Systems and methods for material-related determination models

Abstract

Systems, computer program products, and methods are described herein for material- related determination models. With reference to an example method, the method receives a first dataset including one or more first data entries associated with a material, generates a second dataset including one or more second data entries associated with the material, and outputs the second dataset associated with the material. The one or more first data entries include a material identifier, and generating the second dataset includes providing material identifier data and material composition data to an artificial intelligence (AT) model, simulating the material composition data in a first set of contextual conditions, generating one or more material properties, via the simulation, of the material in the first set of contextual conditions, and generating the second dataset including one or more second data entries associated with the one or more material properties for the material.

Description

SYSTEMS AND METHODS FOR MATERIAL-RELATED DETERMINATION MODELS CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present international application claims priority to U.S. Provisional Patent Application No. 63 / 544,091, filed October 13, 2023, U.S. Provisional Patent Application No. 63 / 605,990, filed December 4, 2023, U.S. Provisional Patent Application No.63 / 663,989, filed June 25, 2024, U.S. Provisional Patent Application No. 63 / 669,054, filed July 9, 2024, and U.S. Provisional Patent Application No.63 / 670,047, filed July 11, 2024, the entire contents of which applications are incorporated by reference in their entirety. TECHNOLOGICAL FIELD

[0002] Embodiments of the present disclosure relate generally to materials and, more particularly, to systems and methods for material-related determination models. BACKGROUND

[0003] Materials of various types (e.g., crystalline materials, amorphous materials, etc.) are used in a wide variety of applications, such as battery chemistry, semiconductor manufacturing, building construction, and / or the like. Given the various material properties, performance, composition, and / or the like associated with these materials and the potential for one or more of these characteristics to vary with time and / or context (e.g., material properties of a material in a first environment versus material properties of the material in a second environment), accurate determinations and modeling of these characteristics may impact successful implementations of these materials. Through applied effort, ingenuity, and innovation, many of the problems associated with conventional material determination methods and systems 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 material-related determination models.

[0005] In one aspect, a computer-implemented method for material related determinations may include receiving a first dataset including one or more first data entries associated with a material, generating a second dataset including one or more second data entries associated with Page 1 of 226 13824520v1the material, and outputting the second dataset associated with the material. In some embodiments, the one or more first data entries may include a material identifier. Further, the method may include accessing a database storing material identification data associated with a plurality of material identifiers and determining material composition data associated with the material identifier.

[0006] In some embodiments, generating the second dataset may include providing the material identifier data and the material composition data to an artificial intelligence (AI) model, simulating, via the AI model, the material composition data in a first set of contextual conditions, generating one or more material properties, via the simulation, of the material in the first set of contextual conditions, and generating the second dataset including one or more second data entries associated with the one or more material properties for the material.

[0007] In some embodiments, the one or more first data entries may include a material identifier and material properties in a first set of contextual conditions. Further, the method may include accessing a database storing material identification data associated with a plurality of material identifiers and determining material composition data associated with the material identifier. Additionally, or alternatively, generating the second dataset may include providing the material identifier data, the material properties in the first set of contextual conditions, and the material composition data to an artificial intelligence (AI) model, simulating, via the AI model, the material composition data in a second set of contextual conditions, generating one or more material properties, via the simulation, of the material in the second set of contextual conditions, and generating the second dataset including one or more second data entries associated with the one or more material properties for the material in the second set of contextual conditions.

[0008] In some embodiments, the one or more first data entries may include material property data in one or more sets of contextual conditions. Further, generating the second dataset may include providing the material property data in one or more sets of contextual conditions to an artificial intelligence (AI) model, simulating, via the AI model, the material property data, generating one or more material identifiers, via the simulation, corresponding to the material property data, and generating the second dataset including one or more second data entries associated with the one or more material identifiers. Additionally, or alternatively, the one or more generated material identifiers may include one or more material identifiers stored in a database. Additionally, or alternatively, the one or more generated material identifiers may include one or more candidate material identifiers, where the one or more candidate material identifiers may be absent from a database, and where the method further Page 2 of 226 13824520v1includes generating a plurality of material composition data for each candidate material identifier of the one or more candidate material identifiers and generating the second dataset including one or more additional second data entries associated with the plurality of material composition data for each candidate material identifier.

[0009] In some embodiments, the method may further include generating a compositional arrangement for the plurality of material composition data for each candidate material identifier of the one or more candidate material identifiers, where the compositional arrangement may include a sequence of chemical equations for each of the candidate material identifiers. Additionally, or alternatively, the compositional arrangement for each candidate material identifier may include one or more method sequences for manufacturing the candidate material identifier.

[0010] In some embodiments, generating the second dataset may include providing data to an artificial intelligence (AI) model, simulating, via the AI model, the data, generating, via the simulation, one or more data elements, and generating the second dataset including one or more second data entries associated with the one or more data elements. Additionally, or alternatively, a plurality of data entries of the one or more first data entries of the first dataset may be generated by one or more sensor devices. Further, the material may include an ordered, periodically repeating atomic structure. Additionally, or alternatively, the material may lack an ordered, periodically repeating atomic structure.

[0011] In another aspect, a computer-implemented method for training a material-related determination model may include receiving a training dataset including one or more training data entries associated with a plurality of materials, adjusting one or more model parameters due to the training dataset, and outputting an updated material-related determination model. In some embodiments, the one or more training data entries may include material composition data for the plurality of materials, material property data for the plurality of materials, manufacturing process data for the plurality of materials, and material context data for the plurality of materials. Additionally, or alternatively, the method may include evaluating the training dataset for missing training data entries of the one or more training data entries, executing, if the training dataset includes at least one missing training data entry, one or more material simulations via an AI model, and updating the at least one missing training data entry of the training dataset via the one or more material simulations.

[0012] In some embodiments, the method may further include providing a first material- related determination model to a first environment and a second material-related determination model to a second environment, generating first environment data and second environment Page 3 of 226 13824520v1data, adjusting one or more model parameters of the first material-related determination model due to the generated first environment data and one or more model parameters of the second material-related determination model due to the generated second environment data, and aggregating the one or more adjusted model parameters of the first material-related determination model and the one or more adjusted model parameters of the second material- related determination model to the material-related determination model.

[0013] 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

[0014] 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.

[0015] Figure 1 illustrates an example system for material-related determinations in accordance with an example embodiment of the present disclosure;

[0016] Figure 2 illustrates a block diagram of example circuitry (e.g., server circuitry) that may be specifically configured in accordance with one or more example embodiments of the present disclosure;

[0017] Figure 3 illustrates a flowchart for an example method for a material-related determination model in accordance with some embodiments of the present disclosure;

[0018] Figure 4 illustrates a flowchart for an example method for determining material composition data for a material identifier in accordance with some embodiments of the present disclosure;

[0019] Figure 5 illustrates a flowchart for an example method for artificial intelligence (AI) model generation of material properties (e.g., material prediction) in accordance with some embodiments of the present disclosure; Page 4 of 226 13824520v1

[0020] Figure 6 illustrates a flowchart for an example method for determining material composition data for a material identifier in accordance with some embodiments of the present disclosure;

[0021] Figure 7 illustrates a flowchart for an example method for AI model generation of material properties (e.g., material prediction) in accordance with some embodiments of the present disclosure;

[0022] Figure 8 illustrates a flowchart for an example method for AI model generation of material identifiers (e.g., material generation) in accordance with some embodiments of the present disclosure;

[0023] Figure 9 illustrates a flowchart for an example method for generating material composition data (e.g., material generation) in accordance with some embodiments of the present disclosure;

[0024] Figure 10 illustrates a flowchart for an example method for AI model generation of data elements in accordance with some embodiments of the present disclosure;

[0025] Figure 11 illustrates a flowchart for an example method for training a material- related determination model in accordance with some embodiments of the present disclosure;

[0026] Figure 12 illustrates a flowchart for an example method for updating a training dataset in accordance with some embodiments of the present disclosure;

[0027] Figure 13 illustrates a flowchart for an example method for a federated learning strategy for a material-related determination model in accordance with some embodiments of the present disclosure;

[0028] Figure 14 illustrates a flowchart for an example method for using a material-related determination model for predictions in accordance with some embodiments of the present disclosure;

[0029] Figure 15 illustrates another flowchart for an example method for using a material- related determination model for predictions in accordance with some embodiments of the present disclosure;

[0030] Figure 16 illustrates another flowchart for an example method for using a material- related determination model for predictions in accordance with some embodiments of the present disclosure;

[0031] Figure 17 illustrates another flowchart for an example method for using a material- related determination model for predictions in accordance with some embodiments of the present disclosure; Page 5 of 226 13824520v1

[0032] Figure 18 illustrates another flowchart for an example method for using a material- related determination model for predictions in accordance with some embodiments of the present disclosure;

[0033] Figure 19 illustrates another flowchart for an example method for using a material- related determination model for predictions in accordance with some embodiments of the present disclosure;

[0034] Figure 20 illustrates a flowchart for an example method for a material-related determination model for evaluating materials in accordance with some embodiments of the present disclosure;

[0035] Figure 21 illustrates another flowchart for an example method for a material-related determination model for evaluating materials in accordance with some embodiments of the present disclosure;

[0036] Figure 22 illustrates another flowchart for an example method for a material-related determination model for evaluating materials in accordance with some embodiments of the present disclosure;

[0037] Figure 23 illustrates a flowchart for an example method for a material-related determination model for optimizing materials in accordance with some embodiments of the present disclosure;

[0038] Figure 24 illustrates a flowchart for an example method for a material-related determination model for generating materials in accordance with some embodiments of the present disclosure;

[0039] Figure 25 illustrates another flowchart for an example method for a material-related determination model for generating materials in accordance with some embodiments of the present disclosure;

[0040] Figure 26 illustrates another flowchart for an example method for a material-related determination model for generating materials in accordance with some embodiments of the present disclosure; and

[0041] Figure 27 illustrates a flowchart for an example method for a material-related determination model for generating a compositional arrangement in accordance with some embodiments of the present disclosure. Page 6 of 226 13824520v1DETAILED DESCRIPTION Overview

[0042] 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.

[0043] The present disclosure is directed to software and / or AI-implemented systems and methods for material property prediction, material selection, material optimization, and / or material generation. In some embodiments, the software and / or AI-implemented methods described herein may include the use of a sensor device. For example, the methods may include the use of a sensor device to gather data associated with a material, in some cases, the material being the material under consideration, or a material similar and / or associated with the material under consideration. The sensors may, for example, be photonic sensors, mechanical sensors, wave-based sensors, and / or the like. In some embodiments, photonic sensors and / or hyperspectral sensors may be used to gather information associated with the compositional material properties of materials. The sensors described herein may be installed at different stages of a material's lifecycle (e.g., a finished product and the performance of the finished product, raw materials, and / or during material production).

[0044] The present disclosure may be applicable to any material where a material may be understood in the common meaning of the word and / or may define an instance of a substance. In some embodiments, a material may generally be in a given state or phase, for example in a solid, liquid, gaseous, plasma, Bose-Einstein condensate state, and / or any other state understood as such by one of ordinary skill in the art in view of the present disclosure. Further, a material may undergo a state and / or phase transition in which the material may be actively transitioning between any two states. The methods of the present disclosure may apply to any such material in any such state and / or state transition. For example, the properties of a material as it undergoes a phase transition from liquid to solid may be predicted. Another embodiment may include generating a material design for a material in its solid, liquid, and / or gaseous forms, for a given use case and / or given target properties. In such embodiments, the model may predict the melting and / or boiling points of the material as one of the material properties, accounting for variables including temperature, pressure, and / or the like. Further, the model may use different methods to simulate and / or predict properties of materials in different states, Page 7 of 226 13824520v1as well as different internal representations to define the material's compositional properties. For example, a material may take the form of a crystal in solid form but may be amorphous in liquid form. Another embodiment may include predicting the properties of a given plasma. Another embodiment may include selecting a material from a predetermined list of materials for a given use case. Another embodiment may include inputting an existing material and generating an optimized version of the material according to some target use case or property or other objective function.

[0045] Embodiments of the present disclosure may further describe matter in a subset of these states, but it is to be understood that the methods herein are not restricted to only those materials that are further described. In some embodiments, examples of materials and / or material types for which the methods of the present disclosure may be applicable may include, but are not limited to, mixtures and / or compounds, mixes and / or composites, solutions, pure elements, crystals, metals, alloys, polymers (e.g., plastics, rubbers, elastomers, and / or the like), organic compounds, fertilizers, biomaterials, cementitious materials, edible materials (e.g., foods), ceramics papers, woods, minerals and / or stones, fuels, semiconductors, electronic materials, superconductors, textiles, glasses, transducer materials (e.g., any material that converts energy from one form to another), piezoelectric materials, magnetostrictive materials, electrochromic materials, materials used in electrical energy generation (e.g., materials involved in batteries and supercapacitors), photonic materials, nanomaterials, meta-materials, magnets and / or magnetic materials (e.g., ferromagnetic, paramagnetic, diamagnetic, and / or the like), insulators, dielectrics, fibers, aerogels and / or foams, nuclear materials, materials for chemicals products, materials for computer and / or electronics products, materials for petroleum and / or coal products, materials for microchips and / or semiconductors, powders, catalysts, batteries, metal organic frameworks materials (MOF), proteins, enzymes, and / or the like.

[0046] In some embodiments, solids may broadly be categorized into crystals, quasi- crystals / semi-crystals / polycrystals, and / or amorphous solids. Further, crystals may be described as highly ordered materials, including a unit cell that is repeated periodically over extended regions with the same orientation. In some embodiments, amorphous solids do not include a regular repeating structure, though particles, atoms, molecules, and / or the like may be principally static in nature. Additionally, and / or alternatively, quasi-crystals and / or semi- crystals may denote materials in between crystals and amorphous solids, which may include crystalline regions as well as non-crystalline / amorphous regions, and / or regions with varying degrees of crystallinity. One example may be polycrystalline materials. Polycrystals may be Page 8 of 226 13824520v1described as materials including many individual crystallites of varying sizes and orientation, where crystallites (also referred to as grains) may have periodic, ordered structure.

[0047] In some embodiments, the models described herein may use the degree of crystallinity as a measure of the crystalline structure of materials, which may determine the internal representations through which a given material may be defined in the models. For example, perfect crystals may be defined internally through a geometrical representation of their unit cell, whilst amorphous structures may be defined using statistical methods and distributions, and materials in between may be defined using a combination of both.

[0048] In some embodiments, crystals may be defined according to the atoms and spatial distribution in 3D of their unit cells. In some embodiments, defects may be artificially or naturally occurring in crystal structures. These may be defined according to the spatial configuration and structural changes that may be induced by these defects, as well as through the chemical equations / nomenclature for these defects, and a measure associated with the occurrence rate of these defects (e.g., one in every million unit cells or other measures indicatives of how often these defects occur in numbers, volume, weight, density, and / or the like). Defects may often be introduced into crystalline structures in a process denoted doping, which may be used to enhance one or a plurality of crystal's properties. This may often be done with relation to semiconductors. In some embodiments, the methods herein may include generating a crystalline structure design that may include doping defects to enhance a property. In some embodiments, the generated design may include the defect. Without loss of generality, the functions of the generative models described herein may have equivalent and / or associated features for predictive models and / or any other model herein. For example, a predictive model may be used to predict properties of pure crystal, followed by which the properties resulting from the introduction of a doping defect may also be predicted. Additionally, or alternatively, the predictive model may predict the properties of doped crystals to begin with. In other embodiments, the method may generate the design for a pure crystal followed by a design adjustment that may include doping.

[0049] In some embodiments, non-crystalline materials and / or amorphous materials may be defined internally by the models described herein through statistical means, drawing from statistical physics and statistical mechanics, through the description of probability distributions describing ensembles of particles, atoms, molecules / any other constituents existing in different states. This may also be related to thermodynamic properties and statistical thermodynamic consideration of materials (e.g., potential energy, kinetic energy, internal energy, heat, enthalpy, Gibbs free energy, entropy, temperature, pressure, volume, compressibility, Page 9 of 226 13824520v1isothermal compressibility, density, and / or the like). These states may denote energy states, entropy states, as well as any other such state as identified by one skilled in the art.

[0050] In some embodiments, the materials may be described internally in the described systems through radial distribution functions, for example, describing how atoms may be packed radially in a system. Methods for generating radial distribution functions may include the use of Ornstein-Zernike Equations, Percus-Yevick approximations, and / or Hypernetted Chain Theory based methods, as well as empirical AI based methods based on data indicative of E&M scattering of materials to detect particle distributions, and / or other methods that may be empirically measured using the methods described in wave-based sensing and / or using other sensor devices. In some embodiments, the models described herein may be used to create mappings or links between microscopic compositional information (e.g., microscopic compositional properties) to macroscopic properties (e.g., bulk properties). In some embodiments, these methods may use Kirkwood-Buff solution theory. Such methods may be used for chemical simulations and predictions in the models. The radial distribution function may be defined as ^^ ( ^^)^^ ^^ ^^( ^^)^^ ^^=^^ ^^ ^^ ^^ ^^^^ ^^, where this may apply for a system / material with components i and j rj, where ^^ may in some embodiments be a function ofthe difference between riand rj. These methods may also include the definition of structure factors, and partition functions (e.g., defined through the product or sum over a particle distribution, or the product or sum over integrals of distributions). In general, materials may be simulated by the models at any temperature, for any number of particles (e.g., atoms, molecules, ions, particles) N, comprising a volume V, and in any other contextual conditions e.g. forces and / or fields being applied onto the material such as gravitational, electromagnetic, weak and strong forces as well as forces in the mechanical sense of the term (e.g. forces from other objects), pressure. In some embodiments, generalized radial distribution functions are applicable to mixtures including many components, types of particles, structures, and / or the like, and may be used in these methods. In some embodiments, and for some materials, the models and methods herein may include using system symmetries to simplify calculations associated with the radial distribution function. In some embodiments, other distribution functions may be used to describe materials.

[0051] In some embodiments, statistical approaches may be used on macroscopic scales or microscopic and / or quantum scales to describe particle distributions. In some embodiments, the angular distribution function may be used in the models. In other embodiments, particularly relevant when considering quantum scales, the methods herein may employ the use of Page 10 of 226 13824520v1wavefunctions for defining particle distributions. This may involve the use of eigenstates and associated eigenvalues, as well as the definition of operators which may induce unitary evolutions onto wave functions. In some embodiments, a material's temporal evolution may be generated and / or predicted and / or simulated by one of the models, which may include the use of unitary operator-based methods. This may include generating internal representations for such operators in the models. Internal representations may in general take the form of tensors, matrices, vectors, and / or scalars. In some embodiments, operators may be represented through tensors and / or matrices, and evolution may be represented through tensor products and / or tensor-vector products. In some embodiments, the architecture of the model described herein may be designed for efficient tensor product computation, which may, in some embodiments, be done with the use of graphical tensor product methods and representations. In some embodiments, quantum simulation methods may be used, and quantum path integral simulations may be used for material simulations. Quantum-classical path integral methods may be used for material simulations, for example, when considering larger scales / volumes. In some embodiments, statistical methods may be used to determine distribution of particle / molecule states, as well as motion. In some embodiments, motion determination may include the use of Brownian motion simulation methods, random walks, quantum walks, quantum-classical walks, and / or other associated methods and techniques.

[0052] Prediction models as described herein may generally be used to predict and / or simulate the properties of materials based on compositional data associated with given materials. Input data may be a material identifier (e.g., name, categorization of material, and / or the like), and / or any other composition data mentioned herein (e.g., 3D model of cell unit, partition function for particle distributions, and / or the like). In some embodiments, a material identifier may be provided, and compositional data may be retrieved, in some cases from a database, and in other cases the models may integrate with other systems to actively seek compositional data. Additionally, and / or alternatively, the model may be integrated with GPT- type models which may be able to provide the compositional data.

[0053] In some embodiments, the models may also be used to simulate material behaviors in a given contextual condition. This may be done for quantum simulations as well as macroscopic simulations for bulk properties. Additionally, and / or alternatively, stability may also be predicted including through predictions of the convex hull.

[0054] In some embodiments, the predictive models may be able to take as input properties in one set of contextual conditions and output a prediction for properties in any other set of contextual conditions. Additionally, and / or alternatively, the models may take as an input a Page 11 of 226 13824520v1chemical industrial process and predict the output of that process (e.g., state of the output material, properties of the output material, etc.). In some embodiments, training of the models may include experimental and / or theoretical data for material identifiers, compositions, and / or properties.

[0055] In some embodiments, the models may be multi-modal models that may be configured to take textual, image, and / or other documentation formats as inputs, as well as compositional information, material properties, and real time information captured by sensors (e.g., of chemical spectra at varying frequencies, processed using Fourier methods and other methods herein). Sensor data may include geometrical / topological data associated with material structure, including molecular structure, unit cells, and quantum structures. This data may be captured through spectroscopy techniques and sensor devices, for example, Raman Spectroscopy, and X-Ray Crystallography based methods. Additionally, and / or alternatively, training data may include chemistry and materials engineering, quantum chemistry, and engineering documentation including textbooks and others. This may infuse existing physico- chemical understanding into the models herein.

[0056] In some embodiments, sensor data from any wave-based sensor devices herein or other devices may be used to capture composition / formulations as well as properties and use empirical data to create a mapping between the two. Experimental datasets may be labelled or unlabeled (e.g., the system may have a material identifier and its properties, but not its composition / formulation). The link between these two data sets may be loose or strong. For example, if properties and composition are monitored by a sensor device embedded in a material, the models may ascertain with a high level of confidence that the measured composition matches the measured properties. If a recipe or composition is provided in a digital record, and properties are measured using sensors in reality, it may be possible that the record may not accurately reflect the reality of the materials. In some embodiments, the models may use interpolation or generative methods to fill in the gaps. Additionally, and / or alternatively, models may use clustering methods to match compositions and properties with a higher degree of likelihood or confidence.

[0057] Additionally, and / or alternatively, physico-chemical simulations may also be used for training. These may include finite element analysis-based simulations, quantum simulations, density functional theory-based simulations, quantum-classical hybrid simulations, and other simulation methods. By ingesting simulated data, the model may make up for missing volumes of data. Page 12 of 226 13824520v1

[0058] Additionally, and / or alternatively, databases including material identifiers, material compositional data and material property data may be labelled and fed to the models herein alongside sensor data matched for material identifiers. In some instances, the database may be incomplete and generative methods may be used to fill in the gaps using likeliest predicted outcomes.

[0059] The outputs for this model may include a list of predicted property attributes in a given contextual condition (e.g., standard temperature or properties). Additionally, and / or alternatively, a spatio-temporal simulation showing the behavior of the material in a given simulated contextual condition may be output for any volume or weight of material. Additionally, and / or alternatively, a predicted list of properties and / or attributes may be variable for a range of contextual conditions (e.g., may be able to see how every property changes with changing temperature, including phase transitions, and / or 3D models of molecules and bonds stretching and elongating as temperature increases).

[0060] The models herein may employ statistical methods, machine learning, density functional theory, quantum simulations, physico-chemical models (in some cases infused into statistical or machine learning methods), and / or any other kind of methods herein to produce the output.

[0061] Material property prediction may be described as a set of methods which may output a plurality of data indicative of expected properties of a material based on first data indicative of a material. In some embodiments, first data indicative of a material may include data associated with the compositional material properties of a material and / or may include data associated with live features of a material, for example as measured by sensor devices.

[0062] As will be appreciated by one of ordinary skill in the art in view of the present disclosure, in some embodiments, the concepts and methods described herein may be described as generalizations of those described in mix optimization related techniques, but for any other material.

[0063] Generative models herein may be used to generate or discover a novel material design based on a given input. The generated material design may include any of the following types of information, including but not limited to compositional data associated with a given material, property data associated with a given material, and / or manufacturing instructions for a given material. In some embodiments, the model may take as inputs a prompt which may define target material objectives and / or use cases and / or desired properties. In some embodiments, if the initial prompt does not constrain the space of possible materials sufficiently, the model may converse with the user, asking questions until it has sufficient Page 13 of 226 13824520v1information. Additionally, and / or alternatively, the input may be a set / combination of desired properties defined as targets. These may be target parameters within the models. The model may then be tasked to generate a material that most closely matches these parameters and / or properties. Additionally, and / or alternatively, the model may take as an input the desired state of matter of the material at a given temperature or temperature range. Additionally, and / or alternatively, the model may take as an input what the desired type of material is (e.g. superconductor, semiconductor, and / or the like alternatively and additionally, material type may be defined through crystallinity (e.g., crystalline, semi-crystalline, polycrystalline, amorphous, etc.).

[0064] In some embodiments, a controlled physical environment may be designed including a predetermined numbers of available manufacturing chemical and / or raw materials, as well as a predefined set of plant and machinery, ovens, and other chemical or manufacturing equipment. This may define a universe of potential material manufacturing steps the model may be able to take that defines the set of possible instruction paths. For every material created by the model, an associated sequence of instructions from this predetermined set of steps or actions may be created. In some embodiments, this physical environment may be automated.

[0065] In some embodiments, the models define internal multi-dimensional vector spaces and / or complex spaces (e.g., Hilbert spaces) that may be used as representations of materials (e.g., material space). This may be a generalization of material space. The dimensionality of the space may be associated with the parameters defined by the model.

[0066] The models described herein may have different modes of use. In one mode, the models may be tasked with generating one or a candidate of potential materials given some objectives. In another mode, the models may be tasked with generating as many materials as possible. In some embodiments, the models may take constraints and / or objectives which may define the space of materials the models have been configured to discover or generate materials in. The space of materials may include material type (e.g., protein, polymer, and / or the like), or type based on structure (e.g., crystalline). Additionally, and / or alternatively, the space of materials may include desired properties or attributes. Additionally, and / or alternatively, the space of materials may include desired product part (e.g., the model may be set to discover new lithium-ion battery materials that may augment batteries). The models may have an internally embedded understanding of the requirements for what makes an effective battery (e.g., energy efficiency) and may therefore be able to output battery materials.

[0067] Additionally, and / or alternatively, the generative models may generate compositional arrangements based on desired properties. Additionally, and / or alternatively, the Page 14 of 226 13824520v1material may generate compositional arrangements based on desired use cases (e.g., material that would be good as a constituent of a building). The model may be able to translate this statement into associated internally embedded properties (e.g., large compressive strength and load bearing capacity).

[0068] In some embodiments, any of the models herein may be able to predict the uncertainty in a given material’s properties in reality, as well as variability in batches, production quality, purity, and / or the like. In some embodiments, training data from sensors may provide accurate characterizations of this variability such that the model may use empirical methods to generate expected uncertainty or variability based on real world data.

[0069] In some embodiments, machine learning and / or deep learning methods may be used. In some embodiment, different modes of the model may exist for different types of materials. Specialized models that may excel in generating semiconductors, glasses, battery components, and / or the like may include the generative methods herein. In one embodiment, an orchestrator model is able to select the best model mode to be used for a given input, for example if the input is a prompt saying, “design an optimal sustainable building material that can withstand sub-0°C temperatures”, the orchestrator model may choose a sub-model that may be specialized in cementitious mixes or SCMs.

[0070] Embodiments of the present disclosure may include any model, model type, AI model type, algorithm, algorithm type, and / or the to implement any of the methods herein in whole and / or in part. This may include any model described in any part of the present disclosure, for example, genetic algorithms, large language models, neural networks, physico- chemical models, graphical neural networks (and any other graph-based AI method), finite element analysis, density functional theory based methods, quantum neural networks, quantum chemical simulation methods, quantum variational eigen solver based methods, quantum- classical hybrid based methods, quantum fermionic Monte-Carlo simulations, generative methods, atomistic simulations, and / or the like.

[0071] In some embodiments, the methods may include gathering data associated with physical materials using wave-based sensing devices, where the wave-based sensing devices may be photonic devices used primarily for gathering compositional data, as well as mechanical and / or other E&M devices used primarily for gathering property data, including data associated with the behavior of materials in different contextual conditions. Further, the data may be used for training one or a plurality of AI models, where the models may predict properties and / or behaviors of materials in varying contextual conditions, select the optimal material from a predetermined set of materials based on a set of objective criteria or desired Page 15 of 226 13824520v1properties and / or parameters / attributes, adjust and / or optimize the composition of a given material to design an alternative optimal material based on a set of objective criteria and / or desired properties and / or parameters and / or attributes, and / or generate a new material composition designed with one or more of some desired properties and / or parameters and / or attributes, some desired behaviors in a given contextual condition, and / or an objective function for which the generated material is optimized.

[0072] In some embodiments, the methods herein include generating a mapping between material composition and properties and / or attributes. In some embodiments, these properties may be emergent properties.

[0073] In some embodiments, the methods herein include creating a compositional arrangement for a given material composition where the compositional arrangement may include a set of instructions for manufacturing the material. In some embodiments, the compositional arrangement may include steps to manufacture a material from raw constituents, where these steps may include the use of combustion ovens, mixers, electrolysis, and / or other processes involved in material creation. In some embodiments, the instructions may include a sequence of chemical reaction equations. Material Related Definitions

[0074] 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, etc.) that are combined together. A mixture may be homogenous in which the composition of the constituent parts are substantially uniform throughout. Alternatively, a mixture may be heterogenous in which the composition or proportion of the constituent parts varies 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 device, systems, methods, techniques, etc. described with reference to cementitious mixtures may be applicable to building materials, extracted materials, or industrial materials of any type without limitation.

[0075] As used herein, the terms “material formulation” and “material design” may be used interchangeably to refer to a proportion of constituent components, parts, or elements that form a material. In some embodiments, the material formulation may refer to a chemical composition of constituent components, parts, or elements forming the material. As described herein, for example, a cementitious material mixture may be formed of a cementitious material (e.g., Page 16 of 226 13824520v1Portland cement), water, aggregates (e.g., sand gravel limestone), admixtures, and / or the like. The relative proportion of these constituent components may be defined by the material formulations described herein. As described herein, the material formulation may refer to a target set of constituent component proportions of which any particular instantiation of that material formulation should be composed. In some embodiments, material designs may refer to proportions of constituent component parts associated with one or more targets for contextual material properties. In another embodiment, material 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 material formulation may include naturally variability in the proportions of constituent components for the same material formulation.

[0076] 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).

[0077] A mix formulation, and the batches, pours, building elements, etc. associated with the mix formulation, may further include various “material properties.” The term “material property” may refer to any physical or chemical attribute, characteristic, parameter, feature, etc. of the materials described herein. The material properties of a material may include one or more of static material properties, compositional material properties, contextual conditions, and / or contextual material properties as defined hereinafter. Although described herein with reference to an example framework for distinguishing between types or categories of material properties, for example static material properties vs. contextual material properties, the present disclosure contemplates that the devices, systems, methods, techniques, etc. 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.

[0078] 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- Page 17 of 226 13824520v1limiting 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.

[0079] As used herein, the terms “compositional material property” and “compositional property” 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). 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 provided by any relationship, proportionality, metrics, etc. 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), by raw material composition (e.g., concrete raw materials, as defined herein, or the like).

[0080] The compositional material properties of a material may further vary in time such that the above formulations described herein may further evolve in time. By way of example, a particular instantiation of a formulation (e.g., a batch or the like) may vary after creation of the instantiation (e.g., after leaving a batching facility or the like), such as by the addition of water to a cementitious mixture during transit. As such, the material identifiers described herein that may, for example, be indicative of the formulation of a material may refer to a set of time- dependent compositional material properties for the material. Said differently, the compositional material properties for a material that are determined by the techniques described herein may represent the formulation of a particular instantiation at the time at which the data on which the compositional material property is generated. Additionally or Page 18 of 226 13824520v1alternatively, the compositional material properties may be representative of a theoretical or idealized formulation as associated with various target contextual material properties as defined herein (e.g., C80 concrete, C60 concrete, C40 concrete, etc.).

[0081] As used herein, the terms “contextual material condition,” “contextual condition,” and “context” 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 material, contextual material conditions may be associated with 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. 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 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 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).

[0082] 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).

[0083] Structural burden data as an example contextual material condition may include load data and / or load path data, stress data, strain data, and / or batching plant data (e.g., volume Page 19 of 226 13824520v1of batch, mixing data, mixing intensity data, rate of rotation, etc.). Truck or transport contextual condition data may be indicative of the volume of the load (e.g., one or more batches in transport), truck rotational data (e.g., rotational velocity or the like), etc. Kiln contextual condition data may include data indicative of the temperature inside the kiln, the raw materials inside the kiln, and / or the volume of materials (e.g., raw materials, desired output materials, waste materials, etc.) inside the kiln.

[0084] Temporal data as an example contextual material condition may include any information used to denote a time or timeframe. In some instances, the temporal data may be indicative of time in absolute terms or relative context dependent terms. For example, the temporal data may include data indicative of a date and time, a period of time or duration (e.g., time between two dates or the like), a season, a year, a construction stage, time stamp data, data stamp data, and / or the like. As described herein, the temporal data associated with an example materials may be data that is associated with one or more processes or operations. For example, the temporal data may be indicative of a particular date and / or time at which one or more pours were poured.

[0085] 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 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 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 non- limiting 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, etc.), 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, etc. metric associated with the example 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, etc.). Page 20 of 226 13824520v1

[0086] As used herein, the term “raw material” may be used to refer to any material described herein that is associated with only static material properties as defined above. By way of a non-limiting example, water, fly ash, sand, and / or the like may be raw materials in the databases and models described herein that are associated with only static material properties (e.g., density and pH, for example). Conversely, the term “composite material” may refer to a material that is identified by both static material properties and compositional properties in the databases and models described herein. The present disclosure contemplates that the provided delineation between raw materials and composite material is in reference to the way in which these materials may be stored and / or identified by the databases and models described herein. For example, a raw material may be reclassified to a composite material whenever such material is defined to have compositional material properties. For example, a fly ash may initially exist in the databases described herein as a raw material. The fly ash, however, may be updated to include material properties other than static materials properties, such as the atomic or molecular constituent components of the fly ash. As such, the fly ash may be reclassified as a composite material. In other embodiments, raw material and composite material may be interpreted by their physical or chemical meanings, namely, where a raw material is a component material used to make a product (wherein the product may be a composite material), and a composite material is a combination of two or more materials with different physical or chemical properties.

[0087] As described herein, the term “batch variability” may be used to refer to the variability in the contextual material properties, the static material properties, and / or compositional material properties of a material (e.g., as defined by an associated formulation) across batches. As would be evident to one of ordinary skill in the art, batch variability may result from the tolerances or other uncertainty of the quantities (e.g., the mixing proportion tolerances), the contextual conditions during batching, and / or also the natural variability in the properties of the raw material. As such, the embodiments of the present disclosure operate to account for batch variability in the performance of the operations described herein.

[0088] 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, chemical structure, etc.), 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 Page 21 of 226 13824520v1as defined herein. By way of a non-limiting example, a material identifier may include a strength-grading based identification methodology in which particular mix formulations are identified by compressive strength (e.g., in megapascals or the like). In particular, a C40 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-controlled water 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.

[0089] Therefore, the material identifiers described herein provide information (e.g., data entries) regarding the particular materials (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-limiting 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.

[0090] As used herein, “material space” may refer to an N-dimensional space, such that all points in the domain of the N-dimensional space represent all possible material formulations (where such space may be an infinite space). In the context of example building materials, material 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 material 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 material may be defined, and the number of dimensions may change depending, for example, upon the information available to a models or databases Page 22 of 226 13824520v1described herein, or upon the information deemed minimally sufficient to characterize a material uniquely (up to some tolerance or precision) with respect to other material formulations.

[0091] As such, the present disclosure contemplates that there are multiple ways of representing an N-dimensional material space. By way of example, in some embodiments, N may represent the number of possible constituent component types (e.g., the material space representing all materials comprising quantities of water, cement, and aggregate will be of dimension 3). Another example representation of material space may be an N-dimensional manifold representing materials by their static material properties where N is the number of types of static properties. Another example representation of material space may be an N- dimensional manifold representing mixes by their contextual material properties where N is the number of types of contextual material properties.

[0092] The dimensions of a material space may also be any combination of these data types. The present disclosure further contemplates that an example material space may include different levels of granularity such that a classification of material families or types are used by the material identifier as opposed to a particular material formulation. Said differently, material space may be defined by any base and / or representation, different dimensionalities may exist, and equivalence relations and / or mappings may be generated between these different bases for material space. These representations may be either discrete or continuous. The material space may further include subcategories (e.g., material families, material types, and / or material classes) of materials in material-space (e.g., as defined by material properties, formulations, identifiers, or the like) that share at least one common characteristic.

[0093] As used herein, the terms “first dataset” and associated “first data entries” are used to refer to data that, in some embodiments, is received by the systems, models, etc. of the present disclosure as an input. By way of a non-limiting example, the first dataset may include data associated with various materials properties that are input by a user, generated by a sensor device (for example, a maturity or temperature sensor), other device, received from a database, received from a prior iteration of one or more of the models described herein, and / or the like, such as in the optimization and material identifier operations described herein. Additionally or alternatively, in some embodiments, the first dataset may include data generated by, received from or associated with a wave-based sensor (e.g. a mechanical or electromagnetic wave-based sensor configured to excite and / or measure a cementitious mixture, or configured to measure electrochemical or electromechanical parameters of a material). Page 23 of 226 13824520v1

[0094] Additionally or alternatively, in some embodiments, the first dataset may include data associated with sensor context awareness as described herein (e.g., data associated with a material, a pour implicating the material, an environment of the material, etc.). Additionally or alternatively, in some embodiments, the first dataset and associated first data entries may be associated with a material identifier. Additionally or alternatively, in some embodiments, the first dataset and associated first data entries may be associated with a spatial representation (e.g., a Building Information Modeling (BIM), floorplan or the like) as described herein. Additionally or alternatively, in some embodiments, the first dataset and associated first data entries may be associated with a measurement type of a material (e.g., a material identifying operation, a sensor device measurement or the like). Additionally or alternatively, in some embodiments, the first dataset and associated first data entries may be associated with a structural progress flow as described herein.

[0095] As would be evident to one of ordinary skill in the art in light of the present disclosure, the first dataset and associated first data entries may be associated with, indicative of, or otherwise related to any of the attributes, characteristics, parameters, metrics, etc. of the material operations, systems, devices, etc. described herein without limitation. Said differently, the first dataset and associate first data entries may refer to the data structure by which data associated with the embodiments described herein is stored, regardless of data type, model used, system deployed, etc. The present disclosure further contemplates that additional datasets (e.g., second dataset or the like) may include data entries associated with any of the same or different data types described herein with reference to the first dataset. In other words, the present disclosure contemplates that any number of different datasets of any type may be used by the embodiments herein.

[0096] 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 a material, contextual awareness, and / or the like without limitation. As described hereinafter, a sensor device may include any relevant circuitry, components, etc. configured to generate data that is indicative of, 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. In some embodiments, the sensor devices described herein may be embedded in, mounted on, Page 24 of 226 13824520v1directed at, or otherwise coupled to a material. Further, in some embodiments, the sensor devices may include “smart aggregates” or “smart dust” (i.e., sensing dust and / or miniaturized self-contained wireless sensor devices) that are placed in the material, such as concrete, steel, etc. during production, batching, etc. Still further, the present disclosure contemplates that any of the sensor devices described herein may be “smart sensors” that, for example, include a MCU, a memory, battery management, battery power, and one or more sensors types configured to perform the techniques described herein. Each of the embodiments described herein may further be multivariate in which a plurality of sensors of the same or different type may be used.

[0097] The sensor devices of the present disclosure may be designed to be integrated throughout the lifecycle of a material, such as into concrete pours or elements (installed prior to pouring, (e.g., on rebar), and covered with concrete). Various attachment methods are designed to ensure optimal functionality (e.g. wireless communication) and secure placement throughout the material lifecycle. As such, the present disclosure contemplates that the attachment designs consider factors such as sensor shape, resonance influence, and aggregate interference, in attachment selection and may make use of various materials and coatings. These attachments are resilient to diverse material environmental conditions and do not compromise the host material’s structural integrity. These attachments ensure secure attachment to different components of the material (e.g., elements of the pour structure such as reinforcement bars, otherwise referred to as ‘rebar’ or formwork, concrete drums in trucks etc.). Attachment methods may include one or more of (1) straps, bands or ties; (2) clamps, clips and fasteners; (3) adhesive and welding techniques; (3) magnetic attachments (that snap on to rebar); (4) innovative materials; (5) other; and (6) floating or sinking configurations (no attachment). The present disclosure contemplates that any attachment mechanism may be used based on the intended application of the sensor device.

[0098] Sensor devices may be used in association with “actuators” which as used herein may be used to refer to any element or circuitry component that is able to cause, generate, adjust and / or generally control any force, field or energy excitation or disturbance (including for example mechanical excitations, or electromagnetic excitations, and in particular wave- based excitations, through force or field couplings). Said differently, the present disclosure contemplates that any element configured to or is otherwise capable of creating any form of excitation (not just movement-based excitations) may be considered an “actuator.” In some embodiments, sensor, sensor device, transducer, actuator, and device may be used interchangeably to reference any of their respective meanings, in a context dependent way. In Page 25 of 226 13824520v1some embodiments, an example “transducer” may be intrinsically resonating in that the configuration of the transducer (e.g., by geometry or the like) produces or is otherwise associated with resonant behaviors (e.g., oscillatory resonance, wave-based resonance modes, etc.).

[0099] As used herein, “wave-based sensor” may be used to refer to any device which may generate, adjust, or control a time-varying excitation (based on an input signal) and / or sense a response to an excitation including, but not limited to, of a target material, or another material coupled (directly or indirectly) to the target material. Such a wave based sensor may be, used to generate or otherwise make use of and sense waves, excitations, and / or oscillations (such as electromagnetic waves, electric currents and / or mechanical stresses) as described herein. Furthermore, “wave-based” may refer to any device, technique, sensory, etc. that employs one or more actuators to excite a host material, or a second material that is coupled to the host material. The excitation may be a time varying signal (e.g., an oscillatory signal, a wave, etc.). Wave-based devices, techniques, and sensing may also employ sensors to measure the response of the host material (directly, or indirectly through the response of the second material, or another material coupled to the host material). For the avoidance of doubt, the “wave-based” techniques described herein may encompass, without limitation, excitations, oscillations, and waves, and may further encompass any device configured to take input signals and generate, adjust, control an excitation of a field, force, or form of energy, such as via an actuator defined herein, as well as a response (e.g., material response, coupled medium response, etc.) to such excitation, oscillation, or wave.

[0100] As used herein in respect of wave-based sensors (or other, related devices), a “frame” may be used to refer to refer to fixtures, surfaces, volumes, membranes, and / or shapes of any kind which may be disposed as part of, in, around or in proximity of wave-based sensors, actuators or device housings as described herein. In some embodiments, devices, including their sensors and / or actuators may be at least partially embedded within frames, disposed within their inner volumes, in proximity to them and / or the like. In some embodiments, the devices described herein, or their component parts (e.g., sensors or actuators) may be physically bonded to frames (e.g., to produce a sensor / actuator-frame composite) or otherwise coupled (e.g., through a field, at a distance). As such, a frame may span any geometry that may or may not be contiguous. In some embodiments, frames may be made of materials or configured in geometries to manipulate waves (including their waveforms and direction of travel), oscillations and / or excitations (for example, through wave reflections, absorption or Page 26 of 226 13824520v1diffraction, polarization, or oscillatory dampening, inertial, inductive, capacitive or elastic effects, and the like).

[0101] As used herein, the terms “contextual awareness data,” “sensor context awareness,” “self-detection data,” and “context awareness data” may be used interchangeably to refer to data that is associated with a first sensor device considering a material, associated with the material under consideration by the first sensor device, associated with a pour implicating the material under consideration by the first sensor device; and / or associated with an environment of the material under consideration by the first sensor device. In some embodiments described hereinafter, sensor context awareness data may refer to S-data, M-data, P-data, and / or E-Data. As used herein, S-data may refer to data entries that are indicative of the sensor device itself, M-data may refer to data entries that are associated with the material surrounding the sensor device (e.g., if the sensor device is embedded) or the material under consideration by the sensor (e.g., if the sensor is directed at or mounted on the material), P-data may refer to data entries that are indicative of the pour or volume in which the sensor device is located or is considering, and E-data may refer to data entries that are associated with the environment of the pour. In some embodiments, sensor context awareness data may include combinations of these data types and / or these data types for connected elements (wherein a connected element represents a connection between building elements (e.g., physically connected, a nearest neighbor, or within each other’s load paths etc.)).

[0102] As used herein, a “data value” may include any piece of information relating to a measurable entity, such as an example temperature reading. A “data type” may refer to a categorization of data values, such as thermal data for the example temperature reading. The terms “data source” and “data entity” may be used interchangeably to refer to a data store that holds data values (e.g., a specific BIM model or the like). The terms “data source type” and “data entity type” may be used interchangeably to refer to a categorization or type of data source or data entity. For example, a data entity may refer to as an instantiation of a data source (e.g., BIM model may be a class of data entities).

[0103] As used herein, a “data element” may include a data value of a certain type stored within a data entity of a certain type (e.g., an element in a BIM model). A data element may, for example, be continuous or discrete. A discrete data element may include a data element that represents discrete information that is self-contained (e.g., a concrete cube test crush result). A continuous data element may include a data element that represents continuous information that may be arbitrarily subdivided or combined (e.g., a slab in a BIM model may be subdivided into pours of arbitrary size). Page 27 of 226 13824520v1

[0104] As used herein, a “measurable entity” may refer to a physical object or entity (e.g., a pour) that may be measured or observed. In this way, the measurable entity represents the actual physical object as opposed to the corresponding digital representation (e.g., digital twin) of the object.

[0105] As used herein, the terms “data,” “content,” “information,” and similar terms may be used interchangeably to refer to data capable of being transmitted, received, and / or stored in accordance with embodiments of the present disclosure. Thus, use of any such terms should not be taken to limit the spirit and scope of embodiments of the present disclosure. Further, where a computing device is described herein as receiving data from another computing device, it will be appreciated that the data may be received directly from another computing device or may be received indirectly via one or more intermediary computing devices, such as, for example, one or more servers, relays, routers, network access points, base stations, hosts, and / or the like, sometimes referred to herein as a “network.” Similarly, where a computing device is described herein as sending data to another computing device, it will be appreciated that the data may be sent directly to another computing device or may be sent indirectly via one or more intermediary computing devices, such as, for example, one or more servers, relays, routers, network access points, base stations, hosts, and / or the like. Data Objects Used by All Models

[0106] In some embodiments, a data object may be a material identifier that may include a material ID, a material name, and / or a material type. By way of example, a C40 mix may be defined as a concrete mix that may reach 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- controlled water bath at a fixed temperature). A C60 has an identical definition but must reach a minimum of 60 MPa instead. Therefore, material identifiers (e.g., names) hold information regarding the particular mixes the models described herein are operating upon. Additionally, or alternatively, material identifiers considered by the present disclosure may include a non- exhaustive list of material types including pure materials, composites, and / or material mixes (e.g., a cementitious material, water, aggregates, admixtures, plasticizers, fibers, and / or the like).

[0107] In some embodiments, a material identifier may include material compositions. A non-exhaustive list of potential material compositions considered by the present disclosure may include chemical and / or molecular formulas, atomic compositions, proportions of raw materials (e.g., by weight, by volume, by molar ratios and / or number of particles, and / or the Page 28 of 226 13824520v1like), proportions of material phases, multi-scale compositions, ternary diagrams, distribution functions, descriptors and / or fingerprints, and / or the like.

[0108] In some embodiments, a material identifier may include material structure. A non- exhaustive list of potential material structures considered by the present disclosure may include unit cells and / or supercells, lattice parameters, symmetries, multi-scale structure (e.g., atomic structure, nanostructure, microstructure, macrostructure, and / or the like), crystallinities, grain sizes and distributions, porosity and pore size distributions, descriptors and / or fingerprints (e.g., bond length, atom locations (e.g., vectors), and / or the like), and / or the like.

[0109] In some embodiments, a material identifier may include material properties. A non- exhaustive list of potential material properties considered by the present disclosure may include static material properties including density, homogeneity, average particle size (e.g., average aggregate particle size or aggregate grading, average binder particle size, and / or the like), fineness, specific gravity, natural variability data (e.g., data about natural variability in raw materials quality or inhomogeneity, and natural batch variability), embodied carbon data, aggregate grading, porosity, and / or the like. Further the non-exhaustive list of material properties may include contextual material properties including temperature data, insulation data (e.g., formwork type, formwork coating, blankets, and / or the like), structural data (e.g., data pertaining to geometry, physical form, structure, layout, arrangement, configuration, and / or content (e.g. rebar) of a pour, such as 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 (e.g. formwork), and / or the like), reinforcement geometry data (e.g., rebar data, information about general surroundings, and / or the like), and / or the like)), environmental data (e.g., meteorological data (e.g., ambient temperature data, humidity data, precipitation data, wind data, storms and lightning data, and / or the like), electromagnetic radiation data, mechanical vibration and / or other mechanical disturbances, geological data (e.g., the type of soil surrounding foundations may affect its behavior), oven data, and / or the like), structural burden data (e.g., how instantiated mix experiences the following : load data, load path data, stress data, strain data, and / or the like), batching plant data (e.g., volume of batch, mixing data, measure of mixing intensity (e.g., rate of rotation), and / or the like), pump contextual condition data, kiln contextual condition data (e.g., temperature inside kiln, raw materials inside kiln, volume of materials inside kiln, and / or the like), temporal data (e.g., any information used to denote a time or timeframe in absolute terms, or relative context dependent terms (e.g., date and / or time, period of time (e.g., 5 days), period of time specifically between two dates or between two hours of the day, season, year, daytime or nighttime, stage of construction, time Page 29 of 226 13824520v1stamp data (e.g., associated with sensor measurements), date stamp data (e.g., associated with sensor measurements), and / or the like), and / or the like.

[0110] In some embodiments, a material identifier may include instantiations of materials in the real world (e.g., batches).

[0111] In some embodiments, a data object may be production process objects. A non- exhaustive list of potential production process objects considered by the present disclosure may include compositional arrangements (e.g., proportions of each material from which a material mix is composed), lists of steps, state machines, lists of equipment, states, state change operators, chemical reactions, and / or the like.

[0112] In some embodiments, a data object may be contextual conditions. A non- exhaustive list of potential contextual conditions considered by the present disclosure may include material contextual conditions data (e.g., durability, pumpability, workability, aesthetic finish, flexural strength, exothermicity, endothermicity, and / or the like), sensor context awareness data (e.g., sensor metadata (e.g., name of a sensor), sensor context awareness data as described in other sections of the present disclosure (e.g., location of a sensor (relative and absolute), orientation of a sensor, rf transmission of a sensor, battery consumption of a sensor, lifetime of a sensor since activation, and / or the like), and / or the like), process contextual conditions (e.g., process control parameters during a material production process (e.g., temperature, pressure, rate of mixing, and / or the like), and / or the like.

[0113] In some embodiments, a data object may be objective functions and / or utility functions as described herein. A non-exhaustive list of objective functions considered by the present disclosure may include objective functions directed to defining a desired output from the models herein, objective functions directed to being used internally during training of the models, and / or the like. Example objection functions may include loss function, cross-entropy loss, mean squared error (MSE), hinge loss, log-likelihood, reconstruction loss, reconstruction loss, Q-learning objective, and / or the like. Objective functions of the present disclosure may be directed to and / or may include L1 regularization, L2 regularization, parameters (e.g., model attributes that change during optimization or learning), hyperparameters, weights, biases, regularization parameters, constraint parameters, multi-objective functions (e.g., weights (that determine importance of each objective terms), pareto-based, evolutionary algorithm methods, and / or the like), and / or the like.

[0114] In some embodiments, objectives can be encoded into utility functions. Utility functions may be similar to objective functions but may be used in cases where a user’s preferences may be defined over multiple possible outcomes into one function. A non- Page 30 of 226 13824520v1exhaustive list of utility functions considered by the present disclosure may include cumulative reward function, expected utility, payoff function, linear utility, multiplicative utility, exponential utility, logarithmic utility, weighted sum utility, risk-aware utility (to penalize risk or uncertainty in material behavior), piecewise utility, pareto utility, and / or the like.

[0115] Potential objective considered by the embodiments of the present disclosure may include minimize cost, maximize performance, minimize embodied carbon, maximize or minimize any property (optionally up to a threshold), maximize strength-to-weight ratio, minimize material cost, maximize durability, maximize recyclability, minimize environmental impact, maximize fatigue resistance, maximize thermal conductivity, maximize corrosion resistance, minimize weight, maximize impact resistance, minimize manufacturing complexity, minimize production time, maximize availability of raw materials, maximize energy efficiency in production, maximize ease of processing, minimize maintenance requirements, maximize lifecycle sustainability, minimize embodied carbon in material, minimize carbon footprint, minimize waste generation during production, maximize use of renewable materials, minimize water usage during production, maximize potential for reuse or repurposing, maximize resistance to wear and tear, maximize UV resistance, maximize fire resistance, maximize electrical conductivity, minimize electrical resistivity, maximize dielectric strength, maximize optical clarity, maximize light absorption for energy applications, maximize electromagnetic shielding effectiveness, minimize electromagnetic interference, maximize chemical resistance, minimize material degradation due to chemical exposure, maximize ease of machining and forming, maximize compatibility with additive manufacturing, maximize resistance to weathering, maximize surface finish quality, maximize thermal insulation, maximize heat dissipation, maximize resistance to damage during shipping, and / or the like. Any combination of the aforementioned objectives may be represented in a multi-objective function.

[0116] In some embodiments, a data object may include constraints. As used herein, a constraint may include any limitation on any data objects described herein, quantitative thresholds, and / or qualitative attributes. A non-exhaustive list of quantitative constraints may include tensile strength ≥ 500 MPa, weight ≤ 5 kg, elastic modulus: 200 GPa ≤ E ≤ 250 GPa, fatigue life ≥ 10⁷ cycles, maximum deformation ≤ 1 mm, shear strength ≥ 50 MPa, operating temperature: -100°C ≤ T ≤ 400°C, thermal expansion coefficient ≤ 10 x 10⁻⁶ / °C, corrosion rate ≤ 0.1 mm / year, impact resistance ≥ 10 J, processing temperature ≤ 1000°C, part thickness ≥ 0.5 mm, machining tolerance ±0.01 mm, production cycle time ≤ 30 min / unit, electrical resistivity ≤ 10⁻⁶ ohm·m, dielectric strength ≥ 100 MV / m, thermal conductivity ≥ 50 W / m·K, Page 31 of 226 13824520v1embodied carbon ≤ 10 kg CO₂-eq / kg, recyclability ≥ 70%, water usage ≤ 100 L / kg, material cost ≤ $50 / kg; manufacturing cost ≤ $200 / unit, surface roughness ≤ 0.8 µm, packaging weight ≤ 25 kg, shock load resistance ≥ 10g, and / or the like. A non-exhaustive list of qualitative constraints may include material must be chemically resistant to acids, material must be non- toxic and comply with environmental regulations, material must have high surface finish quality, material must be visually defect-free, material must be compatible with existing manufacturing processes, and / or the like.

[0117] 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 production processes (e.g., where each “step” in the production process may be represented as a vector or matrix that operates of “material states”), and / or the like. Example embodiments of material spaces may include materials being represented as N- dimensional vectors in material spaces. Additionally, or alternatively, an embodiment may include ‘material production space’ that may denote a vector space to represent material production processes. In such embodiments each ‘type of process’ or ‘step’ (e.g., welding, mixing, and / or the like) may be represented by a different type of vector representation. Further, the representation may be based on the characteristics of the process and / or the representation maybe based on what kind of outputs the process does. In other embodiments, production processes may be represented as operators that act upon vectors in material space. For example, material space may have vectors that represent materials (in any of the above representations (e.g., composition, property, and / or the like). Further, processes may be represented as operators, or matrices or tensors that may act on material vectors and modify or evolve such vectors such that they move in material space. Additionally, or alternatively, matrices may be represented in basis of the vector space. For example, the vectors may become entirely new vectors if the process evolves the material into a completely new state (e.g., chemical reaction). Additionally, or alternatively, a process which doesn’t fundamentally change the nature of the material might just scale it (e.g., cutting a piece of material in half, could make the vector half the length). Page 32 of 226 13824520v1Data Sources, Formats, Types, Methods, and the Like Used by All Models

[0118] 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 sources of the present disclosure may include recorded values from measurement or sensors devices, documents (digital or handwritten), 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 / 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. Training Datasets Used by All Models

[0119] Training datasets used by embodiments of the present disclosure may include a plurality of data objects. A non-exhaustive list of data objects considered by the present disclosure may include compositional data objects, structure data objects, properties data objects (e.g., static and / or contextual), contextual condition data objects (e.g., context awareness), spatio-temporal simulation data objects, production process data objects, prompt data objects, constraint data objects, and / or the like. Training datasets of the present disclosure may be directed to desired material data for a model to learn. For example, a list of possible associations the model of the present disclosure may be trained to learn may include train to go from composition (optionally +structure) → properties, train to go from composition (optionally +structure)→ spatio-temporal simulation, train to go from composition (optionally +structure) → production process, train to go from composition (optionally +structure) → more optimal composition (+structure); given objective, train to go from prompt → to any of composition; structure; properties; objectives; constraints; spatio-temporal simulation; production process,train to go from desired properties → composition, and / or any desired objective → composition. In some embodiments, a training dataset may be structured as a relational database and / or stored as a graph database and / or the like. Page 33 of 226 13824520v1Sensors Used by All Models

[0120] In some embodiments, sensors may be used to gather data for training the models described herein. The data may include compositional properties and data, structural data, as well as material property and performance data. In some embodiments, sensors may be used to construct a labeled training dataset of material identifiers, compositional data, structural data, and properties and performance data. The labeled training dataset may be used to train models to predict properties based on composition and structure, as well as generate materials based on desired properties. Additionally, or alternatively, sensor devices may be used to construct dynamic datasets that consider contextual conditions of materials in their environments of use. Additionally, or alternatively, training datasets may continuously grow as more data is collected. Additionally, or alternatively, models may be retrained based on additional sensor data. In some embodiments, sensor devices may be embedded in, mounted on, or directed at a material to gather data associated with the material.

[0121] In some embodiments, compositional data and / or structural data may be gathered using sensors configured for X-Ray Diffraction, Electron Microscopy, Neutron Diffraction Atomic Force Microscopy, Hyperspectral imaging, FTIR spectroscopy, Raman Spectroscopy, LIBS Spectroscopy, Diffuse Reflectance Spectroscopy, and other high frequency wave-based sensing methods, or photonics or spectroscopic methods. In some embodiments, the methods are used to gather compositional or structural data associated with crystal composition and lattice structures.

[0122] In some embodiments, property data may be gathered using wave-based sensing devices. In further embodiments wave-based sensing devices may include mechanical wave or oscillation-based devices. The devices may include 1-port and 2-port systems, configured, for example, for ultrasonic pulse velocity measurements, mechanical impedance devices, piezoelectric transducer-based devices, optomechanical sensor devices, electromechanical devices, and more. The devices may be used to measure any mechanical property including those listed herein, at one or multiple frequencies. Additionally, or alternatively, further embodiments of wave-based sensing devices may include electromagnetic wave or oscillation- based sensing devices. Including devices configured to sensor materials using electrical currents, magnetic fields, or electromagnetic waves (e.g., Hall effect sensors, resistivity probes and more). Additional sensor devices may include Ellipsometry, UV-Vis Spectroscopy, Photoluminescence Spectroscopy, Refractive Index Sensors, and / or the like. The sensor devices may be used to measure any electromagnetic property including those listed herein. Page 34 of 226 13824520v1

[0123] Additionally, property data may be gathered using types of sensors or sensor techniques including thermal sensors (e.g., thermocouples, differential scanning calorimetry (DSC), thermal conductivity sensors, thermogravimetric analysis (TGA), and / or the like), pressure and strain sensors (e.g., pressure sensors, strain gauges, piezoelectric pressure sensors, and / or the like), and / or other sensors (e.g., pH sensors). Additionally, or alternatively, the sensor data collected by sensor devices may be processed and cleaned. In some embodiments, processing may include a Fourier transform, or derivatives or integrals of the frequency spectra obtained through the sensor.

[0124] Additionally, or alternatively, sensors may be used to collect data associated with the material in real-time during production, synthesis, or use of the material. Additionally, or alternatively, sensors may be used to collect data throughout the material life cycle, monitoring the raw materials, throughout the production process, all the way to the material during use. Additionally, or alternatively, live contextual conditions such as temperature, pressure, geometry, time / aging and more may be collected alongside sensing of the material itself. Additionally, or alternatively, contextual conditions may be linked to associated sensor data such as sensor time series data e.g. the temperature during a particular time, date and location, may be linked to the material sensor data collected at that time, date and location. Additionally, or alternatively, contextual condition data may be added to the training dataset / database. Additionally, or alternatively, contextual condition data may be linked to associated material composition, structure and / or property data in the training dataset. Additionally, or alternatively, contextual conditions may be extracted from APIs (e.g., weather API), records (e.g., BIM Model for geometry), human input or other sensors (e.g., thermometer, barometer). Additionally, or alternatively, contextual conditions may be determined or collected using context awareness methods. Additionally, or alternatively, contextual conditions may be determined or collected using cameras or other image-based sensing devices or methods.

[0125] Additionally, or alternatively, sensor data may be used for model calibration or validation. Additionally, or alternatively, materials may be sensed using one or a plurality of sensor devices after a prediction has been made. Additionally, or alternatively, the sensor data may be compared with the output prediction. Additionally, or alternatively, model parameters or hyperparameters may be adjusted when predictions do not match sensor data.

[0126] Additionally, or alternatively, sensor data may be used for real-time material and material production monitoring and feedback. Additionally, or alternatively, a production process (e.g., crystal growth, material synthesis) may be dynamically optimized based on sensor data. Additionally, or alternatively, this may include changing the contextual conditions Page 35 of 226 13824520v1of a production process to optimize the production process output e.g. changing temperature, pressure, or doping level, to achieve desired properties. Additionally, or alternatively, sensor data may be used to detect defects or impurities in materials from a production process, and dynamically change one or a plurality of aspects of the production process in response.

[0127] In some embodiments, sensor data may be used as an input for models that predict future expected properties of materials based on historical performance data. Further, models may use multimodal data from a plurality of sensors and sensor types, either during training, or model execution. Additionally, or alternatively, sensors may be used to collect materials data at different scales. In some embodiments, the data may be used for multiscale analysis, and multiscale modeling as part of the models herein. Additionally, or alternatively, sensor data may be collected at the atomic scale, nanoscale (e.g.1-1000nm), microscale (e.g.1-1000µm), macroscale (e.g. 1mm+). Additionally, or alternatively, spectroscopic, photonic, and high- energy E&M wave-based sensing methods may be used to collect data associated with the atomic scale, nanoscale and microscale. Further, mechanical sensing methods may be used to collect data associated with the microscale and macroscale. In some embodiments, the models herein may link phenomena across scales. Additionally, or alternatively, the phenomena across scales may be used as part of a prediction method. Further, a model may be trained to link phenomena across scales based on sensor data. In some embodiments, the models herein may use multi-scale identifiers (e.g., identifiers constructed of features indicative of different scales (e.g., bond length (atomic), grain size (nano scale-micro scale), total geometry of the piece of material (micro scale-macro scale) as inputs)).

[0128] In some embodiments, the sensor devices of the present disclosure which capture the physical measurements described herein may be any type of device described in any section herein. The devices may include thermal sensors, wave-based sensors including piezoelectric sensors, spectroscopy sensors, or any combination of any sensors mentioned. A list of representative and non-exhaustive sensors devices considered by the present disclosure may include wave-based sensors, mechanical wave-based sensors, piezoelectric EMI devices, acoustic devices, electromagnetic wave-based sensors, electrochemical devices, magnetochemical devices, electromagnetic wave impedance sensing devices, refractive index sensing devices, ground penetrating radar sensing devices (GPR), terahertz frequencies sensing devices, NMR and / or microwave spectroscopy devices, LIBS spectroscopy devices, FTIR spectroscopy devices, X-ray diffraction devices, hyperspectral imaging devices, LIDAR devices, RADAR devices, temperature sensors, strain gauges, barometers, and / or the like. Page 36 of 226 13824520v1Digital Records Used by All Models

[0129] In some embodiments, models of the present disclosure may be configured to extract of data from records. Extraction of data from records may include extraction of composition data, structure data, property data, constraints, material identifiers, and / or the like (e.g., any data object described herein), material test records as an almost universal source of data, and / or linking data from records to materials or material types / classes in material databases and / or training datasets of the present disclosure. Examples of testing records which may be digitized and / or ingested and / or added to datasets and / or database of the present disclosure to gather data may include crystals and semiconductors (e.g., crystal purity and composition, resistivity and conductivity, crystallographic orientation, crystal defect and dislocation, thickness and uniformity, carrier lifetime, mobility and carrier concentration, optical properties, surface roughness and flatness, dielectric breakdown, thermal conductivity and expansion, etch pit density (EPD), leakage current and junction integrity, wafer bow and warp, and / or the like), metal alloys (e.g., tensile test, hardness test; impact test, fatigue test, chemical composition, microstructure analysis, corrosion test, creep test, fracture toughness test, weldability test, heat treatment records, and / or the like), cementitious materials (e.g., compressive strength, flexural strength, tensile strength, shrinkage, creep, durability (freeze- thaw resistance), permeability, setting time, heat of hydration, air content, chloride penetration, sulfate resistance, and / or the like), polymers (e.g., tensile test, hardness test (shore A / D), impact test (Izod, Charpy), flexural test, compression test, thermal properties (DSC, TGA, HDT, VST), creep test, abrasion resistance, chemical resistance, optical properties, flammability test, environmental stress cracking, density and specific gravity, moisture absorption, and / or the like), battery chemistry materials (e.g., electrochemical performance (voltage, capacity, cyclic stability), conductivity (ionic and electronic), charge-discharge cycling, thermal stability, impedance spectroscopy, rate capability, swelling and expansion, composition and purity, particle size distribution, mechanical strength (for electrodes), safety testing (short circuit, overcharge), and / or the like), amorphous materials (e.g., density, thermal properties (glass transition temperature, DSC, TGA), hardness, fracture toughness, refractive index, chemical composition, transparency (haze and clarity), water absorption, creep and stress relaxation, optical absorption, microstructural analysis, mechanical strength (compressive and tensile), abrasion resistance, and / or the like), and other materials (e.g., tensile strength, hardness, impact resistance, thermal conductivity, electrical conductivity, chemical composition, creep; shrinkage, optical properties, fatigue resistance, density, permeability, abrasion and wear resistance, and / or the like) Page 37 of 226 13824520v1Models and Model Techniques Used by All Models

[0130] In some embodiments, embodiments of the present disclosure may include a plurality of types of execution models. For example, a type of execution model considered by the present disclosure may be an AI model configured as a hybrid AI + physico chemical model. One type of model may be a hybrid physico-chemical and AI model. In such a model, knowledge of the laws of nature may be embedded in the algorithms and used in conjunction with AI algorithms, allowing the model to physically and chemically reason about the systems it is treating and therefore provide explainability for the solutions it reaches, whilst also learning from the provided data using deep learning approaches. Scientific principles may thus be used to augment these deep learning models, which may in turn, use the historical data they gather to refine their understanding. This combination may also be described as the model being infused and / or embedded with physico-chemical knowledge, which may be particularly useful for treating complex problems especially with ill-labelled or incomplete data.

[0131] To describe these types of models in more detail, the physico-chemical and empirical AI components may work together to provide a solution that may be based on a multi-modal internal representation (in which some aspects of the internal solver are based on physical and / or chemical principles, and other aspects on learned representations from empirical data). One instantiation of such a model may be a Convolutional Neural Network (CNN), which may be used as a means to construct an ensemble model, such that the weights of the convolutional networks bias the outputs of several sets of physical or chemical equations, each of which contributing to various aspects of the final model output. The weights of the convolutional neural networks might be learned over the set of empirical data available, whereas the physico-chemical equations that are being weighted by the neural network may have been derived from pre-existing theory. For example, one such physico-chemical component might encode a functional representation of how insulation affects heat transfer in a material, such that modifications to insulation will have a heavily weighted influence on outputs from those functions. Such an internal representation may allow for an accurate prediction or identification of the compositional material properties of a mix which may have been covered with a blanket and would allow for an automated physico-chemical explanation of those results. The inclusion of physical or chemical understanding may also allow for a model to be more robust against missing or partially informative data. For example, a CNN which may also have an internal functional representation of the mechanics of acoustic wave propagation within concrete, may be able to take as input an incomplete or noisy set of acoustic Page 38 of 226 13824520v1wave measurements from a mechanical wave-based sensor within a particular mix, and output a sufficiently accurate prediction, evaluation or recommendation. In contrast, a traditional CNN model may have difficulty learning useful embeddings that are representative of the system with incomplete data.

[0132] Additional types of execution models consider by the present disclosure may include , a hybrid AI + DFT model, a physico-chemical model (e.g., a DFT-based model, molecular dynamics based model, and / or the like), a multiscale model and / or a model leveraging multi scale representations, where the model may generate material data at atomic scale, nanoscale, microscale, macroscale, and / or the like, a support vector machine physical / chemical models, tree-based methods, decision trees, bagging trees, random forests, gradient boosted trees, Bayesian probability theory, artificial neural networks, convolutional networks, recurrent neural networks, transformers, generative adversarial networks, diffusion system, clustering algorithms, k-means clustering, hierarchical clustering, density based spatial clustering, spectral clustering, affinity propagation, gaussian mixture models, embedding / dimensionality reduction methods, principal component analysis (PCA), independent component analysis (ICA), multi-dimensional compression methods, Bayesian networks, causal graphs, ensemble models, and / or the like.

[0133] In some embodiments, embodiments of the present disclosure may include a plurality of types of training models. The following are broad categories of training procedures that may be, in some embodiments, used to train any of the models described herein (e.g., to modify the internal weights relative to an objective function). Further, the training procedures do not imply any specific choice of objective function, and the specific choice is not an integral aspect of any of these training algorithms. The training algorithms do not require the objective function to be specifically minimized (e.g., they are also valid for choices of objective that are maximized at convergence), nor do the training algorithms require the objective functions to characterize a supervised or unsupervised error calculation (they are valid for either case).

[0134] In some embodiments, human choice may be a training procedure used to train any of the models described herein. Human choice may be defined as the use of human understanding and / or intuition to create analytical models from a priori knowledge of the world. This might be a physical or chemical model that was obtained through experimentation, or through logical reasoning on the outside world, or via prior literature in the field.

[0135] In some embodiments, gradient descent may be a training procedure used to train any of the models described herein. Gradient descent is a procedure by which a set of (generally) non-linear and / or linear functions, over (generally) discrete and / or continuous data Page 39 of 226 13824520v1(of arbitrary scope) have their functional parameters (e.g., weights) modified in an iterative manner, where each iteration may be broadly defined by the following steps in the supervised case: executing the model in its current state, comparing the desired output with the executed output, assessing the degree to which the desired output may be reached by modifying the functional parameters, updating the internal parameters in the direction of those updates, and / or halting the procedure when the desired output has been sufficiently found.

[0136] In the unsupervised case, the step of comparing the desired output with the executed output may be modified such that a derived quantity of the output is calculated and minimized (or maximized) depending upon the nature of the unsupervised search. The procedure described above may sometimes be executed in one iteration, or sometimes in many. The procedure may sometimes be executed analytically, and sometimes may be executed numerically. All of these are processes that may be used by any of the models described herein, depending upon the circumstance of the data and the model being trained.

[0137] In some embodiments, reinforcement learning may be a training procedure used to train any of the models described herein. Reinforcement learning is a method by which a model learns how to make decisions by performing actions in an environment (whether physical or virtual) and receiving feedback in the form of rewards and / or penalties. The model may be defined in such a way so as to choose from a set of restricted actions in its environment. The reinforcement learning process iteratively maps situations (inputs) to actions (outputs) in a way that maximizes cumulative rewards over time. The decision as to how the rewards / penalties are quantified in the feedback process may be defined by the meaning of "accuracy" within the context of the model's purpose. Similar to gradient descent, reinforcement learning is iterative - gradually improving its decision-making strategy based on the consequences of its actions. However, unlike gradient descent, reinforcement learning focuses on finding an optimal policy for action selection, rather than directly minimizing the difference between a desired outcome and a model outcome. The permissible actions that the model may affect, and the internal functional parameters that determine the policy regarding which action to choose, are all specified by the person that defines the training process. In addition, unlike gradient descent, the feedback does not occur immediately at each iteration, and a "poor decision" may impact a reward or penalty in a temporally or spatially non-local way. For example, the consequences of a poor decision may manifest hundreds of iterations (and actions) after that decision was made, at which point the associated reward / penalty may occur. Generally, reinforcement learning involves a random search over the space of possible actions at each iteration, optimizing for the set of actions that maximize cumulative rewards and / or that minimize Page 40 of 226 13824520v1cumulative penalties. There are some modifications to reinforcement learning that permit non- random searches over the permissible range of policies. Embodiments of the present disclosure may use all such forms of reinforcement learning.

[0138] In some embodiments, reinforcement learning with human feedback (RLHF) may be a training procedure used to train any of the models described herein. RLHF is a means of modifying the standard reinforcement learning approach to include human feedback into the iterative optimization procedure. In RLHF, a feedback loop is set up between both the natural environment of the model and its internal representation of that environment, but also between a set of human users, who may be providing constant feedback in some form, where that feedback may be translated into numerical reward and / or penalty values. The search procedure still optimizes for the optimal action policy but may now consider the totality of all rewards and penalties, including those provided through human feedback. RLHF may be useful when creating models that encode the preferences of one or more human users, and any of the models described here may be trained using RLHF.

[0139] In some embodiments, a genetic search may be a training procedure used to train any of the models described herein. A genetic search involves taking the functional parameters of a model and encoding them in a vectorized form. That vector may be used as is or may be further operated on to create a continuous or discrete embedding, or to compress the vector. The procedure may be performed, broadly, as follows. (a) The vector / s of functional parameters are randomized. Generally, all parameters may not be randomize / modify in the vector / s, but rather a subset (e.g., 10% of parameters). (b) The procedure is executed a number of times (denoting a single epoch in the genetic process), where an ensemble of randomized (e.g., "mutated") models and outputs is obtained. (c) The outputs from all models in the ensemble are assessed against the desired output, and the models that improve on performance to within a specific threshold are chosen and ranked by their degree of improvement. (d) Out of the set of all sufficiently improved models, a randomized "inter-mixing" between functional parameters is executed, whereby the vector of parameters between a chosen pair will partially inherit parameters from one another, or combine the parameters in some way (e.g., averaging). (e) The ensemble of new models (generated through the inheritance step above) may then be executed and assessed against the desired outputs. (f) The best performing model or models are chosen for the next randomization step, and the procedure is restarted from (a). (g) The procedure ends when a sufficient degree of model accuracy is reached.

[0140] Generally, steps (e) and (f) may be executed in very different ways. For example, step (e) may be continued iteratively, until a meta-stable randomized equilibrium of Page 41 of 226 13824520v1performance is obtained. The process may then move on to step (f) to add more randomization to the procedure, and restart from step (a). Alternatively, the process may step from (e) to (f), choosing the best ranked model / s in the ensemble of step (e) to pass into (f). If the procedure provides more than one model to pass into step (f), the procedure may create a "branching" of the search, whereby the totality of the procedure is applied in parallel across different seed models, and prune parallel branches based on their convergence properties. In another modification, the procedure may choose to alter the fraction of functional parameters being randomly modified at iteration of step (a) - for example, some genetic models reduce the number of variables being randomized with each epoch.

[0141] Embodiments of the present disclosure may include a plurality of types of optimization algorithms (e.g., similar to the objective functions described herein). A non- exhaustive list of optimization algorithms considered by the present disclosure may include genetic algorithms, particle swarm algorithms, simulated annealing, gradient-based optimization (e.g., gradient search), Bayesian optimization, multi-objective evolutionary algorithms, response surface methodology, differential evolution, genetic programming, gradient-free methods, and / or the like. Model Features Used by All Models

[0142] Embodiments of the present disclosure may include a plurality of input features. For example, in some embodiments, a large language model (LLM) may be configured to interact with a user. An example interaction may be the user inputs a prompt and the LLM ingests the prompt. In some embodiments, ingestion of input by any of the models described herein may be in a plurality of different formats including sensor data (e.g., spectroscopic data, microscopy data, and / or the like), digital records (e.g., a batching record), direct user input, and / or the like. Additionally, or alternatively, embodiments of the present disclosure may include a generative data engine configured to generate missing data in the event data is missing. In such embodiments, the generative data engine may be used in training models or execution models.

[0143] In some embodiments, the models described herein may include one or more output features including output confidence intervals alongside material properties. Additionally, or alternatively, the models described herein may be configured for ‘Live’ prediction adjustment and refinement and / or tuning, where the model may be predicted based on data gathered by sensors. Page 42 of 226 13824520v1

[0144] One aspect of this system is that it may be capable of performing arbitrary local adjustments to a given input space,(^^1, ^^2, … , ^^^^),, in order to achieve some desired output(s) provided by the function ^^ = ^^(^^1, ^^2, … , ^^^^),, where the function, f, denotes a model of arbitrary non-linearity and discreteness, operating on inputs of arbitrary continuity or discreteness.

[0145] In contrast with the gradient descent methods described herein — which may be used to alter the internal parameters of model functions during training — this procedure applies a “gradient-like” descent method on the space of input variables (not model parameters), and during the execution stage (not the training stage) of the algorithm. The term “gradient-like” descent is used because the concept of a gradient is generalized by the above stated approach to the discrete dimensions of an arbitrarily discrete function, f (where gradients do not technically exist).

[0146] The conditional form of the differential expression described herein permits obtaining a general form of error propagation over the space of all input variables, ^^(^^1, ^^2, … , ^^^^), where the following function denotes the magnitude of the random error expected over an ensemble of instantiations of the system:

[0147] |∆y|c= ∑^^^^ ^^ ^^=1|^^ ^^ ^^∆ ^^^^| ,in the above expression are all continuous variables, and the|∆y|cvalue denotes the contribution to the total error that may be due to variations in continuous inputs only. The possible deviations of discrete variables may be defined by a conditional form (in a similar way as for the generalized case described here), where

[0149] |∆y||( ^^^^)^^| = ^^ ^^|( ^^^^)^^∀ ^^^^∈ { ^^}^^,the j-th choice for the discrete variable ^^^^. Thus, the generalized uncertainty may be given by the set of all possible conditionals:

[0151] ∑^^ ^^|∆y(x1, … , ^^^^)| (^^^^)^^|,over all j values that define the set of all possible discrete values over the i-th discrete variable, and a sum over all i accounts for the contribution from all possible discrete variables.

[0153] It is also generally possible to obtain a probabilistic value for the variation,|∆y||( ^^ ^^) ^^|∀i, j , where the above sum may be weighted over the discrete variables and theirpossible values with a probability density function, ρij, which accounts for the probability that the i-th discrete variable be chosen at random from an instantiation of the system, and that the j-th value be its instantiated value. The function form of this equation is as follows, Page 43 of 226 13824520v1

[0154] ^^(∆y) = ∑^^ ^^^^^^ ^^|∆ ^^( ^^1, … , ^^^^)| ( ^^^^)^^|where ^^(∆y) is the probability of obtaining the absolute shift,|∆ ^^|.

[0155] In general, the output of the models described herein may be multi-dimensional tensors of point values, where those point values may define the evaluation, adjustment or recommendation of a single variable. However, all models may be placed within an additional probabilistic modelling procedure, which characterizes the probability density function over all possible outcomes for a point value, where that probability density may be taken over some subset of the totality of the data on which the model was trained, or some ensemble of subsets of the totality of data, or some other representative dataset.

[0156] The probability density functions obtained over the space of outputs for each model are generally calculated as the multivariate joint distributions over some set of outputs. The joint distributions are used in the Bayesian sense, to estimate any marginalized distribution required for any given purpose.

[0157] Some non-exhaustive examples of the use of calculated multivariate joint distributions by embodiments of the present disclosure may include calculating the expected uncertainty on a predicted / evaluated outcome, to within a specified confidence interval, calculating the information gained (in a formal information-theoretic sense) by obtaining knowledge through a given measurement of the system, calculating the degree to which outputs may be statistically independent of one another, with respect to the model and the data, and / or calculating the logical correlation between any two output variables.

[0158] In general, the use of probabilistic models over a set of point values may allow for conversion of any point value into one or more range values associated with that model output. For example, the point value for a predicted temperature may be 24.3C, but the probabilistic uncertainty on that output may provide the range of values (23.8C, 25.2C), where the first and last temperature in the range denotes the lower and upper bound on the uncertainty to within a 99.9% confidence level, respectively.

[0159] The present disclosure provides for the explainability of the models’ predictions, evaluations, recommendations, and / or generations. In general, a combination of models, described above, are trained to solve for the problems outlined by some of and / or all of the model descriptions herein. However, a combination of probabilistic inference on uncertainty, and probabilistic or causal graph algorithms on the space of all inputs / outputs from the models herein may be used to trace the causal and logical reasons for model predictions, evaluations, recommendations and / or generations. Page 44 of 226 13824520v1

[0160] In general, the methods described herein do not just provide a set of output values and probabilistic uncertainty on those values, but also provide a model-based reason for those outputs and probabilities. Depending on the specific models utilized, automated explanatory outputs may range from physical / chemical insights (e.g., wherever physical / chemical models are utilized) to internal “representational” understandings, that derive from the internal component dynamics of the computation models that have been numerically derived from the data and the training procedure / s.

[0161] The models may be continually updated, where updating is done as a continuous process of training as new data arrives from any set of information sources.

[0162] The models are designed to be probabilistic in their outputs. To this end, the models herein are capable of generating meaningful probabilistic outputs even in the absence of complete information. For example, a model that requires knowledge of compositional properties, and which only receives some of those values (or even none of them) may provide a probabilistic prediction on how the “average” material (from a set of meaningful materials and / or material properties) will behave, along with an estimated uncertainty on that behavior. In this sense, the models are correct from an information-theoretic perspective, capable of reasoning based on partial information. In this sense, the execution stage of the models herein may be continuously able to receive updated information that modify prior predictions, evaluations and / or recommendations and, in general, may continuously improve in accuracy, and reduce uncertainty, as additional relevant information is provided. Normalization and Self-Detection

[0163] A given material will behave differently in different contextual conditions - its contextual material properties may be different (e.g. Strength, Durability, Shrinkage, Strain, Workability, will evolve differently in environments with different temperatures). Therefore, in order to understand the material properties of different materials, it is vital to account for differences in contextual conditions. One way to overcome this challenge is therefore to create a “baseline” across which materials within different contextual conditions will be comparable. example, a material poured into a cube of sides 10cm, may cure very differently when compared to the same material poured into a cubical slab of sides 3m. The latter may have a much greater thermal mass. Thus, its strength gain curves will be sharply different. By “normalizing” across these two sets of contextual conditions to a common baseline (e.g., behavior of cube in standard conditions), it is possible to identify that these are the same underlying materials. Page 45 of 226 13824520v1

[0164] The Material Optimization models described herein may apply these kinds of normalization to understand the underlying behavior of a material for a target contextual condition. This may be done for example in the training stage by feeding the models large quantities of curing data for pours of the same material with different geometries. The model may then gain an understanding of the relationship between geometry of thermal distribution, which could translate into an understanding of the relationship between geometry and the strength curve. This training may also be done using large numbers of simulations which simulate concrete’s real thermal evolution. Another approach may include using physico- chemical models which understand heat diffusion in physical systems.

[0165] In essence, the above may be summarized as measurement devices produce measurements about materials which may later be used in the models herein. These measurements may be adjusted (or corrected by using self-detection / sensor context awareness data. Therefore, data collected in different contextual conditions become comparable. In doing so, the models may allow for not only the collected data but also the materials themselves in different contextual conditions to be made comparable through this adjustment / normalization. Spatially and Temporally Normalized Models

[0166] In general, a contextual material property may be defined at a certain time and at a certain location within the instantiated use-case of the material in question. For example, a contextual material property might include the compressive and flexural strength of the material at a specific location on the surface of one of its faces, and at a specific time. It may also be the case that a contextual material property may change with both time and spatial position within an instantiated material. In general, the models herein may output contextual material properties that belong to a certain position and / or time, or that are spatially distributed in the instantiated material as a field of values throughout its body and / or surface, or that are temporally distributed (as a time series). In the case where values are not spatially or temporally dependent (such as the average workability of a batched cementitious material), the models herein may account for the contextual material property as a “bulk” value (independent of spatial position) and / or a “constant” value (independent of time).

[0167] Many of the models described in this document relate to optimizing for target contextual material properties. These models are trained in such a way as to be “normalized” with respect to spatial and / or temporal constraints (provided they depend on location or time, respectively). The term “normalization” is used to define the ability of a model to account for the functional variation in spatial and / or temporal location; where that model is able to modify Page 46 of 226 13824520v1the contextual material properties in its outputs based on information about the location and / or time of contextual conditions.

[0168] The following will describe a spatially normalized model that constitutes one example of the spatial and / or temporal normalization that are covered here.

[0169] One case is an example where the inputs to the model may be compositional material properties of a cementitious material, temperature of the material at specified locations, where the temperature are received as time-series (obtained by temperature sensors embedded inside an instantiated cementitious material), geometry of the cementitious material, radial distance of the sensor to the surface of the geometry (giving the location of the temperature within the material), and where the radial distance lies along the line that intersects the sensor and the center of mass of the material, and geographic location of the material. The output of the model may be the temperature of the material (in the form of predicted future time-series) at multiple locations within the material. For example, the model may receive the temperature time-series from one temperature sensor, its radial distance, the geometry of the cementitious material and the geographic location, and output a mesh of temperature time- series, equi-spaced throughout the 3D geometry of the material.

[0170] This example model may be trained on a hybrid model that utilizes functions that may be inspired by physical thermal models, artificial neural networks (trained on data of the four types described above, and for a variety of different cementitious material recipes and geometries) and Bayesian inference. That model may then be embedded inside a “material identifying” model, that will use the predictions of the contextual material properties (in conjunction with an empirically solved physical model) to obtain an assessment of which material is being used.

[0171] The physical model module utilizes the physical principle (based on physical assumptions) that the heat within a material dissipates as the inverse exponential of its distance from the heat source. The weights are solved by training against the sensor data time-series values for all positions, and across all measured instantiation of materials (where each material is identified by its compositional material properties).

[0172] The weights may be trained under the assumption that they are constants at a given time and for a given material composition (in general, the temperature of the surface of the material will vary with time as the ambient temperature varies). A set of weights may be obtained on a per-material basis, that characterizes the thermal properties of a given cementitious material composition. Page 47 of 226 13824520v1

[0173] An artificial neural network may then be used, whose inputs may be the temperature time-series at a location, and whose outputs are the future temperature time-series at that location (e.g., a forecasting model). The forecasting model may then be trained on the temperature dataset (which is the same temperature data obtained from the sensors that have been used to train the physical component model). The artificial neural network will predict the future temperature of any given time series based on past time-series.

[0174] The model may then merge the physical and neural network models into one pipeline of logic. This explains only one of many instantiations of material property modelling and material identifying encompassed by this disclosure.

[0175] The models herein may be configured to be able to act in two principal modes or configurations, designated mainly by the time domain in which the models act. In some embodiments, a principal mode may be the planning mode (e.g., ‘static’ mode). This mode optimizes materials prior to the project having begun and prior to having generated any sensor data. Some features of this mode may include material properties may be predicted, materials may be evaluated against performance requirements or target contextual material properties, materials may be recommended based on a ranking derived from a utility function (e.g., lowest carbon mix), and material compositional arrangements may be adjusted or generated in line with performance requirements or target contextual material properties and a utility function or ranking. These models may be continuously learning and improving from the execution phase (as more data is gathered, predictive power increases).

[0176] In some embodiments, a principal mode may be the execution mode (e.g., once the project has begun - also known as ‘dynamic’ mode). This mode optimizes materials once the project has begun taking place, and once it has possibly generated measurements (e.g., from sensors). Some features of this mode may include recommending adjustments (e.g., from a winter to a summer material) mid-project, dynamic batching optimization, pour to pour adjustment or optimization (iterate on compositional arrangement from one pour to the next based on batch / pour sensor data), and batch to batch adjustment or optimization (iterate on recipe from one batch to the next based on batch / pour sensor data). This data may be gathered through methods described in every other section herein, for example through methods described in material identifiers, especially as used in perturbation mode, which allows for sensor information to be gathered from any batch and / or pour, and inform adjustments to later batches and / or pours within a given timescale (e.g., a day), even if the later batch and / or pours relate to different mix recipes. These features may also happen in real time, in reaction to a measurement of properties of the raw materials (e.g. influence recipe during batching based on Page 48 of 226 13824520v1measured cement reactivity). If the same material is being produced for different environments, then there may be value in multiple environments using sensor devices, all feeding data to the models described herein, for more comprehensive characterization. There may typically be more variation in a material’s contextual conditions inter-jobsite than intra-jobsite, which may allow the models to use more varied data in their analysis. Making changes to the material in transit is also an important feature (e.g., addition of water in transit to compensate for some incoming measurements). Such an adjustment may be a recommendation by the models.

[0177] Each of these modes (which may be dubbed static, and dynamic mix optimization) may lead to optimization for different use cases. In some embodiments, a use case may be the static case that optimizes based on predictions that may be based on statistical performance of particular properties (ideally with known standard deviations / confidences) or physico- chemical knowledge of the principles which underpins them. These predictions may be based on historical measurements (e.g., whom the supplier of a material is, but not its reactivity in that particular batch, however, these predictions may lack data regarding the specific project the models may be optimizing for).

[0178] In some embodiments, a use case may be the dynamic case where optimization may be based on real-time (or near-real-time) measurements from batch / pour sensors. This may be, in some embodiments, a continuous control optimization system. The models may use the live / near-real time data to make iterative adjustments to the compositional arrangement based on the sensor measurements which detect variability in raw materials. In this way, drift on batching equipment may be compensated for. For example, a readymixer may have 100 plants. The model for the planning mode (ensemble model) may be used to generate proto- compositional arrangements for all plants (essentially a trial material). And then plant-specific models (that include the use of the dynamic algorithms / control system optimization) may make refinements to that proto-compositional arrangement, adapted to the needs of each plant based on that plant’s conditions and environment (e.g., a plant may be in a more humid location). Its equipment may have more randomness or drift. The source of its aggregates may have more variance. Also, certain materials may be easier to source at one plant than another plant, or cheaper to source → ensemble model for all plants, vs plant-specific model. In some embodiments, planning and execution modes may be different for readymixers and contractors (e.g., context specific to a plant).

[0179] In some embodiments, material adjustment for readymixers may include the planning case (e.g., how may adjustments to this mix to reduce cost or carbon be made, material prices may have changed, so how may the materials be updated to optimize carbon, etc.) and / or Page 49 of 226 13824520v1the execution case (e.g., real-time recipe swap recommendations to optimize day to day production (to reduce cost or carbon, a raw material is running out, so which raw material may be used instead, etc.).

[0180] An additional feature of the models herein may include incorporating human feedback. One notable instantiation of these would be through an interactive user interface. The user may input feedback, the interface may prompt for clarification in an interactive way (using for example the language model information parser of the utility function being interfaced), and the final feedback may be ingested by the utility functions of the relevant model. One instantiation of this may be through a chat-style interface (e.g., using LLM). In some embodiments, models herein may send alerts to users. For example, with respect to particular strength milestones or time milestones that may have changed due to a change in contextual conditions.

[0181] Additionally, models of the present disclosure may include a materials screening feature. For example, models may use hard constraints to screen and discard materials from the get-go such as in evaluation or generation / discovery models. In such embodiments, material screening may reduce the evaluation and / or the search space.

[0182] In some embodiments, models of the present disclosure may include a materials marketplace as a feature. In such embodiments, one or more models may be executed on a centralized platform which may provide a comprehensive database of material producers, their production facilities, the raw materials available at each location, and the formulations produced. Users may define their exact material requirements, and the system may search its database to identify suitable formulations that meet these specifications, utilizing one or more of the models described herein (e.g. for accurate matching to requirements).

[0183] The requirements may include standard material properties (such as strength, durability, or stiffness) and in-use performance criteria (such as achieving specific performance levels within a set time frame or environmental condition), which may be predicted using one or more of the models described herein. Beyond existing formulations, the system may also be capable of generating new material compositional arrangements based on the parameters provided by the user. These newly generated formulations are evaluated and included in the pool of candidate options, where appropriate. Candidate formulations may be ranked based on a customizable utility function. This may allow users to prioritize different factors, such as cost-effectiveness, sustainability, or performance, according to their specific needs. Once a suitable formulation is selected, a user may proceed and enter into a commercial agreement for the procurement of the material with a chosen supplier through the platform. Page 50 of 226 13824520v1

[0184] In some embodiments, the models herein may continuously learn over time, as outputs of the model are validated, or as training datasets continuously grow (e.g., through acquisition of sensor data). Additionally, or alternatively, the models described herein may be effective at dealing with sets of incomplete data and interpolating the data, in contrast to models that may require complete datasets to produce more accurate outcomes. Further, models herein may be effective at dealing with different levels of “completeness” in datasets.

[0185] Embodiments of the present disclosure may use simpler, more time efficient and / or lower complexity models to work in real-time (e.g., during live optimization of production processes). Additionally, or alternatively, larger, more complex models may be used for less time sensitive tasks, that may provide more accurate outputs. Further, outputs of the larger models may be used to validate outputs of smaller models thereby allowing smaller models to learn and / or be trained on larger model’s outputs.

[0186] In some embodiments, models may be able to identify errors in data and / or mismatches in data and / or uncertainty in data and clean the data and / or resolve the issues (e.g., composition that doesn’t match a particular property). Additionally, or alternatively, data cleaning may be performed in the training dataset. In some embodiments, training data may be stored in a graph database.

[0187] Embodiments of the present disclosure may use an autonomous AI lab that may be configured to implement production processes for a limited universe of raw materials and processes available to it.

[0188] Embodiments of the present disclosure may include orchestrator models and / or multi-version distributed models. Given the multitude of models described herein, the methods may include an orchestration system which may be able to orchestrate across the various models herein. This may orchestrate the use of different models based on different information. In a first instance, this system may have a notion of the use case for which the method herein is used and would be able to route the input data to the correct model (MO-X). In general, it may even be able to orchestrate a sequence and / or parallel combination of use of each model (e.g., use MO-1 & MO-2 in parallel, feed the output data to another MO-X). This system may allow the method to act as a distributed system of models that may fulfil different purposes and may be used multiple times in parallel or in sequence.

[0189] Going one step further, for each one of the models described herein it may be possible to have different versions of the model, which may be trained in different ways to create intentional biases and / or specialize the models towards outperforming in a particular field. For example, one version of a model MO-X may be trained on a large portion of Page 51 of 226 13824520v1incomplete data (which may allow the model to become robust towards incomplete data) whereas another may be trained on predominantly complete data, which may be more accurate than the models trained on partial data and may be used whenever additional data is available. Another example may be a model trained predominantly on mixes composed of SCMs (supplementary cementing materials), and may therefore be particularly effective at predicting, evaluating, and / or generating SCM-based material designs. This latter example may be generalized as training models to effectively work in different volumes or parts of material space (e.g., model for C80 and above, model for materials below C50, and / or the like). In some embodiments, this may be described as an adaptive model. One instantiation of the distributed model system may be a distributed system of GANs (generative adversarial network), where a system of distributed GANs, configured with different biases, may act as an ensemble which may be intentionally skewed towards certain types of mixes over others.

[0190] In some embodiments, the models herein may be trained via data generated from simulations. These simulations may be chemical simulations, in some embodiments. In one embodiment, material simulations may be executed on a quantum processor, and / or using a quantum algorithm, and the output of those simulations may be used to train any of the models described herein, or as an input to any of the models described herein. Additionally, or alternatively, simulations and / or predictions of the models herein may be done on quantum processors and / or using quantum algorithms. Material Simulation and Prediction Model

[0191] Embodiments of the present disclosure may be configured to simulate material and generate material predictions. In some embodiments, the models considered by the present disclosure may predict properties of a material in target contextual conditions. In such embodiments, the models described herein may generate predictions based on material compositional data. Additionally, or alternatively, the models described herein may generate predictions based on property data of another type (or partial property data). Further, the models described herein may generate predictions based on historical properties or compositional data of the same material or anther material. In some embodiments, the models herein configured as a prediction model may generate predictions based on evolutions of material properties over time and / or space for given contextual conditions.

[0192] In some embodiments, the models considered by the present disclosure may be configured to predict material compositional data. In such embodiments, the models may generate predictions based on compositional data of another type (e.g., structure from chemical Page 52 of 226 13824520v1formulation). Additionally, or alternatively, the models may generate predictions based on property data (e.g., to identify material or instantiation of material). Additionally, or alternatively, the models may generate predictions based on prior compositional data or property data. Additionally, or alternatively, the models may generate predictions based on evolutions of compositional data over time and / or space.

[0193] In some embodiments, the models considered by the present disclosure may be configured to simulate one or more units of material over time. In such embodiments, the models may simulate material in a set of contextual conditions (based on contextual conditions). Additionally, or alternatively, the models may simulate chemical reactions or interactions. For example, the models may predict the composition or properties of the final output of the reaction, based on the input raw materials and the one or more contextual conditions during the reaction. Further, chemical reaction may be atomic, molecular, or other basic unit (e.g., grains, composites, and / or the like). In some embodiments, the simulation may include material composition, structure, and / or properties. Additionally, or alternatively, units of materials may be at any scale (e.g., atomic→macro), and / or the simulations may be any spatio-temporal (4D) simulation, or just a spatial (3D) simulation. Further, the material simulation model may include the prediction capabilities other models described herein.

[0194] In some embodiments, the models considered by the present disclosure may be configured to predict composition and / or properties of a material that undergoes a production process based on the production process and the raw materials described herein. In such embodiments, control parameters of processes and / or process contextual conditions may be input into the model for prediction. In some embodiments, the models may be configured to predict properties of a known material. In some embodiments, the models may be configured to predict compositions of output materials. Additionally, or alternatively, the models may generate predictions based on sensor data monitoring the production process.

[0195] In some embodiments, the models considered by the present disclosure may be configured to predict attributes of production processes, based on representations of processes. In such embodiments, a model may predict, determine, and / or estimate attributes of production processes (e.g., cost, carbon, time efficiency, and / or the like) based on a representation of the production process, which may include material data about raw materials, intermediate material, output materials, the production pathway and processes themselves, control parameters, and / or equipment used. Page 53 of 226 13824520v1Formal Description of Inputs and Outputs

[0196] Embodiments of the present disclosure may be configured to map an input and / or combination of input material data types to a specific material data output and / or combination of outputs, dependent on what function a model may be directed to. For example, any of the models described herein directed to predicting properties of a material in target contextual conditions may follow formal input and output descriptions such as X (+ Contextual conditions optionally) → Properties (+ Contextual conditions optionally). For X = Compositional data, the formal descriptions may take the forms of Compositional data → contextual material property, Compositional data → static material property, and / or Compositional data → contextual + static material property. In some embodiments, X = Property such that the model may use past properties to predict future properties.

[0197] Additionally, or alternatively, any of the models described herein directed to predicting compositional data, the models may follow a formal input and output descriptions such as X → Compositional Data. Possible inputs for X may include X = other type of compositional data, X = Property data, and / or X = prior compositional data.

[0198] Additionally, or alternatively, any of the models described herein directed to simulating one or more units of material over time, the models may follow a formal input and output descriptions such as X → Material Simulation. Further, formal descriptions for such embodiments may include Composition + Contextual Conditions → Simulation, Composition + Properties to be simulated + Contextual Conditions → Simulation of properties in action, and / or Composition 1 + Composition 2 +...+ Composition N + Contextual Conditions → Simulation of chemical reaction / interaction.

[0199] Embodiments of the present disclosure may employ model training based on smart sensors (and all the novel embodiments discussed herein), where compositional data may be gathered using spectroscopy / photonics / high frequency E&M wave-based sensors, and / or the like. Further, model training may include digitization of digital records and LLMs configured to understand input data.

[0200] Additionally, or alternatively, the models described herein may include AI to make predictions incorporating the use of knowledge of chemistry (e.g., learned by a GPT), physico- chemical models, and / or generative AI to fill in gaps in data (training or input). Additionally, or alternatively, embodiments of the present disclosure may output confidence intervals and uncertainties on simulations. Additionally, or alternatively, embodiments of the present disclosure may be configured for ‘Live’ prediction adjustment and refinement or tuning based on real-world batches or material instantiations. Page 54 of 226 13824520v1

[0201] Additionally, or alternatively, embodiments of the present disclosure may be configured to predict different contextual conditions may be novel and not in literature, using predictions, such as, 3D + time predictions (so spatio-temporal predictions / simulations).

[0202] In some embodiments, materials may be represented using multi-scale modeling for data representations and for property outputs, and / or graph-based representation of molecules. Additionally, or alternatively, embodiments of the present disclosure may generate predictions of chemical reactions, molecular interactions, atomic interactions, and / or how multiple material may interact. In such embodiments, the modeling may happen at large scales (e.g., simulating reaction in batteries (e.g., reduction and oxidation reactions)).

[0203] Additionally, or alternatively, embodiments of the present disclosure may be configured for quantum representation of materials or encoding on qubits, executing simulation models on quantum computers, and / or sensing using quantum sensors.

[0204] Additionally, or alternatively, embodiments of the present disclosure may employ live retraining over time or models may persistently learn and / or be retrained. Further, models may be retrained on additional data it itself generates, or data gathered from sensors or records.

[0205] Additionally, or alternatively, embodiments of the present disclosure may include multiple specialist models (e.g., for different material types, different material scales, and / or the like) and orchestration across those models. In such embodiments, a model may know how to select the models and / or route to the right models based on inputs and / or the like.

[0206] Additionally, or alternatively, embodiments of the present disclosure may employ transfer learning. In such embodiments, models may use transfer learning to train one model to become effective at another type of process (e.g., teach a specialist model to predict conductivity of crystals, to become effective at predicting conductivity of electrolytes, and / or the like).

[0207] In some embodiments, any of the prediction models described herein may work with each other. For example, if input into the model is a composition, then the model may predict its structure, or multiple structures for the composition. Further, the model may then ask the user which structure for the materials the user wants to simulate or predict. Additionally, or alternatively, the model may output predictions or simulations for all of them.

[0208] Additionally, or alternatively, embodiments of the present disclosure may be configured to generate predictions of material stability, including stability of multi-component materials which may be candidate materials (e.g., novel alloys or composites). In some embodiments, stability may be measured in a number of ways. A non-exhaustive list may include thermodynamic / kinetic / energy / chemical stability (e.g., stability of a material to exist Page 55 of 226 13824520v1in a particular phase (phase diagrams), stability for molecule / chemical not to decompose into constituent elements (e.g., formation energy / chemical stability), stability in reactions (e.g., reaction with air), measuring stability using activation energy, and / or the like), mechanical stability (e.g., does a material break under stress / strain / forces), and / or electrochemical stability (e.g., is a material chemically stable in the presence of electric fields), where models herein may predict an electrochemical stability window, reduction or oxidation potentials / decomposition, and / or electrode-electrolyte stability.

[0209] Additionally, or alternatively, embodiments of the present disclosure may generate predictions of properties based on symmetries, such as symmetries of the material structure (e.g., molecular structure). In such embodiments, predication may be based on knowledge of another material and / or model realizing that the material shares symmetries with the other material.

[0210] Additionally, or alternatively, embodiments of the present disclosure may predict material characteristics of real material instantiations using sensor data. For example, a model may ingest spectroscopy data from spectroscopy sensor monitoring material instantiation, identify material based on spectroscopy data, and / or predict properties based on material identifiers. Further, a model may ingest multivariate sensor data, process the data, and / or generate property predictions.

[0211] Additionally, or alternatively, embodiments of the present disclosure may be configured to simulate materials over time varying contextual conditions, allowing models to predict and / or simulate how materials behave under dynamic conditions (e.g., temperature cycles, mechanical vibrations, stress changes over time, and / or the like).

[0212] Additionally, or alternatively, embodiments of the present disclosure may include material identifiers that may, in some embodiments, be an “incomplete” description of a material in the real world and / or the way the present disclosure may represent materials may be fuzzy to an extent compared to the reality of the material instantiation.

[0213] Additionally, or alternatively, embodiments of the present disclosure may include graph neural networks (GNN). For embodiments including multiscale materials, a hierarchical GNN may be used to model materials at different scales. Further, one or more levels of the graph may represent atomic and / or molecule scales and other levels may represent larger structural features (e.g., grain boundaries in metals / metal alloys or phase distributions in composites).

[0214] Additionally, or alternatively, embodiments of the present disclosure may include PINNs (physics infused neural networks) for material modeling. In one embodiment, physical Page 56 of 226 13824520v1constraints may be represented by differential equations that may be introduced into the loss function of a neural network (e.g., the model may be constrained to adhere to conservation of mass, energy, and / or charge). In some embodiments, relationships such as Hooke’s Law, Heat Conduction Laws, Conservation of Energy, Phase Stability Conditions, Fourier’s Law, and / or the like may be incorporated in the loss function. In such embodiments, the loss function may be defined as: Total Loss = Data Loss + ^^*Physics Loss. In this equation, Data Loss may be a measure indicative of the error between model predictions and real-world observations, Physics Loss may be a measure indicative of a degree of violation of the laws of physics (e.g., stress- strain relationships, Navier-stokes, and / or the like), and ^^ may represent the weighting of physics loss with respect to the data loss. Material Evaluation

[0215] Embodiments of the present disclosure may be configured to evaluate material- related data against a set of target objectives. In some embodiments, the models considered by the present disclosure may evaluate a set of materials against a set of target objectives, and / or may output an evaluation identifier. In such embodiments, the models described herein may evaluate against a single objective. Additionally, or alternatively, the models described herein may evaluate against multi-objectives (multi-objective function or utility function). Additionally, or alternatively, the models described herein may assign a single rank to each material to find a “best” (e.g., dependent on the set of target objectives) material. Additionally, or alternatively, the models described herein may assign ranks for every material for each objective. As an example, a non-exhaustive list of types of objectives considered by embodiments of the present disclosure may include desired properties (e.g., maximize conductivity), desired use cases (e.g., use material as electrode in battery, or as concrete replacement), minimize cost of material, minimize embodied carbon, evaluate based on ease of material production, and / or the like.

[0216] In some embodiments, the models described herein may specify contextual conditions material to evaluate materials based on objectives for given contextual conditions. Additionally, or alternatively, the models described herein may output simulations for material scenario analysis (e.g., to showcase how each material behaves in desired environment). Additionally, or alternatively, the models described herein may use simulations to evaluate materials. Additionally, or alternatively, the models described herein may output all materials that meet a certain threshold. Page 57 of 226 13824520v1

[0217] In some embodiments, the models considered by the present disclosure may evaluate a set of production processes (or aspects of a production process) against a set of target objectives, and may output an evaluation identifier. In such embodiments, the models described herein may evaluate one production process against metrics (e.g., carbon ratings). Additionally, or alternatively, the models described herein may evaluate production processes against each other. In some embodiments, the models described herein may evaluate single “step” production processes (e.g., mixing). Additionally, or alternatively, the models described herein may evaluate multi-step production processes.

[0218] In some embodiments, the models described herein may evaluate control parameters during production and / or production contextual conditions. Further, the production process may be a chemical reaction. As an example, a non-exhaustive list of objectives to evaluate against considered by embodiments of the present disclosure may include desired outputs from processes (e.g., desired output material, desired output material property, desired output material characteristic, desired output material attribute, and / or the like), desired attributes of processes (e.g., length of process, carbon emission of process, cost of the process, and / or the like), and / or the like. Additionally, or alternatively, the models described herein may evaluate the use of particular equipment or machinery against other equipment.

[0219] In some embodiments, the models considered by the present disclosure may evaluate a set of contextual conditions for a given use case against a set of target objectives and may output an evaluation identifier. In some embodiments, contextual conditions may be material contextual conditions (e.g., for a set of concrete pour geometries → evaluate what geometry yields best results according to objective). Additionally, or alternatively, contextual conditions may be production process contextual conditions (e.g., temperature during a controlled process, for a range of temperatures → evaluate what temperature is optimal during material production, etc.). Formal Description of Inputs and Outputs

[0220] Embodiments of the present disclosure may be configured to map an input and / or combination of input material data types to a specific material data output and / or combination of outputs, dependent on what function a model may be directed to. For example, any of the models described herein directed to evaluating a set of materials against a set of target objectives may follow formal input and output descriptions such as Set of material identifiers → evaluation identifier and material identifier pair for each material, Set of material identifiers → material identifier with highest rank (e.g., evaluation identifier = rank), Set of material Page 58 of 226 13824520v1identifiers + contextual conditions → evaluation identifier evaluation identifier and material identifier, and / or the like.

[0221] Additionally, or alternatively, any of the models described herein directed to evaluating a set of production processes (or aspect of a production process) against a set of target objectives may follow formal input and output descriptions such as Set of production process identifiers → evaluation identifier and production process identifier.

[0222] Additionally, or alternatively, any of the models described herein directed to evaluating a set of contextual conditions for a given use case against a set of target objectives may follow formal input and output descriptions such as Set or Range of Contextual Conditions values for given scenario → evaluation identifier and contextual condition value.

[0223] Embodiments of the present disclosure may predict properties from compositions to evaluate novel materials (e.g., versus evaluating based on known properties). Stated differently, the models described herein, in some embodiments, may use prediction models and / or simulation models in conjunction with evaluation models. Additionally, or alternatively, the models described herein may be configured to evaluate based on live sensor data measuring material properties. Further, embodiments described herein may leverage models above (e.g., the prediction models) to obtain a material evaluation. Additionally, or alternatively, the models described herein may evaluate based on multiple objectives together (e.g., one embodiment may use Pareto optimization or genetic algorithms)

[0224] In some embodiments, the models described herein may evaluate based on utility in use cases (rather than just predicted properties). Additionally, or alternatively, the models described herein may evaluate considering material properties and / or output material performance, but also the production process (including energy required for production, which may be indicative of carbon and / or cost). Additionally, or alternatively, the models described herein may include prompting to express requirements for evaluation in natural languages. Further, the prompting may allow for flexibility in types of objectives and / or evaluations. Additionally, or alternatively, the model may ask for additional information to perform more effectively, if not enough information is provided for the model to rank appropriately. Further, the models may construct an objective function and / or extract constraints for evaluation based on an inferred meaning of a prompt.

[0225] In some embodiments, the models described herein may be configured for material screening (e.g., models may discard materials before evaluating them based on hard constraints to increase efficiency). Additionally, or alternatively, the models described herein may evaluate materials based on use cases and / or simulated performance in the field, rather than material Page 59 of 226 13824520v1properties (e.g., evaluate by performance during spatio-temporal simulations). Further, the models herein may have a “use case definition module,” where the user may define a use case → “context-aware evaluation.” In such embodiments, the model may take contextual conditions into account to evaluate materials.

[0226] In some embodiments, the models described herein may include dual-tier evaluation. For example, the models may evaluate materials both on properties as well as real world use cases or performance together. In such embodiments, the models may score both criteria independently. Additionally, or alternatively, the models may give an overall score based on both criteria.

[0227] In some embodiments, the models described herein may include active learning (e.g., the models may use real world sensor data to test how materials are performing in the real world). In such embodiments., information may be fed back into the models to refine the models’ evaluations (e.g., the models may evaluate a set of materials, the set of materials may then be used in the real world, data may be collected on the set of materials in the real world sense them, and if, according to the collected real world data, the evaluation is incorrect, the models may learn from real sensor data). Additionally, or alternatively, the models described herein may do similar processes to learn about production processes and refine the models’ evaluation of the production processes.

[0228] In some embodiments, the models described herein may include multi-scale evaluation (e.g., the models may evaluate materials based on material micro- and / or macro- scale properties and / or structure). Material Optimization

[0229] Embodiments of the present disclosure may be configured to optimize material- related data, properties, performance, compositions, and / or the like. In some embodiments, the models considered by the present disclosure may optimize one of or a plurality of material compositions based on target objectives. In such embodiments, the models described herein may optimize a set and / or plurality of material compositions (e.g., optimize a set of compositional arrangements). Additionally, or alternatively, the models described herein may keep the same chemical composition and / or optimize structure. Additionally, or alternatively, the models described herein may keep the same structure and / or optimize chemical composition. In some embodiments, the models described herein may allow both the structure and chemical composition to vary. A non-exhaustive list of possible material compositions may include atomic composition, molecular composition, proportions of raw materials, and / or the Page 60 of 226 13824520v1like. Additionally, or alternatively, the models described herein may optimize based on target objectives in contextual conditions.

[0230] In some embodiments, the models considered by the present disclosure may optimize one of or a plurality of production processes based on target objectives and material outputs. In such embodiments, the models described herein may include live sensor data monitoring the process lifecycle (e.g., sensing the raw materials, sensing the production processes themselves, sensing the output products, any combination of the previous, and / or the like). Additionally, or alternatively, the models described herein may optimize contextual conditions during any part of the production process (e.g., by changing heat levels in a kiln, by changing speed of a mixer over time, and / or the like). In some embodiments, the production process may be a chemical reaction.

[0231] In some embodiments, the models considered by the present disclosure may optimize one or a plurality of contextual conditions based on target objectives. Additionally, or alternatively, the models described herein may optimize one or a plurality of contextual conditions based on live sensor data monitoring the material instantiation and its contextual conditions. Formal Description of Inputs and Outputs

[0232] Embodiments of the present disclosure may be configured to map an input and / or combination of input material data types to a specific material data output and / or combination of outputs, dependent on what function a model may be directed to. For example, any of the models described herein directed to optimizing one of or a plurality of material compositions based on target objectives may follow formal input and output descriptions such as Material Composition + objective → optimized composition.

[0233] Additionally, or alternatively, any of the models described herein directed to optimizing one of or a plurality of production processes based on target objectives and material output may follow formal input and output descriptions such as Production Process Identifier + objective → Optimized production process identifier. A non-exhaustive list of production process identifiers may include a full representation of the entire production process, a vector / matrix / operator representation of a step, the value of a control parameter / process contextual condition, and / or the like.

[0234] Additionally, or alternatively, any of the models described herein directed to optimizing one of or a plurality of contextual conditions based on target objectives may follow Page 61 of 226 13824520v1formal input and output descriptions such as Contextual Condition in a given scenario + objective → Optimized contextual condition in given scenario.

[0235] Embodiments of the present disclosure may optimize based on data for materials from sensors in a target use case. Further, the optimization via data from sensors may occur in both a 'training' case, and also in a ‘live' case (e.g., where inputs and / or outputs may be measured to change and / or adjust processes). Additionally, or alternatively, the models described herein may optimize production process via data from sensors. For example, sensor devices may sense raw materials, production processes, final products, and / or the like. Further, the models herein may be trained to create a feedback loop from raw materials through the process to final product. Based on the feedback loop, embodiments of the present disclosure may optimize the production process. A non-exhaustive list of what may be altered during optimization may include proportions of raw materials, control parameters during the process, entire steps of the process, and / or the like.

[0236] Additionally, or alternatively, embodiments of the present disclosure may be configured to digitize records and / or parse the records using AI (e.g., test records). In some embodiments, material testing may provide record data which may be used to feed the models to refine the understanding of the models of the material. Further, documentation associated with the production of materials may also provide valuable data, both for training and during execution, when optimizing a production process live.

[0237] Additionally, or alternatively, the models described herein may optimize production processes live, in real time, using sensor data and / or data records. In such embodiments, the models may optimize production control parameters and / or production contextual conditions. Further, the models herein may be configured to adapt to real time changing contextual conditions. Additionally, or alternatively, the models may improve and learn using sensor data. In some embodiments, sensor data may be used for real time predictive maintenance.

[0238] Additionally, or alternatively, the models described herein may leverage prediction models for optimization. Additionally, or alternatively, the models described herein may use rea plurality of compositional arrangements to batch optimize the plurality of compositional arrangements based on available materials.

[0239] Additionally, or alternatively, the models described herein may input a material space as a constraint (e.g., this may be a type of material (only crystals) or this may be a set of atomic elements the model may use (e.g., use only N, C, O, Mg, etc.)). Page 62 of 226 13824520v1

[0240] Additionally, or alternatively, the models described herein may use the prediction and / or simulation model to power optimization (e.g., to predict, simulate, and / or model material properties)

[0241] In some embodiments, the models herein may optimize both a material and the material’s production process, as well as contextual conditions and / or control parameters for both, simultaneously together. Further, the models herein may create a feedback loop between a material and the material’s production process where optimizing one feeds into the optimization of the other. In some embodiments, the models described herein may globally optimize both simultaneously. As will be understood by one of ordinary skill in the art in view of the present disclosure, both compositions and production processes or production parameters may have an impact on properties of materials, so by optimizing both together, they may feed into each other.

[0242] Additionally, or alternatively, the models described herein may optimize both a material and a material’s production process based on target properties and target use cases / or target behavior within an environment and / or contextual conditions (e.g., may use NSGA-I, NSGA-II, NSGA-III algorithm → non-dominated sorting genetic algorithm I, II & III).

[0243] Additionally, or alternatively, the models described herein may optimize both materials and production processes for carbon and / or sustainability.

[0244] In some embodiments, the models herein may use spatio-temporal simulations (e.g., digital twin) to create virtual environments where material may be virtually simulated and / or tested against desired properties and / or use case.

[0245] In some embodiments, the models described herein may use reinforcement learning, genetic algorithms, Bayesian optimization using surrogate models, particle swarm, simulated annealing, and / or the like.

[0246] Additionally, or alternatively, the models described herein may move in search space more efficiently using symmetries. Further, embodiments of the present disclosure may constrain the search space. Material Generation, Design, and Discovery

[0247] Embodiments of the present disclosure may be configured to generate material, design materials, and / or discover materials (e.g., candidate materials). In some embodiments, the models considered by the present disclosure may generates one of or a plurality of material compositions based on target objectives. In such embodiments, the models described herein Page 63 of 226 13824520v1may be configured to discover materials of a certain type, a certain composition, a certain structure, and / or the like.

[0248] In some embodiments, the models considered by the present disclosure may generate a plurality of material compositions continuously (e.g., discovery mode for candidate materials). In such embodiments, the models may be configured to discover materials of a certain type, a certain composition, a certain structure, and / or the like.

[0249] In some embodiments, the models considered by the present disclosure may generate one of or a plurality of material production processes based on a desired material output. In some embodiments, objectives and / or desired attributes of the process itself may include length of the process, carbon emission of the process, cost of the process, and / or the like. Additionally, or alternatively, the models may generate one of or a plurality of material production processes based on target objectives (e.g., the process should make the material as pure as possible, minimize greenhouse gas emissions of production process, and / or the like). Ib some embodiments, the models here may include constraints such as constraints on raw materials, constraints on set of equipment or what production processes are possible, and / or the like. Additionally, or alternatively, embodiments of the present disclosure may transmit production process as instructions to an autonomous laboratory. Formal Description of Inputs and Outputs

[0250] Embodiments of the present disclosure may be configured to map an input and / or combination of input material data types to a specific material data output and / or combination of outputs, dependent on what function a model may be directed to. For example, any of the models described herein directed to generating one of or a plurality of material compositions based on target objectives may follow formal input and output descriptions such as Target Objective → Composition.

[0251] Additionally, or alternatively, any of the models described herein directed to generating a plurality of material compositions continuously (e.g., discovery mode of candidate materials) may follow formal input and output descriptions such as Constraint on material space → Composition.

[0252] Additionally, or alternatively, any of the models described herein directed to generating one of or a plurality of material production processes based on a desired material output may follow formal input and output descriptions such as Desired material output → Production process (including raw materials) to produce desired material output. In such Page 64 of 226 13824520v1embodiments, the models herein may generate materials for a defined target use, and / or discover all possible materials in a given space (e.g., constrained by available inputs).

[0253] Embodiments of the present disclosure may use sensors for training and / or data input. Further, the sensors may include any of the sensor devices as described herein. Additionally, or alternatively, the models described herein may Additionally, or alternatively, embodiments of the present disclosure may be configured to digitize records and / or parse the records using AI (e.g., test records) for training data. In some embodiments, the models herein may be configured to prompt for requirements and configured to limit scope of discovery. Additionally, or alternatively, the models described herein may account for contextual conditions. In some embodiments, the models described herein may be AI models that may include physico-chemical embeddings.

[0254] Additionally, or alternatively, embodiments of the present disclosure may generate new raw materials and may feed outputs into inputs. As such, the models may, in some embodiments, generate intermediate materials. Further, the intermediate materials may be used to see what additional materials may be generated. Additionally, or alternatively, embodiments of the present disclosure may use any of the predictive modelling described herein and / or, in conjunction with, model orchestration.

[0255] In some embodiments, the models described herein may generate multi-scalar versions of materials. Additionally, or alternatively, the models described herein may generate end products, and also generate compositional arrangements to make the end material (generalization of a material). In some embodiments, this may lead into a further “production” model.

[0256] Additionally, or alternatively, embodiments of the present disclosure may execute discovery on quantum computers and / or use quantum simulations. Further, any of the sensor devices described herein may leverage quantum sensing.

[0257] In some embodiments, the models herein may be configured to generate chemical formulas (e.g., using stable diffusion model or other GAN, based on the rules of chemistry, and / or the like). Additionally, or alternatively, the models described herein may simulate structures of molecules. In such embodiments, the simulations may be based on molecular physics.

[0258] In some embodiments, the models described herein may be configured for discovery of material space using generative exploration (e.g., diffusion model, latent diffusion model, and / or the like). Page 65 of 226 13824520v1

[0259] In some embodiments, training of the models described herein may be based on real sensor data (e.g., spectroscopy for composition, wave-based more broadly for properties, and / or the like). Further, training of the models described herein may account for contextual conditions (e.g., use context awareness to monitor the contextual conditions of the material sensed). In some embodiments, training dataset may include multimodal data that may be sourced from material databases, sensor data, documents & records data (e.g., compliance testing for materials), and / or the like. Additionally, or alternatively, the models described herein may undergo prompt training (e.g., training to create mapping between text embedding and prompt). Embodiments of the present disclosure may include a plurality of learning techniques for training such as reinforcement learning, where an ML agent interacts with [x] to understand how changes in [x] affects the properties of the generated material and a reward is generated associated with how closely the output property matches the desired target. In some embodiments, [x] may be composition, [x] may be atomic geometry, [x] may be a proportioning of raw materials, [x] may be a production process, and / or the like.

[0260] In some embodiments, the models described herein may be configured to ingest prompts as inputs. Further, the models described herein may be configured to converse with users and generate and ask clarifying questions when required. Additionally, or alternatively, the models herein may extract relevant information from prompts, and represent this information in “material space.” Further, the models herein may extract desired characteristics, which may be turned into an objective function. In some embodiments, the models herein may use token and transformer-based architecture, where a user may input a prompt, the prompt may be tokenized, the token may be embedded into a vector space, the token space may be mapped to material space, and / or the vectors of material space may be ingested by a generative model. Further, embodiments of the present disclosure may be multimodal models.

[0261] In some embodiments, the models herein may be configured to check stability of generated material identifiers. Further, the models herein may assign confidence to stability. Additionally, or alternatively, the models herein may use predictive model to predict properties of generated material. Additionally, or alternatively, the models herein may simulate generated materials in intended use cases. In some embodiments, simulations may be computationally draining. In such embodiments, to be more computationally efficient, simulations may be performed on subsets of generated materials (if in discovery mode). Further, if a material reaches threshold of proximity to desired property (e.g., as computed through determination of objective function), then the models here may simulate the material. In some embodiments, the Page 66 of 226 13824520v1models herein may recalculate objective function after simulations (if the result is better or worse than expected).

[0262] Additionally, or alternatively, types of input material characteristics that models of the present disclosure may be configured to receive may include desired properties (e.g., conductivity, thermal expansion, dynamic modulus, dielectric constant, band gap, carbon, and / or the like), desired use cases (e.g., as a foundation for a building), and / or the like.

[0263] In some embodiments, the models herein may incorporate “Meta-properties” to generate materials accounting for cost and / or carbon. For example, a first method may be using a GPT / LLM to estimate monetary cost and embodied carbon for producing said material. Further, a second method may be training a model on cost and carbon data for a wide variety of materials and allowing the model to interpolate / infer for the new material based on the old material. In some embodiments, the model may create a mapping and / or function between material space and cost / carbon space. Further, embodiments of the present disclosure may methods described herein to make the function ‘continuous,’ thus allowing for interpolation for candidate materials (e.g., materials not seen previously in material space). Additionally, a third method may be encoding fundamental understanding of material production into models, so the models may work this out from first principles (e.g.,

[0264] CM=SUMi(CRM i*VRMi)+CPP

[0265] CM = Cost of Material; CRM = Cost of Raw Material; VM = Volume of Raw Material; CPP = Cost of Production Process

[0266] ECM=SUMi(ECRM *iVRMi)+ECPP

[0267] ECM = Embodied Carbon of Material; ECRM = Embodied Carbon of Raw Material; VM = Volume of Raw Material; ECPP = Embodied Carbon of Production Process). A fourth method may, in some embodiments, combine material production models, and estimate based on generated production processes and knowledge of processes.

[0268] In some embodiments, the models herein may generate amorphous complex materials that may be candidate amorphous complex materials (e.g., novel and not in literature). Further, the models herein may do so by modeling things as probability distributions at the mesoscale. Additionally, or alternatively, the models herein may move in search space to perform hybrid solution generation and optimization. In such embodiments, this may generate multiple solutions representative of search space / that may cover the search space and, at each iteration, observe how each initial solution moves through search space. Further, the models herein may be configured to continue with the solution that appears most promising and / or appears to be reaching an optimum fastest. Additionally, or alternatively, the models herein Page 67 of 226 13824520v1may generate a large number of “guess” solutions, and evaluate them using the evaluation models described herein, and select the solution that best matches. Further, the models herein may perform multiple iterations and / or rounds of this until an optimal solution is reached.

[0269] In some embodiments, the models herein may generate composition and / or structure based on symmetries (e.g., use symmetries to construct molecule or crystal structures)

[0270] In some embodiments, the models herein may treat production processes as operators acting on states (e.g., causing state evolution of a material). In such embodiments, operators may act on materials representation. Additionally, or alternatively, the models herein may use path integral formulations to represent interactions between materials and equipment. For example, the path may take the form of Starting state of raw materials → Production process → End state of raw materials. In this way, the production process may be a “path” to get from start to end. In such embodiments, path integral formalism and / or modeling methods may be used to model these paths.

[0271] In some embodiments, material generation and / or design, and material production design generation may be used in conjunction. For example, a user may want to estimate carbon intensity and complexity of production using the latter model, which may inform whether a particular material is an effective material. In such embodiments, this may feed into material evaluation (e.g., a material may not be useful if the material cannot be easily produced, and / or if the material has a higher cost compared to an alternative material).

[0272] Embodiments of the present disclosure may include multiple specialist models (e.g., for different parts of prediction, simulation, optimization, and / or the like) and / or model orchestration. Material Production

[0273] Material productions considered in the present disclosure may be configured to employ any of or any combination of data object types as described herein. A non-exhaustive list of data objects that may be used in any material production herein may include materials (e.g., raw materials, intermediate materials, output materials, final product, and / or the like), processes (e.g., may be defined as anything that makes a material evolve from state ^^ to state ^^ + ∆ ^^), production processes (e.g., may be defined as a process with the goal of producing a final product or target material), equipment (e.g., machinery and / or apparatuses which may execute or may be used to execute a process), control parameters (e.g., controllable external parameters of a process), and / or the like. Page 68 of 226 13824520v1

[0274] Additionally, or alternatively, material productions considered in the present disclosure may be configured to employ any of or any combination of models as described herein. A non-exhaustive list of models that may be used in any material production herein may include a model configured to predict composition and / or properties of a material that goes through a production process based on the production process and the raw materials (e.g., Raw Materials + Process → Output Materials), a model configured to evaluate a set of production processes (or aspects of a production process) against a set of target objectives, and output an evaluation identifier (e.g., Process + Evaluation Parameter → Process Evaluation and / or Processes + Target Objectives → Processes Ranking), a model configured to optimize one of or a plurality of production processes based on target objectives and material output (e.g., Process + Target Objective → Optimized Process), a model configured to generate one of or a plurality of material production processes based on a desired material output (e.g., Desired Material Output → Process), and / or the like. Production Processes and Pathways

[0275] As used herein, the terms “Compositional Arrangement”, “Production Pathway” and “Pathway” may be used to refer to any method which evolves one or a plurality of materials from state S to state S + ∆S. For example, a production pathway may include the creation of a metal alloy from its constituent metallic elements, the chemical synthesis of a polymer, the construction of a crystalline material from its constituent parts, the conversion of a pure element into the same pure element configured with another structure, the mixing of raw materials to form a composite material, the construction of a battery from its raw constituents, etc.

[0276] As used herein, the term “Production Process” and / or “Compositional Arrangement” may be used to refer to any step, intermediate step, or plurality of steps that form part of a Production Pathway, in whole or in Part, to evolve one or a plurality of materials from state S to state S + dS or S + ∆S. For example, a production process may include the smelting of metal ores, in the wider process of creating a metal alloy from its constituent metal ores.

[0277] As used herein, the term “Raw Materials” may be used to refer to any material, in the context of a production process or production pathway or compositional arrangements, which is an input to the production process or pathway. For example, the monomer unit may be considered the raw material being input into a polymerization process.

[0278] As used herein, the terms “Output Material”, “Final Material”, and “Final Product” may be used interchangeably to refer to any material, in the context of a production process, Page 69 of 226 13824520v1compositional arrangements, or production pathway, which is an output of the production process. For example, a polymer is the output material of a polymerization process and more.

[0279] As used herein, the terms “Intermediate Material” and “Intermediate product” may be used to refer to any material, in the context of a multi-step production process, compositional arrangement or pathway, which is an output of one process, and an input of the next process. For example, cement is an intermediate material in the production process for the creation of concrete, from quarried material (e.g. from limestone).

[0280] As used herein, the term “Production Equipment”, may be used to refer to any apparatus or machinery which executes or is used to execute a production process, in whole or in part. For example, production equipment may refer to one or a plurality of any of the following: CNC cutter, extruders, furnace, kiln, grinding machine, batching machine, mixer, blenders, injection molding machine, cooling systems, chemical reactors, crystallizers, filters / separators, and more.

[0281] As used herein, the terms “Process Parameter”, “Control Parameters”, “Process Contextual Conditions”, “Process Control Parameters, “Process” and “Process Parameters” may be used interchangeably to refer to any parameters or variables that may be controlled during a production process or pathway and that may influence the production process or its output. For example, this may refer to temperature, pressure, time / duration, flow rate, pH, raw material proportions, intermediate material proportions, agitation / mixing speed, heat / convection transfer, E&M fields, and / or the like present during the process and more. Description of Embodiments

[0282] In some embodiments, the disclosure herein protects methods and systems associated with the prediction, evaluation, optimization, or generation of production pathways and / or production processes for the production of materials.

[0283] The models herein may represent production pathways, and associated materials, equipment and control parameters in a number of ways. In some embodiments, a production pathway may be represented as a set of production processes that may occur sequentially, in parallel or as both. In some embodiments, the representation of one or a plurality of production pathways that may either be ingested, output, or otherwise interacted with by the models herein may include any one of or combination of: a set of material identifiers M = {m1, m2, …, mN}; the supply availability of each material, which may be in some embodiments represented as a function, additionally or alternatively, a function of the relevant material and of time (e.g., SA(t, mi)); a set of processes P = {P1, P2, …, PM}, which may represent the state change, Page 70 of 226 13824520v1transformation, or mapping between raw materials and final materials (and optionally intermediate materials); a set of process parameters, process contextual conditions, or control parameters, C = {c1, c2, …, cl}, which may define the contextual conditions of the process; a set of equipment E = {E1, E2, …, EN}, which may either execute or may be used to execute a production process in whole or in part. Additionally, or alternatively, a production pathway may include, one of or a plurality of raw materials being ingested, optionally based on supply chain availability, into a set of processes, the set of processes transforming raw materials into one of or a plurality of final products, where every individual process in the production pathway may include associated equipment to execute the process, and a set of process contextual conditions which may act as control variables during the process. Additionally, or alternatively, a production pathway may have attributes associated with it (e.g., associated carbon or greenhouse gas emissions impact, monetary cost, energy consumption, time efficiency of pathway (including total estimated process cycle time), material yield and / or waste, environmental impact (including water usage, air pollution, waste generation and more), product quality (including through measures of defect rate or failure rates), process difficulty (e.g., a measure of how difficult a process may be to achieve, in the case where a model may generate a novel pathway), and / or the like). Production pathway attributes may, in some embodiments, be features predicted by the models described herein, or may be included in the representation or description of the pathway.

[0284] A non-exhaustive list of examples of production processes or pathways considered by the present disclosure may include polymerization, mixing, extrusion, cooling, cutting / finishing, smelting, refining, casting, hot rolling / cold rolling, melting, crystal growth (Czochralski process), doping, cutting / wafering, polishing and etching, precursor gas preparation, chemical vapor deposition (CVD), plasma-enhanced CVD (PECVD), hydrogenation, hydration, annealing, fiber preparation, resin preparation, fiber impregnation, molding, curing, finishing, precursor solution preparation, co-precipitation, calcination, milling, mixing and slurrying, coating, drying, assembly, raw material mixing, forming, powder preparation, sintering, heating in kiln, clinker cooling, grinding, packaging, vacuum induction melting, heat treatment, machining, catalyst preparation, purification, separation, functionalization, forging, testing, shaping, cutting, grinding, polishing, forming, coating, shaping, combustion, oxidation, reduction, hydrolysis, radical polymerization, condensation polymerization, addition polymerization, decomposition, precipitation, electrochemical reactions, catalytic reactions, pyrolysis, hydration, and / or the like. Page 71 of 226 13824520v1

[0285] A non-exhaustive list of examples of equipment used in production processes or pathways considered by the present disclosure may include reactor vessel, mixer, heat exchanger, centrifuge, conveyor belt, furnace, distillation column, filter press, spray dryer, extruder, homogenizer, ball mill, kiln, autoclave, crystallizer, evaporator, pulverizer, conveyor dryer, rolling mill, sieve, granulator, magnetic separator, paddle dryer, rotary dryer, agitator, fluidized bed dryer, clarifier, electrostatic precipitator, shredder, vibrating screen, injection molding machine, baler, arc furnace, induction furnace, alloying furnace, powder compactor, sintering furnace, electrolyzer, sol-gel reactor, cold isostatic press, hot isostatic press, melt spinner, twin-screw extruder, high-shear mixer, polymerization reactor, vacuum oven, die casting machine, electroplating bath, vacuum furnace, tape casting machine, CVD chamber, PVD system, roll-to-roll coater, planetary ball mill, slurry mixer, calendering machine, blown film extruder, electrospinning machine, annealing furnace, hydraulic press, injection molding machine, die casting machine, forging press, rolling mill, stamping press, blow molding machine, vacuum forming machine, compression molding machine, powder compaction press, metal injection molding machine, sheet metal brake, stretch forming machine, 3d printer, CNC milling machine, lathe, extrusion press, wire drawing machine, and / or the like.

[0286] Examples of materials, including raw materials, intermediate materials, or final materials, involved in production processes or pathways considered by the present disclosure may include any of the material types listed herein.

[0287] A non-exhaustive list of examples of control parameters used in production processes or pathways considered by the present disclosure may include temperature, pressure, flow rate, mixing speed, reaction time, pH, concentration, viscosity, humidity, cooling rate, heating rate, deposition rate, plasma power, stirring speed, gas composition, voltage, current, atmosphere composition, curing time, sintering time, casting speed, rotation speed, particle size, drying time, annealing time, compression force, extrusion speed, rolling force, heating time, polymerization time, load, torque, tensile strength, shear rate, grain size, seed crystal orientation, pulling rate, growth rate, supercooling, nucleation rate, solvent concentration, crystal size, supersaturation level, solution flow rate, substrate temperature, purity level, electrolyte concentration, electrode thickness, cathode-to-anode ratio, calcination temperature, charging rate, discharging rate, electrolyte flow rate, solid-state diffusion rate, binder concentration, conductivity, slurry viscosity, coating thickness, electrode porosity, SEI layer formation rate, cycling stability, active material loading, and / or the like.

[0288] Examples of broad categories of equipment may include heat treatment equipment, machining equipment, forming equipment, joining equipment, additive manufacturing Page 72 of 226 13824520v1equipment, cutting and shearing equipment, surface treatment and coating equipment, chemical processing equipment, and / or the like.

[0289] Examples of heat treatment equipment, along with examples of control variables, may include furnaces with a non-exhaustive list of control variables including temperature setpoint, heating rate, cooling rate, power input, atmosphere gas flow rate, pressure, chamber temperature uniformity, soak time, heat flux, quenching speed, quenching medium temperature, chamber pressure, and / or gas composition, induction heaters with a non- exhaustive list of control variables including frequency, power input, temperature, heating rate, cooling rate, and / or time, kilns with a non-exhaustive list of control variables including temperature, airflow rate, heat ramp rate, soak time, and / or cooling rate, and hot presses with a non-exhaustive list of control variables including temperature, pressure, press time, heat ramp rate, cooling rate, and / or power input.

[0290] Examples of machining equipment, along with examples of control variables, may include CNC machines with a non-exhaustive list of control variables including feed rate, spindle speed, cutting depth, tool position, coolant flow rate, cutting force, tool wear, tool temperature, toolpath, material removal rate, and / or power input, lathes with a non-exhaustive list of control variables including spindle speed, feed rate, depth of cut, tool position, coolant flow rate, and / or power input, milling machines with a non-exhaustive list of control variables including spindle speed, feed rate, depth of cut, toolpath, coolant flow rate, material removal rate, tool wear, and / or tool temperature, grinding machines with a non-exhaustive list of control variables including wheel speed, feed rate, depth of cut, coolant flow rate, power input, and / or material removal rate, and drilling machines with a non-exhaustive list of control variables including spindle speed, feed rate, hole depth, coolant flow rate, and / or power input.

[0291] Examples of forming equipment, along with examples of control variables, may include forging presses with a non-exhaustive list of control variables including force, die temperature, press speed, die lubrication, temperature setpoint, cooling rate, and / or cycle time, rolling mills with a non-exhaustive list of control variables including roll speed, roll gap, roll force, temperature setpoint, lubrication, roll pressure, material thickness, and / or cooling rate, extruders (metal or plastic) with a non-exhaustive list of control variables including screw speed, barrel temperature, die temperature, extrusion pressure, feed rate, cooling rate, die gap, material flow rate, and / or power input, injection molding machines with a non-exhaustive list of control variables including mold temperature, injection pressure, injection speed, cooling time, clamping force, material flow rate, screw speed, nozzle temperature, hold pressure, and / or cycle time, and blow molding machines with a non-exhaustive list of control variables Page 73 of 226 13824520v1including air pressure, mold temperature, material temperature, blow time, cycle time, and / or cooling time.

[0292] Examples of joining equipment, along with examples of control variables, may include welding machines (arc welding) with a non-exhaustive list of control variables including current, voltage, electrode feed rate, welding speed, shielding gas flow rate, arc length, power input, and / or torch position, laser welding machines with a non-exhaustive list of control variables including laser power, beam focus, welding speed, pulse duration, shielding gas flow rate, beam position, and / or power input, soldering machines with a non- exhaustive list of control variables including solder temperature, soldering time, flux flow rate, preheat temperature, cooling rate, and / or power input, and ultrasonic welding machines with a non-exhaustive list of control variables including frequency, power input, welding time, pressure, amplitude, weld force, and / or cooling rate.

[0293] Examples of additive manufacturing equipment, along with examples of control variables, may include 3d printers (FDM) with a non-exhaustive list of control variables including nozzle temperature, bed temperature, layer height, extruder speed, print speed, infill density, cooling fan speed, print orientation, filament flow rate, and / or power input, SLS / SLM printers (selective laser sintering / melting) with a non-exhaustive list of control variables including laser power, scan speed, layer thickness, powder bed temperature, beam focus, hatch spacing, cooling rate, and / or power input, SLA printers (stereolithography) with a non- exhaustive list of control variables including laser power, exposure time, layer height, resin temperature, print speed, post-cure time, cooling rate, and / or power input, and DEDs (directed energy deposition) with a non-exhaustive list of control variables including laser power, powder feed rate, deposition speed, beam focus, layer thickness, cooling rate, and / or shielding gas flow rate.

[0294] Examples of cutting and shearing equipment, along with examples of control variables, may include laser cutters with a non-exhaustive list of control variables including laser power, cutting speed, beam focus, assist gas flow rate, cutting depth, beam position, material feed rate, and / or power input, plasma cutters with a non-exhaustive list of control variables including current, voltage, cutting speed, torch height, gas flow rate, and / or power input, water jet cutters with a non-exhaustive list of control variables including water pressure, abrasive flow rate, cutting speed, nozzle diameter, material feed rate, and / or power input, and guillotine shears with a non-exhaustive list of control variables including blade speed, blade angle, cutting force, material feed rate, and / or stroke length. Page 74 of 226 13824520v1

[0295] Examples of surface treatment and coating equipment, along with examples of control variables, may include electroplating baths with a non-exhaustive list of control variables including current, voltage, bath temperature, agitation speed, electrolyte concentration, plating time, and / or power input, anodizing tanks with a non-exhaustive list of control variables including current, voltage, bath temperature, agitation speed, anodizing time, electrolyte concentration, and / or power input, powder coating guns with a non-exhaustive list of control variables including voltage, powder flow rate, spray distance, air pressure, curing temperature, curing time, and / or power input, and chemical vapor deposition (CVD) reactors with a non-exhaustive list of control variables including temperature, pressure, gas flow rate, substrate rotation speed, deposition rate, and / or power input.

[0296] Examples of chemical processing equipment, along with examples of control variables, may include batch reactors with a non-exhaustive list of control variables including temperature, pressure, agitator speed, reaction time, feed flow rate, cooling rate, heating rate, and / or power input, continuous flow reactors with a non-exhaustive list of control variables including temperature, pressure, feed flow rate, reactor length, reaction time, power input, and / or catalyst concentration, and distillation columns with a non-exhaustive list of control variables including reflux ratio, column pressure, feed flow rate, column temperature, heating power, cooling rate, and / or product flow rate. State Machine Embodiment

[0297] In an alternative embodiment, the production pathway may be represented as a state machine. Additionally or alternatively, the state machine may be represented as a tuple <S,P,C>, wherein S is the set of material states, P is the set of processes and C is the set of control parameters. Additionally, or alternatively, the state machine may be a state machine for the production pathway of a crystal for semiconductor applications. Additionally, or alternatively, this crystal production process may be a Czochralski process, wherein for example:

[0298] S = {si} = {Idle,Heating,Melted,Seed Crystal Introduction,Pulling and Rotating,Crystal Growth Complete,Cooling,Finished}

[0299] P = P(si): sj, defines a mapping from state i to state j, for example: P(Idle)→Heating; P(Heating)→Melted; P(Melted)→Seed Crystal Introduction; P(Seed Crystal Introduction)→Pulling and Rotating; P(Pulling and Rotating)→Crystal Growth Complete; P(Crystal Growth Complete)→Cooling; P(Cooling)→Finished Page 75 of 226 13824520v1

[0300] C = {Temperature; Pressure; Pulling speed; Rotation speed; Flow rate; Time (duration for each phase)} = {T,P,v,ω,F,t}. Wherein C defines additional constraints on P = P(si, C) → sj Graph Network Embodiment

[0301] In another embodiment, the production pathway may be represented as a graph network. In a further embodiment nodes may represent materials or material states, and edges may represent production processes. Additionally, or alternatively, a pathway may be represented by a path along nodes and edges. Additionally, or alternatively, nodes may encode material composition data and / or material property data as node attributes. Additionally, or alternatively, edges may encode control parameter data and / or equipment data as edge attributes. Additionally, or alternatively, equipment data and control parameter data may be represented as additional nodes on the graph. Additionally, or alternatively, equipment or control parameter nodes may be connected to the process that is applicable to them. Additionally, or alternatively, intermediary nodes may be used to connect equipment or control parameter nodes to process edges. Additionally, or alternatively, the starting node or plurality of nodes on a graph network may represent the raw material(s), the end node or plurality of nodes may represent the final product, and any intermediate nodes may represent intermediate materials.

[0302] In some embodiments, the production process may be a production process for polymer synthesis. Additionally, or additionally, graph based methods may be used to model or represent production processes for polymer synthesis. For example, this may include a production pathway for polymer synthesis from a monomer (such as polyethylene from ethene).

[0303] Example material nodes may include M1 through M5 where: M1 is a Monomer; M2 is a Ziegler-Natta Catalyst; M3 is an activated monomer; M4 is a partially polymerized polymer chain; M5 is the final polymer output.

[0304] In one embodiment, M1 and M2 each have an edge connecting to M3 (representing the activation process); M3 connects to M4 (Polymerization); and M4 to M5 (Termination): P_123 represents the activation process; P_34 represents the polymerization process; P_45 represents the termination process.

[0305] Control parameters may include: C_123 = {Temperature T1(x,t), Pressure P(x,t)}; C_34 = {Temperature T2(x,t), Pressure P(x,t), Stirring Rate SR(x,t)}; C_45 = {Temperature T3(x,t) < T1 or T2}. Page 76 of 226 13824520v1

[0306] Equipment may include E_123 may be a catalytic reactor; E_34 may be a polymerization reactor; E_45 may be a cooling system.

[0307] In some embodiments, the production process may be a production process for metal alloys production. Additionally, or alternatively, graph based methods could be used to model or represent production processes of metal alloy production. For example, this may include a production pathway for steel beam production from iron ore and carbon e.g.

[0308] Example materials nodes may include M1 through M7 where: M1 is iron ore; M2 is scrap steel; M3 is carbon; M4 is molten iron; M5 is molten steel; M6 is cast steel slabs; M7 is rolled steel beams.

[0309] Example production process edges may include P1(M1, M2, M3) → M4, where P1 represents melting; P2(M4) → M5, where P2 represents mixing and refining; P3(M5) → M6, where P3 represents casting; P4(M6) → M7, where P4 represents rolling

[0310] Example equipment encoded in and associated to each process graph may include: E1, a blast furnace; E2, a basic oxygen furnace; E3, a casting machine; E4 a hot rolling mill.

[0311] Example control parameters encoded in and associated to each process graph may include C1 = {Temperature T1(x,t), Pressure P(x,t), Carbon Concentration C(x,t), Melting Time tMelt}; C2 = {Oxygen Flow Rate O(x,t), Mixing Rate M(x,t}, Temperature T(x,t)}; C3 = {Casting Speed SC(x,t), Cooling Rate dT(x,t) / dt}; C4 = {Rolling Temperature T(x,t), Rolling Force F(x,t), Rolling Speed Sroll(x,t)}.

[0312] In some embodiments, the production process may be a production process for producing materials involved in battery chemistry, for example anodes, cathodes, electrolytes, separators, current collectors, battery casings, and other such materials. Additionally, or alternatively, graph-based methods may be used to model or represent production processes of such materials. For example, this may include a production pathway for cathode production, such as Lithium Nickel Manganese Cobalt Oxide (LiNiMnCoO₂).

[0313] In some embodiments, the production process may be a production process for producing amorphous materials. Additionally, or alternatively, graph based methods could be used to model or represent production processes of such materials.

[0314] In an alternative further embodiment, nodes may represent materials (raw, intermediate or final), processes, equipment or parameters, and edges may represent the transitions or relationships between these nodes. Additionally, or alternatively, this may be represented as a directed acyclic graph. Additionally or alternatively, directed edges may represent relationships between nodes for example an edge from a material to a process may represent that the material is being input into the process; an edge from a process to a material Page 77 of 226 13824520v1may represent that the material is being output from the process; an edge from a process to an equipment may represent that the process requires the equipment; an edge from a control parameter to a process may represent that the control parameter is required by the process.

[0315] Additionally, or alternatively, the graph-based representation may be space and / or time dependent. Additionally, or alternatively process time dependence may include time dependent process contextual conditions. Additionally, or alternatively, time dependence may be represented through intermediate nodes through a process edge which breaks the graph into discrete time slices. Additionally, or alternatively, edges may be dynamic and time-evolving. Additionally, or alternatively, time dependence may be encoded through time dependent functions associated with edges and / or nodes, for example: the node itself may be a time dependent function, the edge may be a time dependent function, and / or node or edge attributes may be time dependent functions. Additionally, or alternatively, control parameters may be space and / or time evolving functions (e.g., temperature over time).

[0316] Additionally, or alternatively the graphs described herein may be any of the following examples Directed Acyclic Graph (DAG); Bipartite Graph; Multigraph; Hypergraph; Flow Network; Labeled Graph; Weighted Graph; Dependency Graph; Petri Net; Knowledge Graph; State Machine Graph; Process Network Graph. Operators Acting On Functions and Matrices Operating On Functions

[0317] In another embodiment, the production pathway may be represented as a set of functions and operators. Additionally, or alternatively, the function may be material state functions. Additionally, or alternatively, the functions may be represented as vectors in a vector space. Additionally, or alternatively, operators may be represented as matrices or tensors. Additionally, or alternatively, an input material undergoing a process may be represented as an input function being transformed by an operator. Additionally, or alternatively, an input material undergoing a process may be represented as a vector being transformed by a matrix. Additionally, or alternatively, control parameters may be represented as transformation matrices and / or operators, which may transform process matrices and / or operators, wherein the matrix multiplication of both may represent the full process transformation. Additionally, or alternatively, these matrices may be spatially or temporally dependent. Energy Transfer

[0318] In another embodiment, production pathways may be represented as a set of basic operations, acting on materials. Additionally, or alternatively, the set of basic operations may Page 78 of 226 13824520v1form a complete basis set and / or an incomplete basis set. Additionally, or alternatively, the set of basic operations may be represented in terms of energy and / or force transfer onto materials. Additionally, or alternatively, based on this energy and / or force representation, the models herein may build an internal representation which characterizes processes in terms of energy and / or forces, optionally where these processes may be represented as vectors in an N- dimensional vector space (or Hilbert space, complex space, etc.) of fundamental forces and energies. Additionally, or alternatively, processes may be represented as transformations of raw materials to final products through energy transfer. Additionally, or alternatively, types of energy transfers that represent processes, and associated example processes may include for example:

[0319] Thermal Energy Transfer: Heating; Cooling; Drying; Calcination; Annealing; Quenching; Sintering; Tempering; Heat treating.

[0320] Mechanical Energy Transfer: Cutting; Grinding; Compressing; Rolling; Forging; Extrusion; Mixing; Shearing; Machining; Drilling; Polishing; Shaping; Impact forming; Bending; Stretching.

[0321] Chemical Energy Transfer: Oxidation; Reduction; Polymerization; Precipitation; Electrochemical reactions; Combustion; Catalysis; Hydrolysis; Decomposition; Co- precipitation; Electroplating; Corrosion.

[0322] Electromagnetic Energy Transfer (including electric, magnetic, and E&M radiation and / or wave energy transfer): Electrolysis; Arc Furnaces; Resistive Heating; Induction Heating; Microwave Heating; Laser Processing; Plasma Generation; Photopolymerization; Sputtering; Magnetic Separation; Magnetic Levitation; Magnetic Forming; Magnetic Heating

[0323] Mass Transfer: Diffusion; Filtration; Separation; Absorption; Adsorption; Distillation; Osmosis; Sedimentation; Centrifugation; Leaching; Solvent extraction.

[0324] Phase Transitions: Melting; Solidification; Vaporization; Crystallization; Sublimation; Condensation; Evaporation; Freezing; Deposition

[0325] In some embodiments, the condition or properties of materials throughout a production process, across time and space may be represented and / or encoded through state variables and / or state variable functions s(x,t). These may be discrete functions of space and time or may be continuous. Additionally, or alternatively, state variables may be a function of the discrete production processes along a production pathway. Additionally, or alternatively, state variable functions may be vectors of a plurality of functions. Additionally or alternatively, each vector component state variable function may represent a specific material property or contextual conditions that may vary spatio-temporally across process steps si(x,t), for example: Page 79 of 226 13824520v1Temperature T(x,t), Pressure P(x,t), Stress ^^(t,x); Strain ^^(t,x). Additionally or alternatively, process control variables or control parameters may also be represented as functions of space and time u(x,t). Additionally or alternatively, this may also be represented by a vector of control parameter functions ui(x,t) for each parameter type, for example: applied temperature or heat flux uT(x,t), applied mechanical force or pressure uF(x,t), applied electric field or current uE(x,t), applied tool velocity uV(x,t) (e.g., of a CNC cutter, laser or extruder). Additionally or alternatively, equipment may be represented as transfer functions G, wherein an input material is inputted into a piece of equipment, which changes the state of the input material to an output product or intermediate material, based on control parameters as well soutput(x,t) = G[sinput(x,t), u(x,t)]. Additionally, or alternatively, in some embodiments, state variable evolution may be modeled using AI methods. Additionally, or alternatively, in some embodiments, state variable evolution may be modeled using physico-chemical equations, such as dynamics equations, empirical laws, differential equations including partial differential equations and ordinary differential equations and / or others. For example:

[0326] Thermal state variable evolution may be governed by the behavior of a heat equation over the duration of a production process. For example, the temperature spatio- temporal field for a material T(x,t) may behave according to the following heat equation^^ ^^^^ ^^ = ∇ ∙ ^^∇ ^^ +^^( ) ^^ ^^^^, where k may be the thermal conductivity of the material, Q may beheat generation term, ^^ the material density, and ^^^^the specific heat capacity.

[0327] Mechanical state variable evolution may be governed by the behavior of a mechanical equation of motion over the duration of a production process. For example, the spatio-temporal displacement field u(x,t), and / or the stress tensor ^^(x,t) for a material may be 2 ^^ governed by the following physical model and / or equation ^^^^^^ ^^2= ∇ ∙ ^^ + ^^, where f represents external forces.

[0328] Chemical state variable evolution may be governed by the behavior of chemical reaction equations over the duration of a production process. For example, the concentration of a material Ci(x,t) during a chemical reaction for a reagent material i, may evolve according to the reaction-diffusion equation^^ ^^ ^^^^ ^^ = ^^^^∇2^^^^+ ^^^^( ^^, ^^, ^^), where Di may be the diffusioncoefficient and Ri(C,T,P) mayreaction rate, dependent on concentration, temperature and pressure.

[0329] Phase state variable evolution may be governed by phase field equations over the duration of a production process. For example, the phase field ^^(x,t) of a material may evolvePage 80 of 226 13824520v1^^ ^^ 1^^ ^^ according to a phase-field equation such as ^^ ^^ = (− ^^) ^^ ^^ + ^^( ^^, ^^, where n accounts for stochastic thermal fluctuations and F functional.

[0330] Mass flow state variableby fluid dynamics equations over the duration of the production process. For example, the mass flow which may be described as a velocity field for a fluid for example v(x,t) may be modeled using the Navier- Stokes equation.

[0331] Additionally, or alternatively, initial conditions and boundary conditions for state variables may be represented by spatio-temporal functions. Additionally, or alternatively, the models herein generate predictions, evaluations, optimization, and generations based in whole or in part on initial conditions and / or boundary conditions. Additionally, or alternatively, the physical models and equations described herein may be used to model material properties, including material properties in contextual conditions, and material performance by any of the prediction or simulation models herein. Materials

[0332] In some further embodiments, materials in a production pathway may include raw materials, intermediate materials and output materials. Additionally, or alternatively, materials may be represented in the production methods, models, and systems herein as material identifiers. Additionally, or alternatively, the material identifier may include any associated characteristic of the material such as composition data, properties and any other such entities described elsewhere herein. Additionally, or alternatively, a material identifier may be indicative of the state of the material in the production pathway. Additionally, or alternatively, the state of the material may be represented by a time or space dependent state variable. Additionally or alternatively, the state of the material may be represented as a spatial or temporal state function e.g. MS(x,t). Additionally or alternatively, the state of a material throughout the pathway may be represented by one, a plurality, or a set of material characteristics, which may be functions of space, time, both, or step in the production process e.g., properties, composition, contextual conditions, which may include for example: Material Type T(t,x); Atomic Composition A(t,x); Temperature T(t,x); Pressure P(t,x); Stress σ(t,x); Strain ^(t,x); Material density ρ(t,x); Concentration of a chemical species i Ci(t,x) and other such characteristics. In some embodiments. In some embodiments, state variables may be represented as vectors in material space. Additionally, or alternatively, these vectors may be time evolving and / or spatially dependent. Additionally, or alternatively, the state of a material Page 81 of 226 13824520v1may be represented by a state machine, wherein each state in the state machine is representative of the material’s evolution through the pathway. Processes and Control Parameters

[0333] In some embodiments, production pathways may be represented as a set of transfer functions, where an individual production process may map to an individual transfer function. Additionally, or alternatively, processes may be spatially or temporally dependent, and / or may be represented as spatial or temporal series. Additionally, or alternatively, the space and / or time dependence of may be represented by associated space and / or time dependent control parameter functions. Additionally, or alternatively, temporal series production processes may include for example: Heat Treatment; Additive Manufacturing; Chemical Reactions; Machining or Material Removal. Additionally, or alternatively, heat treatment may include annealing, quenching, tempering and other such processes, wherein temperature may be varied over time (e.g. increased, held stable, and decreased; increased at an increasing rate; increased at a decreasing rate; decreased at an increasing rate; decreased at a decreasing rate; increased or decreased in a discontinuous manner). Additionally, or alternatively, additive manufacturing processes may include 3D printing processes wherein material deposition varies over time (e.g. speed of deposition, thickness of layer vary over time). Additionally, or alternatively, in chemical synthesis or polymerization, chemical reactions as well as control reactions such as reaction time, temperature, and mixing speed evolve in time. Additionally, or alternatively, spatial series production processes may include for example: Laser Cutting / Welding; Casting and Molding; Thermoforming; Diffusion-Based Processes; Additive Manufacturing (Spatial Distribution). Additionally, or alternatively, for example: laser cutters move across space, over time, and may also alter laser intensity; during injection molding, spatial temperature gradients form; during thermoforming, heated polymers or plastics may experience different forces and stretching at different spatial locations. Additionally, or alternatively, production processes may include both time and space dependence. Process Contextual Conditions and Control Parameters

[0334] In some embodiments, every individual process in a production pathway may have its own set of associated process contextual conditions cPi. Additionally, or alternatively, control parameters may be defined as spatial or temporally dependent and / or spatial or temporal series. Temporal series and / or time dependent processes. Additionally, or alternatively, control parameters may be scalar, vector or tensor values. Additionally, or alternatively, control Page 82 of 226 13824520v1parameters may be discrete or continuous variables. Additionally, or alternatively, control parameters may have associated constraints for example limited temperature ranges, speeds or pressure. Equipment

[0335] In some embodiments, every individual process in a production pathway may have its own set of associated equipment EPi. Additionally, or alternatively, equipment may have associated specification data or technical data. Additionally, or alternatively, such specification data may include all known attributes or characteristics of such equipment. Additionally, or alternatively, the models herein may ingest a specification record for one or a plurality of equipment and extract specification data. Additionally, or alternatively, constraints may be extracted from specification data. Additionally, or alternatively, this may include constraints on control parameters. Additionally, or alternatively, control parameters may be extracted from specification data. Additionally, or alternatively, the models herein may be used to discover or design, in whole or in part, novel types of equipment.

[0336] Examples of specification data may include the following characteristics of equipment: Capacity; Power requirements; Material compatibility; Operating temperature range; Pressure range; Dimensions; Construction materials; Control systems; Safety features; Speed / Feed rate; Efficiency; Tolerance / Accuracy; Maintenance requirements; Environmental conditions; Compliance and certifications; Noise level; Cooling requirements; Output specifications; Throughput time; Installation and set-up requirements; Energy efficiency rating; Carbon emissions during operation; Recyclability of equipment components; Energy source (renewable or non-renewable); Waste production; Water usage; Lifecycle environmental impact; End-of-life disposal options; Sustainability certifications (e.g., LEED, Energy Star); Carbon footprint of manufacturing process. General Models, Model Techniques, and Model Features Path Integral Embodiment

[0337] In some embodiment, the models herein may use path integral representations for modeling, evaluating, optimizing, and / or generating optimal production pathways. Additionally, or alternatively, the path integral may encode production pathway properties such as cost, energy, and time. Additionally, or alternatively, the path integral may encode this information through an action functional. Additionally, or alternatively, each possible path may have an associated weighting according to a probability distribution over all paths. Additionally, or alternatively, the path integral may sum over all possibilities. Additionally, or Page 83 of 226 13824520v1alternatively, the optimal pathways may be defined as those that minimize the action functional. Additionally, or alternatively, this representation may be used by manufacturing process optimization and / or generation models for searching the space of possible production pathways and determining optimal candidates based on desired targets. Additionally, or alternatively, pathways may be represented by graph networks. Additionally, or alternatively, path integrals may be used to evaluate pathways of nodes and / or edges on graph networks. Additionally, or alternatively, the action functional may be computed for each path on the graph. Additionally, or alternatively, optimal paths are node and edge paths which minimize the action functional.

[0338] Additionally, or alternatively, in some embodiments of the present disclosure, sensor devices may be used to collect data associated with production processes as they occur. Additionally, or alternatively, data from records associated with production pathways and / or processes may be used to collect data associated with production processes. Additionally, or alternatively, sensor data and / or records data may be used to train any model herein. Additionally, or alternatively, sensor data and / or records data may be used for validation of an output of any of the models herein. Additionally, or alternatively, sensor data and / or records data may be used to improve model accuracy. Additionally, or alternatively, sensor data and / or records data may be used to collect data associated with any one or plurality of the following: material identifiers, material compositions, material properties, material states (e.g., as represented by node, edge, variable functions, vector, or otherwise), production process, control parameters, production process equipment. In some embodiments, any of the models herein may be able to simulate a 4D Spatio-Temporal Simulation (e.g., digital twin) of a production pathway.

[0339] Material production considered in the present disclosure may include a plurality of models directed to predicting, generating, simulating, optimizing, and / or the like any aspect of material production and / or material production processes as described herein.

[0340] In some embodiments, models may be configured to predict composition and / or properties of a material that goes through a production process based on the production process and / or the raw materials. As an example, such a model may have the formalism of Raw Materials + Process → Output Materials. In such embodiments, the aforementioned production model may be used in tandem with material property prediction model (e.g., the model predicts output material based on raw materials + production process, and then uses material prediction model to predict the properties of the output material).

[0341] In some embodiments, the prediction may be based on sensor data generated by sensors monitoring any or all of the following during the process themselves: raw materials, Page 84 of 226 13824520v1intermediate materials (during and in between processes), equipment involved in each process, control parameter values, and / or the like. Further, the output of a production process may be predicted based on live sensor data, versus predicting the output of a production process theoretically. Additionally, or alternatively, training data may include all production processes data objects described herein. Further, models may be trained to create associations between raw materials snd processes, and output materials. Training dataset may include sensor data, records data, chemical reaction databases, material properties and compositions databases, manufacturing method database, and / or the like. In some embodiments, the prediction models may include physico-chemical models.

[0342] In some embodiments, graph neural networks may model and predict production process outputs. In such embodiments, entities may be included such as nodes being material states, edges being production processes, and / or the like. Additionally, or alternatively, the model problem statement may include predict full information for the final node of the graph (e.g., final material state), based on known information about all previous nodes and edges. This may include predicting composition, and properties, optionally in certain contextual conditions.

[0343] In some embodiments, features of the graph neural networks may include predicting the final node of the graph on incomplete data (e.g., not all attributes of every node and edge must be present, may have some incompleteness, nodes and edges may be completely missing, but the model may generate an output), confidence interval, likelihood, or uncertainty in the output (e.g., uncertainty increases as less information regarding prior nodes and edges exist), and / or specialized models may be effective at dealing with missing nodes or edges or incomplete information.

[0344] In some embodiments, multi-scale models may be configured to understand how production processes evolve materials at the atomic level, nano level, micro level, and / or macro level. In such embodiments, the models may be specialized models for different types of production processes (e.g., chemical reactions, thermal processes, mechanical processes, and / or the like), different types of equipment (e.g., cutting equipment, heating equipment, irradiating equipment, electrical equipment, and / or the like), and / or different types of materials (e.g., crystals, amorphous materials, glass, metal alloys, polymers, and / or the like). Additionally, or alternatively, transfer learning may be used to train specialized model to predict in another area, or to generalize to many areas.

[0345] In some embodiments, models herein may be configured to predict properties of production processes, based on representation of the processes. In such embodiments, training Page 85 of 226 13824520v1datasets may include production pathways properties such as carbon emission from processes. Further, the model may learn such associations. For example, for carbon emissions the model may be trained to understand chemical reactions happening as part of the production process and may infer that carbon (or other greenhouse gases) may be emitted as byproduct of a reaction (e.g., may learn to predict how much CO2 is generated by combustion of different substances). Additionally, or alternatively, the model may be trained to understand energy consumption of a particular type of equipment and may learn how to predict or infer it for similar equipment used analogously (e.g., may convert energy use to carbon emissions). Further, these steps may be similarly performed for cost and time duration. In some embodiments, the model may sense the end material to understand yield.

[0346] In some embodiments, a LLM and / or GPT may be used to infer this information based on a prompt that describes the production process. Additionally, or alternatively, the models may be based on quantitative physico-chemical understanding of processes. Additionally, or alternatively, the models may extract equipment characteristics from specification. Further, the models herein may use hybrid physics and data-based models. In some embodiments, the model may predict total production pathway properties, by breaking down the pathway into its constituent processes, and making predictions for each production process individually. Further, the model may then sum all of the individual predictions to understand the cost, carbon, time, and / or the like of the total process.

[0347] In some embodiments, graph neural networks may be used to model and predict properties of production processes. Additionally, or alternatively, uncertainty in pathway may be predicted as a property (e.g., uncertainty in final output material (e.g., material failure, defects), uncertainty in process itself (e.g., equipment failure, process step failure), and / or the like).

[0348] In some embodiments, the models herein may be configured to evaluate a set of production processes (or aspect of a production process) against a set of target objectives and output an evaluation identifier. As an example, such a model may have the formalism of Process + Evaluation Parameter → Process Evaluation and / or Processes + Target Objectives → Processes Ranking. In such embodiments, models may check for regulatory compliance of processes. Additionally, or alternatively, the models may evaluate processes against supply chain (e.g., availability of raw materials). Further, evaluation may be based on objective functions or multi-objective functions. Additionally, or alternatively, evaluation may be based on action functional in path integral representation. Page 86 of 226 13824520v1

[0349] In some embodiments, the model may generate an aggregate score function that evaluates a production pathway along multiple metrics at once (e.g., S(P)=wC*C(P) / Ctarget +wE*E(P) / Etarget+wI*I(P) / Itarget+wT*T(P) / Ttarget). Additionally, or alternatively, the production pathway may be evaluated in whole or in part, at any level of granularity (e.g., any subset of the production pathway can be evaluated or any subset collection of production processes). Additionally, or alternatively, configurations of control parameters may be evaluated against other configurations of control parameters.

[0350] In some embodiments, a part of a production pathway may be evaluated against an analogous part of another production pathway. For example, for two production pathways PA and PB, it is possible that overall, PA scores better than PB, but that PB, scores better on one part. In this case, this information may be useful, and the models herein are able to generate evaluations that show this nuance. Additionally, or alternatively, when optimizing, the models may combine the best parts of two or more production processes with each other to create an optimal process.

[0351] In some embodiments, sensor data may be used as input to evaluate processes in real time. Additionally, or alternatively, evaluations may be compared with reality by verifying output evaluation using sensor data. In some embodiments, production process prediction models described herein may be used to predict properties of production pathways and evaluate them based on predicted properties. Additionally, or alternatively, the model may extract industry benchmarks from industry regulations or other documentation and evaluate production process against the benchmarks.

[0352] In some embodiments, the models may evaluate pathways in real time based on sensor data and contextual condition data. In such embodiments, a feedback loop may allow the system to switch pathways if the current chosen pathway does not have the optimal evaluation anymore (e.g., dynamic pathway evaluation). Additionally, or alternatively, an objective function may have dynamic weights for target objectives (e.g., cost, carbon, time, or the like) In some embodiments, a scenario simulation engine for pathways may be used to enable simulating changes to process.

[0353] In some embodiments, the models herein may be configured to optimize one or a plurality of production processes based on target objectives and material output. As an example, such a model may have the formalism of Process + Target Objective → Optimized Process.

[0354] In some embodiments, the production process optimization models herein may include graph network representations of production processes. In such embodiments, the Page 87 of 226 13824520v1models may have initial material(s) state, and final material(s) state, as well as any intermediate nodes and edges. Further, the models may determine all possible paths to reach end node from starting node. Additionally, or alternatively, the models may predict properties of each path and may compare to objective function to find optimal path. Additionally, or alternatively, the model may compute action functional in path integral framework, and path which minimizes action functional may be optimal.

[0355] In some embodiments, the production process optimization models herein may include prompts to convey objectives. In such embodiments, objectives may be attributes of the final output material. Further, objectives may be an attribute and / or property of the production process and / or pathway itself. For examples, objectives may include cost minimization, energy minimization, time minimization, product maximize product quality, minimize environmental impact, and / or the like.

[0356] Embodiments of the present disclosure directed to optimization of productions processes may include a plurality of types of optimizations. For example, the types of optimizations may include keeping production processes themselves constant and vary control parameters, allow control parameters and production processes to vary, allow any combination of control parameters and / or production processes to vary, vary equipment used (e.g., to use equipment which emits less carbon or greenhouse gasses equivalent), keep processes constant but vary the sequence of processes, and / or the like.

[0357] In some embodiments, the optimization models may use prediction models to determine properties or outputs of production process, to then compare it against objective functions and move in search space. In such embodiments, physics-based models and data model hybrids may be used. In some embodiments, optimization algorithms may include linear programming methods, mixed-integer programming methods, genetic algorithms, simulated annealing, and / or the like. Additionally, or alternatively, the models may include multi- objective optimization (e.g., Pareto optimization).

[0358] In some embodiments, the model may include real time sensor based optimization. In such embodiments, raw materials, processes, control parameters, equipment, and output material may be monitored in real time. Further, output material may be monitored directly after the process, as well as in use to measure performance. In such embodiments, the production process may be optimized in a number of ways in real time, including adjusting raw materials, adjusting processes, adjusting control parameters, adjusting equipment, and / or adjusting any combination of the above. Page 88 of 226 13824520v1

[0359] In some embodiments, reinforcement learning and / or adaptive learning may be used to enable model to learn best optimization strategies. Additionally, or alternatively, the model may be able to explain the optimization it has generated for a particular process. Additionally, or alternatively, dynamic weighting may be used for objective functions.

[0360] In some embodiments, the models herein may be configured to generates one or a plurality of material production processes based on a desired material output. As an example, such a model may have the formalism of Desired Material Output → Process. In such embodiments, the desired output may be a material composition, desired material property, desired use case, and / or the like. Additionally, or alternatively, graph networks of the production process may be generated. Additionally, or alternatively, path integral formalism of the production process may be generated.

[0361] In some embodiments, entirely novel pathways may be generated. For example, this may be accomplished via the model’s fundamental quantitative understanding of physics, chemistry, chemical processes, as well as manufacturing processes and other processes. Further, novel pathways may be generated based on energy representation described herein. Additionally, or alternatively, LLM based methods may be used to generate new pathways.

[0362] In some embodiments, entirely novel equipment and / or optimal control parameters may be generated. Additionally, or alternatively, the model may be configured to work backwards (e.g., generation of likely intermediates materials based on final desired product). Additionally, or alternatively, diffusion models, transformer-based models, and other generative models may be used for candidate generation.

[0363] In some embodiments, the generative production process models may be configured to work with material generation models. For example, a material generation model may generate novel material and / or material identifier, a material identifier is fed into this production pathway generation model, and a production pathway may be generated for the novel material. In this way a production pathway, which may be an existing pathway, or a novel pathway, may be generated for a novel material. Additionally, or alternatively, autonomous labs may be used by the models herein. In some embodiments, the model may include generated sustainable processes (e.g., introducing a bias into the model for sustainable solutions). Additionally, or alternatively, GANs (e.g., GAN models) may be used, and may employ the use of discriminators.

[0364] In some embodiments, a list of pathway generation algorithms may include, for example, search tree exploration (e.g., start with one or a plurality of raw materials nodes, generate edges for every process that can match the raw material(s), alongside new nodes, Page 89 of 226 13824520v1predicting the outputs of these production processes, recursively apply algorithm for new nodes, to generate path until satisfactory material is reached which matches desired objective and / or desired property and / or desired use case), reverse of the previous (e.g., in situations where the process starts with a desired material composition, generate processes that could produce the final material, and work backwards recursively), and / or the like. Additionally, or alternatively, heuristics and / or rules may be included, which may be based on physical or chemical laws, for example, to discard certain pathways to avoid explosion of branches.

[0365] In some embodiments, while generating pathways, the model may evaluate pathways as they are being constructed and discard poorly performing pathways in favor of highly rated pathways, may conduct a physical feasibility check (e.g., to check thermodynamic feasibility of a process or chemical pathway, as well as kinetic feasibility), may evaluate control parameters to ensure they fall within feasible ranges for equipment operations, and / or the like. Additionally, or alternatively, after pathways are generated, the model may be combined with optimization model to optimize generated solution. Additionally, or alternatively, production pathway generative models may work together with material and pathway prediction models, evaluation models, and optimization models, and / or material generative models. Additionally, or alternatively, generated pathways may be stored in databases and used for training of the model and / or other models. In some embodiments, any of the models described herein may be AI based. Material Identification

[0366] As used herein, a “data engine” may refer to a data aggregation system that combines material measurements (including measurements related to material properties sourced from sensor devices), material & device contextual conditions (including those derived from measurements), historical knowledge (including prior knowledge about the material under consideration, and also knowledge and measurements about prior materials), any expectations and requirements for the material under consideration, and user defined parameters about the desired identification representation and classification system, alongside other related data. This data is prepared and aggregated into a unified format, ready for processing.

[0367] As used herein, an “AI Engine” may refer to an Artificial Intelligence Engine (made up of one or more models and optionally an orchestration layer) that parses the data from the Data Engine and performs the inference required to deliver an absolute material identifier mode and a perturbative material identifier mode. In the absolute material identifier mode, the goal Page 90 of 226 13824520v1of the system is to determine a material identifier and to (optionally) classify the material. The absolute identifier determination is made on the basis of measurements of the material & contextual conditions (for the material and sensor devices used). In addition, in absolute material identifier mode, the models can generate a representation of material -space, and a classification system. In the perturbative material identifier mode, the goal of the system is to detect relative material changes (so called ‘perturbations’ or ‘perturbative’ changes to materials, or anomalies) against a target or expected material. Optionally, the material expectation or target can also be generated by the system. In addition, perturbative material identifier can detect the cause of an anomaly or perturbation (through causal analysis of the data) and can recommend a compensatory action (an action to revert to the expectation / target).

[0368] In some embodiments, the system may leverage generative models (e.g., in both example absolute and perturbative modes) in which a generative model is used to determine missing data and / or data gaps. A Generative Model Engine of the present disclosure may be generated over continuous material and material identification, with the intent to complete missing data or to aid the material optimization and / or material identifier operations described herein. The Generative Model Engine may include an ensemble of model types, ranging from probabilistic (which assess the information-theoretic meaning of missing data, based on the available corpus of data), to empirical (which generate empirical mappings between data and material designs, based on an available corpus of training data).

[0369] Embodiments of the present disclosure pertain to an advanced system for monitoring, analyzing, predicting, and / or generating materials, utilizing artificial intelligence (AI). The system may be designed to analyze and report on various aspects of a material’s physical and temporal material properties throughout its lifecycle.

[0370] The core of the present disclosure is an AI Engine (e.g., the processor described herein), which may be trained on a substantial corpus of pre-existing data. This training equips the AI Engine with the capability to analyze and interpret data collected from various materials. The types of data used may include, but are not limited to, measurements of temperature, ultrasonics, and impedance (including mechanical, electrical, electrochemical, wave- impedance, acoustic, elastic, and magnetic impedance), along with conductivity, pH levels, and various forms of spectroscopy and imaging (including hyperspectral imaging). The device data measurement types, as detailed herein, are applicable here, encompassing outputs from wave- based sensors. In addition to these data types, data related to the material’s position, orientation, geometry, and formwork. This may include employing context awareness models, methods, and devices to understand sensor contextual conditions (pertaining to the sensor itself) and Page 91 of 226 13824520v1material contextual conditions (related to the local material volume under observation). These measurements may provide a comprehensive overview of the material’s condition and behavior over time.

[0371] The multivariate data streams thus collected may then be served to the data engine. The data engine may combine these diverse data types, including measurements, documents, human-input data, third-party data, and model output data. This combination may inform several model inputs: (1) material measurements, (2) contextual conditions (material & device), (3) historical data (including prior knowledge about the material under consideration and historical materials), (4) expectations & requirements, (5) parameters related to the desired identification representation & classification system, and / or (6) other data such as output from other models. In some embodiments, the model inputs are then transformed into a proprietary data schema in preparation to be fed as input to the AI Engine and its models. A key model within this system is the material identification / perturbation detector.

[0372] In some embodiments, the material identification engine and the material perturbation detector may be configured to recognize patterns within multivariate data and map these patterns onto material properties that define a material. This process facilitates the determination of the identifier for the likely material. The operation commonly referred to as ‘material identifier’ may encompass this methodology. Material identifier may encompass a variety of methodologies. For instance, one approach may involve using sensor measurements (e.g., strain gauges, viscosity, acoustic, resistivity, temperature sensors) to report on the physical properties such as fineness, strength, durability, and workability. These properties can then be used to deduce possible material compositions through a supervised machine learning (ML) model that has been trained on example data. The ML model may establish a linkage between the physical properties and corresponding potential candidate compositions. Another approach for material identifier may involve using sensor data (such as from spectroscopy, acoustic, resistivity, and temperature sensors) to analyze the chemical composition of the sample material. This chemical composition can then be utilized to infer possible physical properties, again using a supervised ML model trained on example datasets. In this scenario, the ML model may map the material composition to the corresponding candidate compositions. Moreover, a combination of these two methods can be applied to reduce uncertainty and improve the sensitivity and specificity of material identifier. These examples are representative of material identifier by composition, each illustrating a different basis or representation of composition. In example embodiments, material identifier can also be performed in property Page 92 of 226 13824520v1representation, arbitrary identifier (name) representation space, or an entirely different representation space.

[0373] Additionally, the Generative Model may be employed at any stage of this process to augment incomplete or low-quality datasets, thereby enhancing the performance and output of the AI Engine models. Following each successful identification, there may be the possibility of updating or retraining the AI Engine to maintain or improve its efficacy. Example System Details, Inputs and Outputs Example Inputs

[0374] As an example material, concrete, being a composite material comprising various constituents, presents complexities in modeling or predicting its behavior. Additionally, the environment of a concrete pour, notably the construction site, constitutes a complex and variable system. Consequently, numerous contextual conditions and diverse types of measured data must be processed by the AI engine (e.g., the processor described herein). This processing is essential for accurately parsing and understanding the identifiable aspects of any given concrete material design. The AI engine’s ability to effectively navigate and interpret this multifaceted data landscape is used for reliable and precise identification and analysis of concrete material properties in varying environmental and compositional scenarios.

[0375] In some embodiments, the input data for the AI engine may be classified into two primary categories, contextual condition data and measurements. Contextual condition data may encompass information unrelated to the compositional or material properties of the concrete, or the properties of the device itself, thereby characterizing the specific instantiation of its use-case at any given time. In example embodiments, the contextual condition data may include material contextual conditions and device contextual conditions. Material contextual conditions may include the shape of the concrete, its geographic location, the time of year it is poured, or the ambient weather temperature. Device contextual conditions may include the location or orientation of the sensor. Contextual conditions may be derived from various sources, including measurements, documents, human-input data, third-party data, and outputs of other models. Examples of key categories may include location + organization (via GPS or radio frequency signal trilateration), pour (matching location or geometry to pour plans, BIM, or images), batch (from label pictures), date and time (via synchronization with devices like GPS, NTP servers), construction schedule (integration with systems like Primavera P6 or OCR of paper schedules), drawings and specifications (through digital integration, image recognition, OCR), climate (assessed via GPS and sensors for micro-climates), weather status Page 93 of 226 13824520v1and forecast (via climate data and weather services), temperature (local conditions, swings, shadows, airflow, heat sources), wind chill (via anemometers, humidity sensors), ambient conditions (external vibrations, sunlight exposure), and / or the like.

[0376] Measurements may encompass sensor data of various kinds, including measurements from various embodiments and hardware devices described in other sections (including wave-based sensors). For instance, measurements may include sensor measurements based on continuous time or high sampling frequency data, such as composition (via different types of spectroscopy), temperature (via thermocouples, thermistors or high resolution digital temperature sensors), conductivity and electromechanical impedance (via electrodes driving DC or AC voltages and various negative terminals with current meters to evaluate the path resistance for each anode to cathode pair), mutual inductance and coupling index (via RF driver and loop antenna to detect changes in mutual inductance in the presence of rebar and other conducting or ferromagnetic bodies), electromechanical impedance and ultrasonics (via piezoelectric, normal microphone and hydrophone sensors), pH (via digital pH sensors, ion-sensitive field-effect transistor (ISFET), and image processing solution of dipstick pH tests), pressure and mechanical (e.g., acoustic) vibrations (via piezoelectric sensors wireless surface acoustic wave (SAW) sensor), electrochemical impedance, electromagnetic wave impedance, acoustic impedance, elastic impedance, magnetic impedance, hyperspectral imaging, and / or the like form the vector space of time-series data. In another instance, measurements may include sensor measurements based on discrete time or lower sampling frequency data, such as spectroscopy (including LIBS), NMR, Imaging (IR, visual spectrum), colorimetry, and / or the like form the vector space of spatio-temporal data. In yet another instance, measurements may include sensor measurements from context awareness such as position of the device in relation to the concrete pour or truck, whether it is within, on, or nearby, the orientation of the device in similar contexts, element matching with BIM and / or position of the pour, content and properties of rebar within the concrete, the geometry of the pour, the types and properties of insulation or formwork used, the time of the first pour, details about backpropping or temporary works related to the pour, information about adjacent pours or elements (either through BIM matching or other means), and / or the like form of the vector space or scalar data.

[0377] Other inputs to the system may include a variety of data types, including historical data, expectations and requirements, identification representation parameters, classification system parameters, and others, such as outputs from other models. Page 94 of 226 13824520v1

[0378] Historical data may be categorized into priors or prior knowledge about the material under consideration, and knowledge about previously identified materials. Prior knowledge may include information on material properties, contextual conditions, and compositional properties, which can range from known facts to probabilistic or low-confidence information. Optionally, priors may be accompanied by a confidence level. These priors can be instrumental in refining the identification process. Knowledge about previously identified materials may be used for training and updating the AI models. The training dataset, which is continuously expanding with every new identification, may include measurements and labeled identifications of prior materials. Additionally, historical data relating to pre-existing materials can be directly inputted into the system, particularly when establishing material identifier expectations for a specific project site.

[0379] Expectations and requirements may be useful inputs, especially in perturbative cases. They relate to the anticipated properties of a target material in a given contextual condition. These expectations can cover a range of aspects, including compositional properties, material properties (both static and contextual), identifiers, sensor signals, and contextual conditions, or they may pertain to an arbitrary representation of material space. Requirements, akin to expectations, may be derived from specifications and other documents.

[0380] Identification representation parameters may be used to guide the model to the desired identification representation. These parameters can range from fully specified representations (e.g., identification based on specific material properties) to more flexible criteria, leaving the exact representation to the model’s discretion. Parameters may include the type of representation (e.g. by property, sensor signal, composition, and / or the like), desired basis (if known), and level of granularity. The model’s output may vary depending on the specificity of the representation parameters provided. For instance, if a fully defined representation (e.g., identification of materials based on their 28-day cylinder strength, workability after 6h, and shrinkage after 28 days) is provided, the output of the model will be provided in that representation. On the other hand, a loosely defined or absent representation may allow the model to determine the most suitable output. For example, if no representation is provided, the model may output a representation. If representation parameters are loosely provided, then the model may be directed towards a particular representation.

[0381] Classification system parameters may be analogous to representation parameters but apply to the classification systems defined over these representations. These parameters can be left unspecified, allowing the model to choose the optimal classification system, partially defined to indicate a preference, or fully defined to ensure outputs in a particular Page 95 of 226 13824520v1classification system. Finally, other inputs include outputs from other models, which may further inform and refine the system’s processing and identification capabilities.

[0382] Data for the system may be aggregated from a multitude of sources and through various means such as devices, documents, human-input, third party integrations, and other models. Techniques for sensor data collection and transmission, as detailed herein, 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. 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. Outputs from other models within the system are also incorporated as part of the data collection. These models provide additional layers of analysis and interpretation, enriching the overall data set used for decision-making and predictions. Example System and Outputs

[0383] In some embodiments, as described herein, the system may include a data engine (for data aggregation and preparation), and an AI engine. The AI Engine may further be divided into two distinct modes: (1) absolute material identifier and (2) perturbative material identifier. Each mode may incorporate four specialized models. Additionally, an orchestration system may be used to facilitate interaction between these models, and a generative model may be used to address data gaps. In the absolute material identifier mode, the models may include (i) the representation generator; (ii) the classification system generator; (iii) the material identification engine; and (iv) the material classification engine. These models may collectively contribute to the comprehensive identification and classification of materials in a non- Page 96 of 226 13824520v1perturbative context. In the perturbative material identifier mode, the models may include (i) the expectation determinator, which establishes the anticipated outcomes or material properties; (ii) the perturbation detector, designed to identify deviations or anomalies; (iii) the perturbation cause analyzer, which delves into the underlying causes of detected perturbations; and (iv) the compensation recommendation engine, which proposes solutions or adjustments to counter the identified perturbations. Example Data Engine

[0384] The Data Engine may be used to process and prepare data for analysis by the AI Engine. In some embodiments, the scalar data, which may include contextual conditions and related measurements, may be parsed through a data mapper. This data may then be formatted into the converge data schema. Once cast into this schema, the AI Engine may engage in a pre- filtering process, the extent of which depends on the specific use-case requirements of the AI Engine.

[0385] The sensor data may be represented as a multivariate N-dimensional vector space of time-series data. Each vector in this space, potentially sampled at varying rates, may correspond to a different type of data (like temperature or ultrasonics) taken at each physical location. The system may handle a multitude of these N-vectors, with M representing the number of spatial locations sampled, either within or outside a concrete pour. This may include the handling of spatio-temporal data (such as from spectroscopy, imaging, or infra-red sensors), impedance data (which are complex numbers), and other irregular data values. These data may be sampled and formatted in a way that the system, using attendant physics models, can interpret to represent conditions. The vector spaces, or signals, are generally not orthogonal, and any correlation between signals may be managed through dimensionality reduction techniques.

[0386] In embodiments where further feature engineering is warranted, the signals may undergo transformations as necessary, including normalization, standardization, Fourier transforms, and / or the like. Scalar features may then be extracted and sent to the data parser for interpretation through the internal schema.

[0387] An input vector, X, is subsequently composed. This vector may combine the mapped vector of scalar data and the transformed time-series signal vector, readying it to be input into the AI Engine or its constituent models. Page 97 of 226 13824520v1Example AI Engine Models and Outputs

[0388] In the Absolute Case of the AI engine, by internalizing multivariate data sources, a virtually complete model of materials may be constructed. This model may be defined through multiple representations, including a model based on providing a Material ID, a model based on the Chemical & Material composition of the material, a model based on the Physical Properties of the material , and other arbitrary identification bases. The configurations of this model may be versatile, designed to accommodate varied and even incomplete data. In one embodiment, the primary model may be a supervised learning model, which requires labeled information for its operation. To reduce the extent of labeling required, physico-chemistry based equations may be incorporated into these models. This approach integrates the fundamental principles of physico-chemical interactions within the learning process. As the system evolves, unsupervised learning techniques may be employed. These techniques are instrumental in identifying patterns and correlations within the data without the need for labeled datasets, thus enhancing the model’s ability to handle diverse and complex data structures. Additionally, generative model builder tools may be developed for creating mappings between contextual conditions and material properties to their respective material compositions, formulations, and designs. The generative model may be used in instances where there is missing information, invoked to fill these gaps, thereby ensuring the continuity and comprehensiveness of the model.

[0389] In the absolute mode of the AI engine, the functionality may be distributed across four distinct models, Representation Generator, Classification System Generator, Material Identification Engine, and (Material Classification Engine, each serving a specific purpose in the process of material identification and classification.

[0390] The Representation Generator may be tasked with generating a desired representation for material -space. The representation could be based on various criteria such as compressive strength, workability, shrinkage measures, or material formulation. Once a representation is established, the Classification System Generator may generate a classification system over this chosen representation. This involves segmenting the volume of the material - space representation into sub-volumes, each representing a specific class or family within the material space. Material Identification Engine may be responsible for identifying the material within the given representation. This identification can be based on various aspects such as material properties, material composition, name or arbitrary identifier, sensor signals, or an entirely different representation which may have been generated by the model itself. An additional step in this process may involve further processing or combining these Page 98 of 226 13824520v1representations to generate a unique fingerprint and rebasing of material -space into fingerprint space. Following the identification of material, Material Classification Engine may classify the identified material within the established classification system and representation. This model takes the identification and places it within the classification of the representation. Geometrically, this classification process can be visualized as follows: the Representation Generator outputs a volume V_s, which represents the material space. Model Classification System Generator then divides this volume V_s into multiple smaller volumes V_(C_i ), each representing a different class or category within the material space. Material Identification Engine may output a volume V_m within the overall representation space R, which defines the specific material that has been identified. Material Classification Engine may then be responsible for determining in which class volumes V_(C_i ) the identified material volume V_m is located, or with which it overlaps. If the identified material volume V_m overlaps with more than one class volume V_(C_i ) (for example, if V_m is disjoint and spans multiple classes, or is contiguous but sits on the boundary between two classes C_i), then the material may be assigned to both classes, or classified into the class with which it has the highest volume overlap. In cases where there is ambiguity in classification, a new representation, basis, or classification system may be employed to resolve the ambiguity. This new system could either be generated by the models within the AI engine or selected through other means, ensuring a precise and accurate classification of the identified material. Additionally, a generative model may be employed across all these models to manage missing data.

[0391] In some embodiments, the representations may include identification by name (arbitrary identifier), identification by compositional properties (what is it?), and identification by properties (how does it behave?). In identification by name, the identifier or fingerprint of the material may be defined as an “ID” - an artificial nametag generated by the engine. This ID may optionally be based on prior material names that have been fed into the system from historical data. In identification by compositional properties, the identifier or fingerprint of the material may be determined by its material composition. This may include detailing the chemical constituents of the material, possibly listed through cement chemist notation, as well as its material and mechanical composition. The latter might involve ratios of aggregate to cement to water, presence of admaterial tures, and the size and type of aggregate among other relevant composition material properties. Similar to identification by name, this identification method may also include an accompanying ID for easy reference. In identification by properties, the identifier / fingerprint may be defined through a physical and mechanical property profile of the material within a specific context. This context characterizes the Page 99 of 226 13824520v1particular instantiation of the material in a given use case, encompassing the totality of context data. Physical and mechanical properties could include those of the binder, aggregate, admaterial ture, and fiber, among others. These properties may be inferred by assessing relevant data, then matching this data to a particular component of the expected performance of the material design, based on a corpus of training data. Derived metrics such as the strength, durability, workability, embodied carbon, cost, and time to maturity may be calculated or inferred from these data sources. Like the other representations, the identification by properties may also be accompanied by an ID. In some other embodiments, the output of the material identification engine may include other representations provided or generated by the AI engine.

[0392] Once the representation of the material is defined, the AI Engine can generate the output identification of the material by matching to existing database classification, augmenting existing database classifications, or generating a new database classifications. In some embodiments, matching to existing database classifications may involve comparing the output fingerprint of the material to a database of concrete material es. This database could be based on an existing standard or relate to previous material es identified by the AI engine. The matching process can be executed through supervised learning techniques. In this context, the AI Engine may be trained using labeled data that matches the categories or classifications in the existing database. Through this training process, the AI engine may “learn” the distinctive material properties of each material in the database over numerous iterations. As the AI engine processes and assimilates this information, it may gradually gain the ability to accurately output the identification of a material by finding the closest match or the most relevant category within the existing database. This method leverages historical data and established classifications to enhance the accuracy and reliability of material identification.

[0393] In some embodiments, augmenting existing database classification may include classifying the output by weighting existing materials in the database. This method effectively augments the existing database by comparing and relating the new material to previously identified material es. Utilizing the engine’s database of past identified materials, or an existing standard database, the new material is classified based on its similarity to the material es already cataloged. For instance, a new material, “New Material A,” may be analyzed and found to have similarities with “Material I,” “Material II,” and “Material III” from a particular database (referred to as “database D”). These similarities may be assessed along specific metrics, which could be various properties or compositions of the material es, denoted as “X,” “Y,” and “Z.” In a more quantifiable sense, this classification could involve a percentage breakdown, indicating that “New Material A” comprises certain proportions of the existing material es in Page 100 of 226 13824520v1the database. For example, it might be determined that “New Material A” is composed of 20% of the material properties of “Material A,” 50% of “Material B,” and 30% of “Material C.”

[0394] In some embodiments, generating a new database classification may include classifying the output fingerprint into an entirely new classification, one that is fully generated by the AI engine. To this end, the AI engine may use advanced techniques such as dimensionality reduction and meta-regression models, or the initial layers of a Convolutional Neural Network (CNN). These techniques form the core of the engine’s internal classifier. The key advantage of this approach is its ability to optimize continuously across a wide range of variables. It enables the engine to not only classify existing material compositions but also to provide recommendations for potential new material compositions that might not currently exist but could be realized based on the engine’s recommendations. In example embodiments, a translation layer may be used to bridge the gap between the engine’s internal classification system and the known or nearest known material IDs and their corresponding properties. This translation ensures that the new classifications are not isolated from existing knowledge bases, allowing for a coherent and comprehensive understanding of the materials.

[0395] The Perturbative Case of the AI Engine may be used to detect anomalies in material identifiers and determine their root causes. In this mode, the AI engine operates as a relative identification system, capable of differentiating between two material es, but not necessarily equipped to absolutely identify each material independently. In some embodiments, the AI engine may assess whether the material under consideration is the same as a reference material . If a discrepancy or perturbation is detected, indicating that the material is different, this information is relayed to the user, through a notification system. This capability allows for the identification of deviations from expected material properties. In some other embodiments, the AI engine may not only detect but also report the source of a perturbation throughout the concrete lifecycle. The AI engine can provide automated insights regarding the cause of the anomaly, detailing the ‘when’, ‘what’, and ‘why’ aspects. This feature adds a layer of diagnostic capability, enhancing the utility of the system in practical scenarios. In some other embodiments, the AI engine may suggest compensatory actions to rectify identified perturbations. For example, the AI engine may recommend adding water or admaterial ture to a material to achieve a desired contextual material property. Additionally, the AI engine may evaluate the expected impact of these recommended actions, allowing for informed decision- making. In still other embodiments, the AI engine may detect early anomalies by utilizing the range of devices and models described herein, including sensor devices and context awareness models. By employing sensors throughout the value chain and construction process, the AI Page 101 of 226 13824520v1engine can facilitate early detection and reporting on the source of perturbations. This provides users with timely insights regarding the causative factors of anomalies, encompassing the ‘when’, ‘what’, and ‘why’.

[0396] The perturbation and / or anomaly identification and determination system within the AI Engine has several use cases, each used for ensuring the integrity and consistency of materials throughout their lifecycle. These use cases include ID matching, chain of custody matching, and comparison to related historical or contemporaneous pours. In ID matching, the AI engine may be tasked with verifying whether the material currently under consideration matches a target material. The target material could be specified by a user or suggested by another model. This matching process is vital for confirming that the material being used or analyzed is indeed the one intended or expected. In chain of custody matching, the AI engine may track the continuity of a material over time. The system assesses whether the material identified at a later time T′ is the same as the one identified at an earlier time T. An example in the context of concrete would be to ascertain if the material identified in the pour is the same physical volume of concrete that was identified back in the batching plant. In comparison to related historical or contemporaneous pours, the AI engine may compare concrete material es used in different pours at a construction site. It determines whether the material used in, say, Pour X is the same as that in Pour Y.

[0397] In the perturbative mode, the functionality may be distributed across four models, including Expectation Determinator, Perturbation Detector, Perturbation Cause Analyzer, and Compensation Recommendation Engine.

[0398] The Expectation Determinator may determine material identity or material classification expectations. In the simplest case, the user may input a pre-defined target material identity or material class (as defined by its composition, properties, identifier, or other representations), which may become the expected material or class. In more complex cases, the model may consider the element type and prior similar elements on the same jobsite, to determine expected material identity or class (by property, composition or otherwise). In general, the model may infer expectations for material identity and / or class for a given scenario (e.g., for different contextual conditions), and by extension, what material es or classes not to expect in those scenarios.

[0399] The Perturbation Detector may detect or determine material anomalies or material perturbations. Perturbation Detector examines if the material currently being evaluated matches the expected material identity or class. This expectation is set by Expectation Determinator and could be based on various factors such as properties, Page 102 of 226 13824520v1composition, material identifier, sensor signals, or any other representation. Perturbation Detector then assesses if the material identity aligns with the expected identity. If there is a discrepancy between the two, it indicates a perturbation or anomaly. This discrepancy could be in terms of composition, properties, or any other defining characteristic of the material. In determining whether the material identity differs from the expected identity, the model may also take into account the possibility of false positives and false negatives. Upon detecting a perturbation, the model is designed to report this anomaly, providing insights into the nature and extent of the deviation from the expected material. As described herein, the Perturbation Detector may be used in ID matching, chain of custody matching, and comparison to other pours.

[0400] The Perturbation Cause Analyzer may identify not only the occurrence of anomalies in material identification but also in pinpointing their sources and assessing their impacts. When an identification mismatch is detected, such as an unexpected alteration in material composition (e.g., additional water in a concrete material), the model may analyze a range of data elements to determine the cause of this discrepancy. Key factors under scrutiny include the timing of the perturbation, the material’s contextual conditions at that time, and any associated actions taken, like the addition of substances to the material . Following the identification of the cause, the model proceeds to evaluate the impact of this anomaly on the material. This evaluation may include quantifying the magnitude of the impact on the material’s properties and composition, including both compositional and contextual material properties. For instance, in the case of extra water in concrete, the model may assess how this affects the material ’s strength, workability, curing time, and overall suitability for its intended application.

[0401] The Compensation Recommendation Engine may respond to anomalies or perturbations identified in material batches by recommending compensatory actions aimed at correcting identified anomalies and restoring the target or expected properties of the material. In particular, upon detecting an anomaly or perturbation, the model may propose specific actions that can be taken to counteract the identified issue. The model may also provide predictions about the expected impact of these actions. The output may also include contextual details such as the timing of the recommended compensation action and the associated material contextual conditions during that time. The model may also assess and quantify the magnitude of the expected impact of the recommended actions on the material, covering various properties of the material, including both its compositional and contextual properties. Page 103 of 226 13824520v1

[0402] In some embodiments, the perturbative mode of the AI Engine may include a time-evolving analysis to uncover the origins of anomalies. This approach involves correlation and causation analysis over time, providing insights into the development and emergence of anomalies. In one embodiment, the perturbation detector model not only identifies potential anomalies but also assigns likelihood scores to these predictions. Once an anomaly is identified and scored, the perturbation cause analyzer may analyze the anomaly’s likely origin, such as unexpected additions during material processing or transportation. This information is then passed on to the compensation recommendation engine (e.g., the processor described herein), which proposes compensatory actions to mitigate the anomaly, ensuring the material still meets the predefined specifications or expectations. Furthermore, the AI engine may be configured to interact with users for enhanced training and adaptability. Users can accept or reject identified anomalies, contributing to the model’s learning process. They also have the capability to input unnoticed anomalies into the detector, enhancing the system’s comprehensiveness and accuracy. Throughout these processes, the Generative Model is employed to manage any missing data, filling gaps to ensure continuous and complete data analysis. Example Implementation of Identification, Classification & Perturbation Detection

[0403] In some embodiments, the machine learning classifier used to detect perturbations may be a supervised learning classifier. Here, the classifier, designated as F_i for identification, F_c for classification, and F_p for perturbation, may predict the material type output (Y) from a set of potential multiple identifiers (I), classes (C), or perturbations (P), respectively. Each model, equipped with its internal tunable parameters (w_i for identification, w_c for classification, w_p for perturbation), may receive input data (X), which can come in various forms and combinations, with some inputs possibly missing. In its simplest form, a classifier F(X;w) aims to maximize the probability that its prediction corresponds to a given class label conditioned on input X.

[0404] In the standard classification framework functioning within a supervised learning capacity, the learned model (mapping F), necessitates a rich training dataset for the development of a reliable model. This framework may employ both standard statistical techniques and AI methods to reduce dimensionality and manage the complexity of the data. Techniques like PCA (Principal Component Analysis), t-SNE (t-distributed Stochastic Neighbor Embedding), and UMAP (Uniform Manifold Approximation and Projection) may be utilized to transform the data into orthogonal bases, simplifying the multi-dimensional data into Page 104 of 226 13824520v1formats that are easier to analyze and interpret. In addition to these statistical methods, AI techniques such as encoder-decoder models and autoencoders play a significant role in dimensionality reduction. Furthermore, the AI engine may be capable of extending its applications to an unsupervised classification setting. This extension may be facilitated by coupling the dimensionality reduction with standard clustering techniques like k-means clustering and density-based clustering methods, or with Gaussian material ture models.

[0405] Within the framework of the AI engine, multi-class labeling may be extensively utilized in machine learning and neural network applications, guid...

Claims

WHAT IS CLAIMED IS:

1. A computer-implemented method for material related determinations, the method comprising: receiving a first dataset comprising one or more first data entries associated with a material; generating a second dataset comprising one or more second data entries associated with the material; and outputting the second dataset associated with the material.

2. The method of Claim 0, wherein the one or more first data entries comprise a material identifier.

3. The method of Claim 0, further comprising: accessing a database storing material identification data associated with a plurality of material identifiers; and determining material composition data associated with the material identifier.

4. The method of Claim 3, wherein generating the second dataset comprises: providing the material identifier data and the material composition data to an artificial intelligence (AI) model; simulating, via the AI model, the material composition data in a first set of contextual conditions; generating one or more material properties, via the simulation, of the material in the first set of contextual conditions; and generating the second dataset comprising one or more second data entries associated with the one or more material properties for the material.

5. The method of claim 0, wherein the one or more first data entries comprise a material identifier and material properties in a first set of contextual conditions.

6. The method of Claim 0, further comprising: accessing a database storing material identification data associated with a plurality of material identifiers; and determining material composition data associated with the material identifier. Page 221 of 226 13824520v17. The method of Claim 6, wherein generating the second dataset comprises: providing the material identifier data, the material properties in the first set of contextual conditions, and the material composition data to an artificial intelligence (AI) model; simulating, via the AI model, the material composition data in a second set of contextual conditions; generating one or more material properties, via the simulation, of the material in the second set of contextual conditions; and generating the second dataset comprising one or more second data entries associated with the one or more material properties for the material in the second set of contextual conditions.

8. The method of Claim 0, wherein the one or more first data entries comprise material property data in one or more sets of contextual conditions.

9. The method of Claim 0, wherein generating the second dataset comprises: providing the material property data in one or more sets of contextual conditions to an artificial intelligence (AI) model; simulating, via the AI model, the material property data; generating one or more material identifiers, via the simulation, corresponding to the material property data; and generating the second dataset comprising one or more second data entries associated with the one or more material identifiers.

10. The method of Claim 0, wherein the one or more generated material identifiers comprise one or more material identifiers stored in a database.

11. The method of Claim 0, wherein the one or more generated material identifiers comprise one or more candidate material identifiers, wherein the one or more candidate material identifiers are absent from a database, and wherein the method further comprises: generating a plurality of material composition data for each candidate material identifier of the one or more candidate material identifiers; and Page 222 of 226 13824520v1generating the second dataset comprising one or more additional second data entries associated with the plurality of material composition data for each candidate material identifier.

12. The method of Claim 0, further comprising generating a compositional arrangement for the plurality of material composition data for each candidate material identifier of the one or more candidate material identifiers, wherein the compositional arrangement comprises a sequence of chemical equations for each of the candidate material identifiers.

13. The method of Claim 12, wherein the compositional arrangement for each candidate material identifier comprises one or more method sequences for manufacturing the candidate material identifier.

14. The method of Claim 1, wherein generating the second dataset comprises: providing data to an artificial intelligence (AI) model; simulating, via the AI model, the data; generating, via the simulation, one or more data elements; and generating the second dataset comprising one or more second data entries associated with the one or more data elements.

15. The method of Claim 1, wherein a plurality of data entries of the one or more first data entries of the first dataset is generated by one or more sensor devices.

16. The method of Claim 1, wherein the material comprises an ordered, periodically repeating atomic structure.

17. The method of Claim 1, wherein the material lacks an ordered, periodically repeating atomic structure.

18. A computer-implemented method for training a material-related determination model, the method comprising: receiving a training dataset comprising one or more training data entries associated with a plurality of materials; adjusting one or more model parameters due to the training dataset; and Page 223 of 226 13824520v1outputting an updated material-related determination model.

19. The method of Claim 18, wherein the one or more training data entries comprise material composition data for the plurality of materials, material property data for the plurality of materials, manufacturing process data for the plurality of materials, and material context data for the plurality of materials.

20. The method of Claim 19, further comprising: evaluating the training dataset for missing training data entries of the one or more training data entries; executing, if the training dataset comprises at least one missing training data entry, one or more material simulations via an AI model; and updating the at least one missing training data entry of the training dataset via the one or more material simulations.

21. The method of Claim 18, further comprising: providing a first material-related determination model to a first environment and a second material-related determination model to a second environment; generating first environment data and second environment data; adjusting one or more model parameters of the first material-related determination model due to the generated first environment data and one or more model parameters of the second material-related determination model due to the generated second environment data; and aggregating the one or more adjusted model parameters of the first material-related determination model and the one or more adjusted model parameters of the second material- related determination model to the material-related determination model.

22. The method of Claim 1, wherein the first dataset comprises one or more objectives, and wherein the second dataset comprises one or more material identifiers.

23. The method of Claim 22, wherein a compositional arrangement associated with the material comprises the second dataset.

24. The method of Claim 1, wherein generating the second dataset comprises: Page 224 of 226 13824520v1searching a material space associated with the material for a material identifier; extracting the material identifier; storing the material identifier in the second dataset; and iteratively repeating the searching, extracting, and storing steps for a plurality of material identifiers.

25. The method of Claim 7, wherein the simulation is executed by an AI model, wherein the AI model is trained on records and sensor data, wherein the sensor data comprises spectroscopy data, and wherein the one or more material properties of the material in the second set of contextual conditions comprises features of the spectroscopy data. Page 225 of 226 13824520v1

Images