w ith a second property of the material, wherein a modularity of the model is associated with an influence or causal relationship.

16. The method of claim 15, wherein the influence or causal relationship is indicative of a relationship between: the first dataset and the first output; the first dataset and the second output; the first input and the second output; and / or the first output and the second output.

17. The method of claim 15, the method further comprising: generating an attribution dataset comprising one or more attribution data entries associated with the influence or causal relationship between the first property' and the second property.

18. The method of claim 17, the method further comprising:ingesting a first weight set comprising one or more first weight entries associated with the first dataset; encoding the first dataset to generate a first transformed dataset; and generating, using the first weight set and the first transformed dataset, the first output.

19. The method of claim 18, the method further comprising: generating, for each first weight entry of the one or more first weight entries, a type associated with a degree of freedom associated with the first weight entry to generate a first typed weight set; and storing the first typed weight set.

20. The method of claim 19, the method further comprising: analyzing the second output and the first typed weight set to derive a first conclusion; and generating the attribution dataset comprising the first conclusion.

21. The method of claim 19, the method further comprising: analyzing a first entry of the typed weight set to determine an agentic model of a plurality of agentic models associated with a type of the first entry; perturbing, via the agentic model, a weight of the first entry to generate a perturbed first output; comparing, via the agentic model, the first output and the perturbed first output to generate a first output comparison; and generating the attribution dataset comprising the first output comparison.

22. The method of claim 19, the method further comprising: analyzing a data entry7of the first dataset to determine an agentic model of a plurality of agentic models associated with a type of the data entry; perturbing, via the agentic model, a value of the data entry7to generate a perturbed first output; comparing, via the agentic model, the first output and the perturbed first output to generate a first output comparison; and generating the attribution dataset comprising the first output comparison.

23. The method of claim 19, the method further comprising: analyzing a data entry of the first dataset and a first entry of the typed weight set to determine an agentic model of a plurality of agentic models associated with a type of the data entry and a type of the first entry: perturbing, via the agentic model, a value of the data entry' and a weight of the first entry to generate a perturbed first output; comparing, via the agentic model, the first output and the perturbed first output to generate a first output comparison; and generating the attribution dataset comprising the first output comparison.

24. The method of claim 18, the method further comprising: identifying a data cluster within the first dataset; generating one or more causal features associated with the data cluster; and generating the attribution dataset comprising the one or more causal features.

25. The method of claim 18. the method further comprising, when generating the first output: ingesting an output of the first module in a first intermediate module; and generating, via an output of the first intermediate module, the first output.

26. The method of claim 25, wherein the attribution dataset comprises an uncertainty measurement associated with the output of the model, and wherein the method further comprises: identifying a module out of the first module, the first intermediate module, and the second module with a higher contribution to the uncertainty measurement; and generating an attribution data entry' of the one or more attribution data entries comprising data indicating the module identified with the higher contribution.

27. The method of claim 25, wherein the first intermediate module is a first module of N intermediate modules and wherein N is a positive integer number.

28. The method of claim 27, wherein an Ithintermediate module of the N intermediate modules is configured to receive an output of an ( / - 1) intermediate module of the / Vintermediate modules, and wherein an Nlhintermediate module of the N intermediate modules is configured to generate the first output.

29. The method of claim 18, the method further comprising: ingesting a first subset of the first dataset to generate the first output; generating, using the first output and using the second module, the second output; and generating, using the second output and a second subset of the first dataset, an attribution data entry of the one or more attribution data entries comprising an interpretation of the second output in a context of the second subset, wherein the first subset and the second subset are absent shared first data entries.

30. The method of claim 18, the method further comprising: varying a first data entry of the one or more first data entries to generate a varied first dataset; generating, using the varied first dataset, a varied first output; generating, using the varied first output and the second module, a varied second output; and generating a continuous function mapping comprising the varied first data entry and the varied second output.

31. The method of claim 18, the method further comprising: perturbing, for each first weight entry of the one or more first weight entries, a first weight entry to generate a perturbed first weight set; generating, for each perturbed first weight entry of the perturbed first weight set and using the first module, a first output set comprising one or more first output entries; comparing the first output to each first output entry of the first output set; identifying, via the comparison, a redundant weight of the one or first weights; and pruning the redundant weight from the first weight set.

32. The method of claim 18, the method further comprising: generating a plurality of first w eight groups each comprising at least two first w eight entries of the one or more first weight entries; generating, for each first weight group of the plurality of first weight groups and using the first module, a first output set comprising one or more first output entries;comparing the first output to each first output entry of the first output set; identifying, via the comparison, a redundant weight group of the plurality of first weight groups; and pruning the redundant weight group from the first weight set.

33. The method of claim 15, wherein the material is a cementitious mixture.

34. The method of claim 33, wherein the output comprises a data visualization of data indicating a relationship between compressive strength of the cementitious mixture and a time to cure for the cementitious mixture.

35. The method of claim 33, wherein the output comprises a prediction of time required to reach a compressive strength value for the cementitious mixture.

36. The method of claim 35, wherein the prediction is based on environmental conditions associated with a location and a time of year associated with the cementitious mixture.

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