Inter-atomic potential for scalable hamiltonian enhanced autoencoder-based machine learning

Abstract

A method for training and subsequently executing a machine learning network of both an autoencoder and a machine learning model in the context of machine learning inter-atomic potential is disclosed. The systems described herein are configured to embed atomic locations and categories of a given atomic system, and apply them to an autoencoder to learn auxiliary attributes, and to a machine learning model to learn local energy. The auxiliary attributes are then used to generate an auxiliary Hamiltonian description. Attributes, such as the total energy of the atomic system, are determined by combining both the auxiliary Hamiltonian description and the local energy. By processing machine learning via both an autoencoder and a machine learning model, such methods ensure that both long range and short range effects are considered while also appropriately achieving realistic discontinuities and / or transitions within potential energy surfaces.

Description

Technical Field

[0001] This disclosure relates to a combination of training and executing autoencoders and machine learning models to determine the long-range and short-range energies of a given atomic system. Background Technology

[0002] Various machine learning techniques have proven useful in predicting the interaction energies, forces, and other properties of a wide range of atomic systems. However, the use of a given machine learning model for large-scale atomic systems requires a crucial balance between short-range effects and transitions (e.g., magnetic transitions). Providing scalable machine learning techniques for implementation as iterative processes, such as molecular dynamics, remains a challenge. Summary of the Invention

[0003] Compared to previous implementations of machine learning inter-atomic potentials (MLIPs), this disclosure utilizes both an autoencoder and a machine learning model to determine properties of an atomic system, such as the total energy in the system. The autoencoder ensures that a particular MLIP architecture is scalable and can be applied to larger-scale simulations, such as molecular dynamics, with accuracy similar to ab initio methods. The combination of accuracy and scalability is at least partly due to the constraint on the potential space of the autoencoder, giving it a fixed dimension. Thus, the output is a set of discretized states. These discretized states can then be used to determine an auxiliary Hamiltonian description of a given atomic system, which can be efficiently extended to large systems. When combined with local energies learned using deep neural networks, one or more Gaussian processes, or some other type of MLIP-based model, the resulting total energy accounts for both large-scale and small-scale effects within the system and appropriately allows discontinuities and / or transitions in relation to the specific atomic system and simulation environment. Attached Figure Description

[0004] Figure 1 The illustration depicts a system for training and utilizing machine learning models, such as neural networks, according to some embodiments.

[0005] Figure 2 The illustration depicts a computer-implemented method for training and utilizing machine learning models, such as neural networks, according to some embodiments.

[0006] Figure 3 The diagram illustrates a high-level workflow for machine learning of inter-atomic potentials for a given atomic system, according to some embodiments.

[0007] Figure 4 The illustrations depict some embodiments. Figure 3 An extension of the advanced workflow diagrams described in [the document], where backpropagation is used to determine the relevant forces of a given atomic system.

[0008] Figure 5A The diagram illustrates a workflow for autoencoder-assisted energy determination in the context of machine learning of interatomic potentials in atomic systems, according to some embodiments.

[0009] Figure 5B Further illustrations are provided according to some embodiments. Figure 5A The workflow diagram described in the document further details the benefits of using an autoencoder.

[0010] Figure 6 This diagram illustrates another workflow for autoencoder-assisted energy determination in the context of machine learning of interatomic potentials in atomic systems, according to some embodiments.

[0011] Figure 7 The illustration shows an example implementation of applying autoencoder-assisted energy determination to a scenario of dissolving salt in water, according to some embodiments.

[0012] Figure 8 This is a flowchart illustrating a process, according to some embodiments, of performing an autoencoder to learn auxiliary properties of an atomic system and applying the learned auxiliary properties to determine the long-range and short-range effects of the atomic system.

[0013] Figure 9 This is a flowchart illustrating an iterative molecular dynamics-based process according to some embodiments. Detailed Implementation

[0014] This document describes embodiments of the present disclosure. However, it should be understood that the disclosed embodiments are merely examples, and other embodiments may take various and alternative forms. The drawings are not necessarily drawn to scale; some features may be enlarged or minimized to show details of specific components. Therefore, the specific structural and functional details disclosed herein should not be construed as limiting, but only as a representative basis for teaching those skilled in the art to adopt the embodiments in various ways. As will be understood by those skilled in the art, various features illustrated and described with reference to any of the drawings may be combined with features illustrated in one or more other drawings to produce embodiments not explicitly illustrated or described. The combinations of features shown provide representative embodiments for typical applications. However, for a particular application or implementation, various combinations and modifications of features consistent with the teachings of this disclosure may be desired.

[0015] Unless the context clearly specifies otherwise, the terms “a,” “an,” and “the” as used herein refer to the singular and plural indicators, respectively. For example, a “processor” programmed to perform various functions means one processor programmed to perform each function, or more than one processor collectively programmed to perform each of the various functions.

[0016] The applications of machine learning-based inter-atomic potentials (MLIPs) are wide-ranging and diverse. However, prior to the development of this disclosure, past implementations of MLIPs compromised (1) the ability to scale to include interactions beyond a finite number of neighboring atoms, (2) the ability to learn long-range effects, and / or (3) the ability to account for discontinuities and / or transitions. When using MLIPs to compute energies and forces, it is important to have the flexibility to incorporate all three capabilities, depending on the type of atomic system, and for more complete and comprehensive analysis. The following paragraphs describe in detail the context of each of these challenges faced by past implementations of MLIPs, followed by an explanation of how this disclosure overcomes the need to prioritize one of these effects at the expense of one or more others.

[0017] Past implementations of MLIP have struggled to scale deep learning networks beyond a finite number of neighboring atoms, especially for very large atomic systems. In the past, deep neural networks would use the cutoff radius of neighboring atoms. Information in the deep neural network is then passed between atoms only within a fixed cutoff distance. A further limitation is that common message-passing deep neural networks (such as Niquip) apply this cutoff distance at each layer of the deep neural network, making it... A given depth neural network has layers Effective cutoff radius and according to The number of effective adjacent atoms in the scaling. Scaling makes it virtually impossible to partition atoms in a given atomic system across different processors during a given production run, as is often associated with large-scale simulation techniques such as molecular dynamics. Furthermore, The computational cost of scaling increases cubically because the number of atoms increases exponentially. The scaling increases by the cube. This lack of scaling capability remains unresolved, even with techniques such as Allegro, which divides energy into energy per atom. ,in yes The set of all atoms in the neighborhood (i.e., within the cutoff radius), and none others, and in which It corresponds to two atoms and Effective paired energy.

[0018] Past implementations of MLIP (again, such as Allegro limited to purely local energies) have failed to overcome the difficulty in learning long-range effects (such as electrostatics and delocalized electrons, e.g., magnetic conductors). Compared to interactions trapped within a few angstroms (typically), the energies and forces associated with long-range effects can be strongly influenced by longer-range interactions within an atomic system. This leads to a significant increase in... The value of can lead to increased instability, computation time and / or memory requirements, or it can lead to the complete neglect of long-range effects, which in turn can result in a significant loss of accuracy for a given simulation. This can be achieved by focusing on some central atoms. The interaction within the neighborhood of the atom loses its effect on long-range interactions (e.g., the interaction between the central atom and the surrounding area). and beyond the cutoff radius Analysis of the interaction between another atom.

[0019] Even when using an auxiliary network to learn electrostatic point charges with a density functional theory (DFT) dataset, this DFT dataset can then be fed into known methods for calculating long-range electrostatic forces and energies (e.g., Ewald summation), where a comprehensive approach to incorporating both short-range and long-range effects into a given type of simulation was previously lacking. Other attempts include fitting point charges to DFT-based charges, such as by using Hirshfeld or Mulliken charge partitioning schemes, or deriving effective charge values ​​from other quantities, such as fitting only to the total energy without considering local energies.

[0020] None of these attempts have solved the problem of achieving scaling capability while simultaneously achieving stable incorporation of long-range effects. In particular, a significant drawback of this prior art is that atomic charges can fluctuate frequently and significantly, and therefore the entire potential energy surface can be extremely sensitive to the initial configuration of the simulation and small perturbations in atomic positions during the simulation. Furthermore, the total charge must always be forced to be neutral, for example... ,in This is the total charge of the atomic system, and its sum is zero. The enforced neutrality constraint means that charge updates cannot be performed locally without considering all atoms in the system. In summary, the sensitivity of charge values ​​to precise atomic placement and the requirement for enforced charge neutrality previously made it impossible to partition the atomic system into purely local components and perform efficient molecular dynamics simulations.

[0021] Previous applications of MLIP have failed to effectively capture discontinuities in potential energy surfaces in terms of their ability to account for discontinuities and / or transitions. Typically, there are segments of potential energy surfaces that are smooth relative to atomic positions, and other segments corresponding to transitions (e.g., magnetic transitions, bond breaking, charge transfers), at which the potential energy surface should exhibit abrupt changes. Past applications of MLIP have failed to address transitions that would cause discontinuities in the potential energy surface due to abrupt changes in a given transition, while simultaneously allowing the potential energy surface to be continuously differentiable and reasonably smooth (and therefore stable) in each region.

[0022] To address these challenges, according to some embodiments, this disclosure employs an autoencoder with a constrained latent space to learn one or more auxiliary properties of an atomic system. By fixing the latent space based on hyperparameters or some other dimension-based scheme that allows the autoencoder to map the atomic positions and types of the atomic system, the resulting learned auxiliary properties are defined by a finite number of discrete states (e.g., charge states, oxidation states, magnetic states, or some other atomic property). These discrete states can be used to construct an auxiliary Hamiltonian, which is analytical and therefore more easily scalable to longer ranges than conventional MLIP methods. In parallel, the atomic positions and types of the atomic system can also be used as input to machine learning models (such as deep neural networks) to learn local energies. The combination of the auxiliary Hamiltonian description and the learned local energies allows the specific MLIP architecture described herein to determine the total energy of a given atomic system with high accuracy, while simultaneously addressing the three challenges previously faced by the scientific community.

[0023] Specifically, this disclosure provides a scalable solution that assumes the autoencoder ensures the mapping produces a finite set of discretized states while still being configured to benefit from applications using large-scale models such as deep neural networks. Furthermore, the combined architecture using the autoencoder and machine learning model appropriately accounts for both long-range and short-range effects. Moreover, this disclosure describes discontinuities and / or transitions more precisely because the discretized set of states allows for abrupt changes in auxiliary properties learned by the autoencoder, enabling the methods and systems described herein to better simulate bond breaking or magnetic phase transitions in spin glasses, etc.

[0024] The following description continues with a general introduction to the machine learning techniques associated with the methods described herein for machine learning of interatomic potentials. Next, various embodiments of the architecture based on autoencoders and machine learning models are discussed. Then, this disclosure demonstrates the versatility of the methods and systems described herein for determining macroscopic and microscopic properties of various molecular compositions and for implementation in larger-scale simulations, such as molecular dynamics (MD).

[0025] Figure 1 The illustration depicts a system 100 for training and utilizing neural networks, such as deep neural networks. It should be understood that, although the following paragraphs of this document discuss... Figure 1 and Figure 2 The example embodiments given involve deep neural networks, but Figure 1 and Figure 2 Additional embodiments can be applied to any other type of neural network-based or non-neural network-based machine learning model (e.g., Gaussian process) that is configured to be developed, trained, and optimized for various machine learning applications of interatomic potentials.

[0026] Furthermore, and in connection with the description herein, a “deep” learning model, such as a deep neural network, can be defined as having multiple hidden layers (e.g., one, two, or dozens of hidden layers) between the input and output layers of the model. Deep learning models can also be used to describe machine learning models configured to learn complex patterns and representations based on training and / or validation datasets used as inputs to the deep learning model. Additional embodiments relating to this type of machine learning model are described in this paper with respect to machine learning model 210, network 306, deep neural network 406, network 518, learning 618, and box 810.

[0027] In some embodiments, system 100 may include an input interface for accessing training data 102 of the neural network. For example, as... Figure 1 As shown, the input interface can be composed of a data storage interface 104, which can access the training data 102 from the data storage device 106. For example, the data storage interface 104 can be a memory interface or a permanent storage interface, such as a hard disk or SSD interface, but it can also be a LAN, local area network, or wide area network interface, such as a Bluetooth, ZigBee, or Wi-Fi interface, or an Ethernet or fiber optic interface. The data storage device 106 can be an internal data storage device of the system 100, such as a hard disk drive or SSD, but it can also be an external data storage device, such as a network-accessible data storage device.

[0028] In some embodiments, data storage device 106 may further include a data representation 108 of an untrained version of the model (e.g., a version of a machine learning model that has not yet been trained), which can be accessed by system 100 from data storage device 106. However, it should be understood that training data 102 and the data representation 108 of the untrained neural network may also be accessed from different data storage devices, for example, via different subsystems of data storage interface 104. Each subsystem may be of the type described above for data storage interface 104. In other embodiments, the data representation 108 of the untrained neural network may be generated internally by system 100 based on the design parameters of the neural network and therefore may not be explicitly stored on data storage device 106. System 100 may also include a processor subsystem 110, which may be configured to provide an iterative function as an alternative to the layer stack of the neural network to be trained during operation of system 100. Here, the layers of the replaced layer stack may have weights shared with each other and may receive the output of the previous layer as input, or, for the first layer of the layer stack, receive initial activation and a portion of the layer stack's input. Processor subsystem 110 can also be configured to iteratively train the neural network using training data 102 (e.g., thus generating an updated version of the machine learning model relative to a first "untrained" version of the model). Here, the iterations of training performed by processor subsystem 110 can include a forward propagation portion and a backward propagation portion. Processor subsystem 110 can be configured to perform the forward propagation portion by determining an equilibrium point of the iterative function, where the iterative function converges to a fixed point, in addition to other operations that may be performed to define the forward propagation portion. Determining the equilibrium point includes finding the root solution of the iterative function by subtracting its input from the numerical root-finding algorithm, and by providing the equilibrium point as an alternative to the output of the layer stack in the neural network. System 100 may also include an output interface for outputting a data representation 112 of the trained neural network, which may also be referred to as trained model data 112. For example, also as Figure 1 As shown, the output interface can be comprised of a data storage interface 104, which in these embodiments is an input / output (“IO”) interface through which trained model data 112 can be stored in data storage device 106. For example, the data representation 108 defining an untrained neural network can be at least partially replaced by the data representation 112 of the trained neural network during or after training, because the parameters of the neural network (such as weights, hyperparameters, and other types of parameters of the neural network) can be adapted to reflect training on the training data 102. This also... Figure 1The figures are illustrated by reference numerals 108 and 112, which refer to the same data records on data storage device 106. In other embodiments, data representation 112 may be stored separately from data representation 108, which defines an "untrained" neural network. In some embodiments, the output interface may be separate from data storage interface 104, but it can typically be of the type described above for data storage interface 104.

[0029] Figure 2 The illustration depicts a computer-implemented method for training and utilizing a neural network according to some embodiments. System 200 may include at least one computing system 202. Computing system 202 may include at least one processor 204 operatively connected to memory unit 208. Processor 204 may include one or more integrated circuits implementing the functions of a central processing unit (CPU) 206 and, in some embodiments, a graphics processing unit (GPU). CPU 206 may be a commercially available processing unit implementing an instruction set such as x86, ARM, Power, or MIPS instruction set families. During operation, CPU 206 may execute stored program instructions fetched from memory unit 208. The stored program instructions may include software controlling the operation of CPU 206 to perform the operations described herein. In some examples, processor 204 may be a system-on-a-chip (SoC) that integrates the functions of CPU 206, memory unit 208, network interface, and input / output interface into a single integrated device. Computing system 202 may implement an operating system for managing various aspects of operation.

[0030] Memory cell 208 may include volatile and non-volatile memory for storing instructions and data. Non-volatile memory may include solid-state memory, such as NAND flash memory, magnetic and optical storage media, or any other suitable data storage device that retains data when the computing system 202 is deactivated or loses power. Volatile memory may include static and dynamic random access memory (RAM) for storing program instructions and data. For example, memory cell 208 may store machine learning model 210 or an algorithm, training dataset 212 for machine learning model 210 (e.g., density functional theory (DFT) training dataset), original source dataset 214, autoencoders, etc.

[0031] The computing system 202 may include a network interface device 220 configured to provide communication with external systems and devices. For example, the network interface device 220 may include wired and / or wireless Ethernet interfaces defined by the Institute of Electrical and Electronics Engineers (IEEE) 802.11 series of standards. The network interface device 220 may include a cellular communication interface for communicating with cellular networks (e.g., 3G, 4G, 5G). The network interface device 220 may also be configured to provide a communication interface to an external network 222 or the cloud.

[0032] External network 222 may be referred to as the World Wide Web or the Internet. External network 222 can establish standard communication protocols between computing devices. External network 222 can allow for the easy exchange of information and data between computing devices and the network. One or more servers 224 can communicate with external network 222.

[0033] The computing system 202 may include an input / output (I / O) interface 218, which may be configured to provide digital and / or analog inputs and outputs. The I / O interface 218 may include an additional serial interface (e.g., a Universal Serial Bus (USB) interface) for communicating with external devices.

[0034] The computing system 202 may include a human-machine interface (HMI) device 216, which may include any device that enables the system 200 to receive control input. Examples of input devices may include HMI inputs such as a keyboard, mouse, touchscreen, voice input device, and other similar devices. The computing system 202 may include a display device 226. The computing system 202 may include hardware and software for outputting graphical and textual information to the display device 226. The display device 226 may include an electronic display screen, projector, printer, or other suitable device for displaying information to a user or operator. The computing system 202 may also be configured to allow interaction with remote HMIs and remote display devices via a network interface device 220.

[0035] System 200 can be implemented using one or more computing systems. While this example depicts a single computing system 202 implementing all the described features, various features and functions can be decoupled and implemented by multiple computing units that communicate with each other. The specific system architecture chosen can depend on a variety of factors.

[0036] System 200 can implement machine learning algorithm 210 configured to analyze raw source dataset 214. Raw source dataset 214 may include raw or unprocessed sensor data, which may represent the input dataset for the machine learning system. Raw source dataset 214 may include DFT training datasets and / or any other atomic descriptions related to the atomic positions and atom types of various systems. In some examples, machine learning algorithm 210 may be a neural network algorithm designed to perform a predetermined function. For example, a neural network algorithm can be configured in the context of machine learning inter-atomic potentials to learn the local energies of the system.

[0037] Computer system 200 may store a training dataset 212 for machine learning algorithm 210. Training dataset 212 may represent a previously constructed dataset used to train machine learning algorithm 210. Machine learning algorithm 210 can use training dataset 212 to learn weighting factors associated with a neural network algorithm. Training dataset 212 may include a source dataset having a corresponding outcome or result that machine learning algorithm 210 attempts to replicate through the learning process. In the context of machine learning of interatomic potentials, machine learning algorithm 210 can predict the energy and / or other atomic properties of a given atomic system.

[0038] Machine learning algorithm 210 can operate in learning mode using training dataset 212 as input. Machine learning algorithm 210 can be executed in multiple iterations using data from training dataset 212. With each iteration, machine learning algorithm 210 can update its internal weighting factors based on the achieved results. For example, machine learning algorithm 210 can compare its output (e.g., annotations) with what is included in training dataset 212. Since training dataset 212 includes expected results, machine learning algorithm 210 can determine when performance is acceptable. After machine learning algorithm 210 achieves a predetermined performance level (e.g., 100% conformity to results associated with training dataset 212), machine learning algorithm 210 can be executed using data not in training dataset 212. The trained machine learning algorithm 210 can be applied to new datasets to generate annotated data.

[0039] Machine learning algorithm 210 can be configured to identify specific features in raw source data 214. Raw source data 214 may include multiple instances or input datasets, with annotation results expected for those instances or input datasets. Machine learning algorithm 210 can be programmed to process raw source data 214 to identify the presence of specific features. Machine learning algorithm 210 can be configured to identify features in raw source data 214 as predetermined features (e.g., evidence that an atomic system including water molecules has hydrogen and oxygen). Raw source data 214 can be derived from various sources. For example, raw source data 214 can be actual input data collected by a machine learning system. Raw source data 214 can be machine-generated for testing the system. As an example, raw source data 214 may include a DFT training dataset associated with different concentrations of salt already dissolved in water.

[0040] In this example, machine learning algorithm 210 can then process the raw source data 214 and output an indication of the predicted local energy. Machine learning algorithm 210 can generate a confidence level or factor for each generated output. For example, a confidence value exceeding a predetermined high confidence threshold can indicate that machine learning algorithm 210 is confident that the identified feature corresponds to a specific feature. A confidence value below a low confidence threshold can indicate that machine learning algorithm 210 has some uncertainty regarding the presence of a specific feature.

[0041] Figure 3 The illustration shows a high-level workflow diagram for a given atomic system according to some embodiments.

[0042] In some embodiments, as used and described herein, MLIP can be used to set the atomic positions of a given atomic system. and corresponding atom types Mapping to scalar energy ,like Figure 3 As shown, and by extending the mapping to additional properties, such as force. ,like Figure 4 As shown in the figure. In some embodiments, this can be considered equivalent to learning the potential energy surface of an atomic system.

[0043] As used in this article, atom type can refer to atomic number, isotope, element description, or any other attribute used to distinguish different atom identities in a simulation.

[0044] As shown in process 300, the atom position and atom type can be referred to as atom descriptor 302 or atom description 302. For example, in some embodiments where process 300 is similar to a process flow performed for a client, the client may provide a request to determine the total energy of a given atomic system and then send it to the operating system. Figure 3The computational system of the method shown provides atomic description 302. It should be understood similarly that the atomic positions and types within atomic descriptor 302 refer to data providing the simulated atomic structure of the atomic system at compile time based on the provided atomic positions and types.

[0045] Embedding 304 refers to the input that converts atomic positions and types into interatomic potentials, which is represented in the diagram as follows. These inputs to the interatomic potential are also referred to as atomic descriptors in this paper. Embeddings can be designed to be invariant or covariant with respect to certain sets of symmetries in the atomic system or physics (such as translation, rotation, atomic exchange, or various crystal symmetries). This paper discusses... Figure 5A , 5B This embedding is discussed separately in section 6. The embedding 304 is then provided as input to the "network" 306, which learns about one or more properties of the atomic system. Figure 3 and 4 Designed to demonstrate the overall process flow of MLIP, Figure 5A , 5B Figure 6 illustrates the combined use of autoencoders and machine learning models during the learning phase 306.

[0046] Then, one or more properties learned during the 306 learning phase are used to calculate the total energy of the atomic system, which is... Figure 3 It is also known as output 308.

[0047] Process 300 can be applied to a variety of computational simulations, such as those that reconstruct structures from experimental data, molecular dynamics simulations, methods for finding specific atomic configurations of atomic systems, atomic Monte Carlo or advanced gauge Monte Carlo simulations, and even simulations for identifying possible interactions and / or transition states.

[0048] Figure 4 The illustrations depict some embodiments. Figure 3 An extension of the advanced workflow diagrams described in [the document], where backpropagation is used to determine the relevant forces of a given atomic system.

[0049] Similar to Figure 3 The process described in section 400 depicts the set of atomic positions and atomic types embedded into the atomic descriptor during the embedding stage 404. Then, during the learning stage 406, one or more machine learning models are applied to determine the total energy of the atomic system, as shown in output 408.

[0050] like Figure 4As shown in the diagram, learning 406 refers to deep neural networks. Deep neural networks typically have several layers that learn using backpropagation, where the network's weights are optimized to minimize a loss function, such as... , and among them Training data is extracted from higher-fidelity methods such as DFT. Backpropagation can also be referred to as backpropagation through a network model, where the network weights are adjusted based on the model's error rate. A technical example of applying backpropagation is PyTorch's autograd feature.

[0051] In some embodiments, backpropagation can also be used to predict force, in Figure 4 The force is represented as 410, which is the derivative of the total energy with respect to the atomic position. Then, loss functions (such as...) can also be used. Furthermore, the deep neural network is further trained on the force using high-fidelity forces (such as those in the DFT). According to some embodiments, the loss function may also focus on the stress tensor, or a combination of two or more of the above.

[0052] Figure 4 The specific embodiment shown mentions that learning 406 is implemented using a deep neural network (e.g., Niquip, Allegro) to determine the total energy and force using backpropagation. However, other embodiments of process 400 may mention that learning 406 is implemented using one or more Gaussian processes (e.g., FLARE). As used herein, one or more Gaussian processes may refer to one or more such processes used to implement the model when combined. The model can then be referred to as a Gaussian process model or a Gaussian-based model.

[0053] Depending on the specific implementation of processes 300 and 400 for a given problem statement provided by the client, it should be understood that learning 306 and 406 can be customized to refer to a deep neural network or one or more Gaussian processes. Furthermore, Gaussian processes and deep neural networks can be defined as two main categories of MLIPs. Therefore, the workflow diagrams shown in all the accompanying figures and their corresponding texts herein are intended to refer to MLIP implementations, including those using Gaussian processes or deep neural networks, depending on the specific implementation disclosed herein.

[0054] In addition, Figure 9 The other illustration shows the use Figure 4 Example embodiments of molecular dynamics algorithms of the method type described herein.

[0055] Figure 5A and 5B The diagram illustrates a workflow for autoencoder-assisted energy determination in the context of machine learning of interatomic potentials in atomic systems, according to some embodiments.

[0056] As described above, and to ensure that one or more models contained within learning 306 or learning 406 are configured to capture significant topological and / or charge transitions while eliminating parasitic noise when such transitions do not occur, learning 306 or learning 406 may resemble a combination of autoencoder 506 and learning network 518. As described above, learning network 518 may resemble a deep neural network or be configured to combine into one or more Gaussian processes based on Gaussian models.

[0057] Furthermore, the autoencoder 506 can be defined as a latent space with limited dimensions, such that it can then be configured to learn atomic system-specific transitions.

[0058] In some embodiments, the autoencoder 506 may resemble a PyTorch module with parameters learned during the training phase. These parameters may then be fixed and used to predict one or more auxiliary properties 508, such as charge, during a given iteration of process 500.

[0059] An autoencoder can also be defined as a dimension. Automatic encoders with limited potential space, which in Figure 5A This is referred to as the latent space representation. The value of can correspond to the number of expected states, or it can be a hyperparameter chosen during the training phase. Furthermore, the dimension... The determination of may be further influenced by the complexity of the given atomic system or the type of auxiliary properties being learned.

[0060] In some embodiments, the autoencoder 506 may be similar to a variational autoencoder, a regularized autoencoder, a sparse autoencoder, or any other type of artificial neural network that maps atomic descriptors 502 through a restricted-dimensional latent space 506 to predict auxiliary properties 508.

[0061] like Figure 5A As shown, the output of autoencoder 506 is a learned auxiliary property defined by a finite set of discrete states. This is also referred to as auxiliary state 508 in the figure. The set of discretized states is equal to the number of selected dimensions of the latent space of autoencoder 506. In some embodiments, this may also be referred to as the dimension of the hyperparameter. For example, the learned auxiliary property 508 may refer to atomic charge, where the atomic charge changes only upon detection of a substantial change in the local environment in which the atomic system is simulated.

[0062] In some embodiments, auxiliary attribute 508 may be one or more charge states ( ), oxidation state, magnetic state ( Or some other atomic property that is particularly relevant to the given atomic system under study. In addition, within the decoder 528, there may be transformations between the confined latent space and the floating-point physical properties (charge state, oxidation state, magnetic state) of the auxiliary Hamiltonian.

[0063] Then, one or more auxiliary properties are used to determine the auxiliary Hamiltonian description of the atomic system. As shown in the figure, the auxiliary Hamiltonian description encompasses the analysis of both short-range and long-range effects, while also taking into account discontinuities and / or transitions associated with the given atomic system. Examples of such transitions are shown in... Figure 5B The diagram is shown in the image and discussed separately below. Furthermore, Figure 5A The embodiments shown depict an auxiliary Hamiltonian describing the energy of an atomic system. However, Figure 5A Other embodiments may depict auxiliary Hamiltonians that describe the forces of an atomic system.

[0064] In parallel, embedded atomic descriptors are also provided to learning 518, as indicated by atomic descriptors 514 and embedding 516. It should be understood that in Figure 5A In the embodiments depicted, the sequences shown by 502, 504, 506, 508 and 510 may occur in parallel with the sequences shown by 514, 516, 518 and 520, or in sequential order. Figure 6 The embodiments shown also illustrate the sequence of processes 600, which will be discussed further below.

[0065] As described above, learning 518 can be analogous to some form of deep neural network or Gaussian-based model configured for machine learning of inter-atomic potentials and for learning the local energy 520 of the atomic system. Following the example given above, if and when the target property being learned is related to energy, then the auxiliary Hamiltonian 510 can describe the energy of the atomic system, and learning 518 can be configured to learn local energy such that a total energy 512 can be determined for the atomic system. In other embodiments, if the target property being learned is directly related to force, then the auxiliary Hamiltonian 510 can describe the force of the atomic system, and learning 518 can be configured to directly learn force such that a total related force 512 can be determined for the atomic system.

[0066] After learning the auxiliary Hamiltonian description and the local energies of the atomic system, the total energy of the atomic system can then be determined. In some embodiments, the total energy determination is based on the strict local energies learned in learning 518 and on the analytical auxiliary Hamiltonian description 510 determined via autoencoder 506. This ensures that the total energy determination takes into account long-range effects. In some embodiments, the auxiliary Hamiltonian description may be similar to an Ewald summation per atomic charge or may include learned parameters. The magnetic Hamiltonian is described.

[0067] Returning to reference atomic descriptors 502 and 514, they are specifically local atomic descriptors because they are for the central atom. Atoms in the neighborhood j The analysis. Therefore, learning 518, if performed using an MLIP-based model such as Allegro, outputs local energy. .

[0068] Another element related to the architectures shown in 500 and 600 is the configuration and consideration of charge neutrality. For example, the autoencoder 506 can be configured to enforce charge neutrality during execution. When the autoencoder receives an instruction that it should adhere to charge neutrality, it learns auxiliary properties while simultaneously conforming to charge neutrality.

[0069] In some embodiments, and for electrostatic applications, the loss function of the autoencoder can be generalized to include, in addition to the conventional loss, the charge neutrality of auxiliary states in the latent space. This constrains the autoencoder to learn the latent space based on the input coordinates and the atom type, which governs the total charge of the atomic system (e.g., typically zero).

[0070] In the dynamic process, there may be additional steps related to charge neutrality to ensure However, without the high volatility of charge and therefore the need for frequent reassessment of global neutrality, this disclosure is configured to keep the charge approximately constant in most steps due to the finite number of discrete states, and thus less likely to change accordingly. Furthermore, the computational system is configured to infer when auxiliary states change based on the input coordinates and type (e.g., via the product of the list of auxiliary variables and the autoencoder), thus allowing recalculation only when strictly necessary during the dynamic process. This is analogous to how in modern scalable dynamic processes (e.g., LAMMPS) the list of atomic neighbors is not computed at every time step. This also... Figure 9 The diagram in the middle is shown.

[0071] In some embodiments, the customer may include an indication of whether charge neutrality is mandatory or not. In other embodiments, the architecture shown in 500 and 600 may be configured to determine whether charge neutrality should be observed. For example, based on incoming information from the customer, it may indicate whether this is an electrostatics-related issue.

[0072] In some scenarios involving certain atomic systems, such as when dealing with liquid solids, charge neutrality is not mandatory. However, in scenarios where salt dissolves in water (see also the section on...),... Figure 7(as described in the text) Excess charge in the study area would not correspond to a reasonable explanation or simulation of salt dissolving in water, thus forcing charge neutrality. In yet another example, some scenarios involving point charges would require the autoencoder to conform to charge neutrality, while scenarios involving polarizability or magnetic moment might not require such a constraint.

[0073] Force can be calculated as and assistance The summation. Because autoencoders are designed to keep auxiliary properties approximately constant, the derivative of the latter term can be approximated by, for example, an analytical term used in electrostatics. .

[0074] The network's output can be energy, force, stress, polarizability, point charge, electrostatic field, magnetic moment, and / or any other atomic system-wide and / or atom-specific property, which can be used for simulations such as molecular dynamics, structure or construction searches, Monte Carlo simulations, or any other atomic simulations.

[0075] like Figure 5B As shown, the autoencoder 506 can be analogous to the autoencoder shown with encoder 524, latent space representation 526, and decoder 528. Relative to the dimensions of encoder 524 and decoder 526, the latent space representation 526 is analogous to a lower-dimensional space configured to map atomic descriptors to one or more auxiliary properties of a given atomic system. Furthermore, the autoencoder 506 can be analogous to an artificial neural network or any other feedforward network configured to learn auxiliary properties of an atomic system.

[0076] Encoder 524 is used to encode the input, which is a combination of atomic positions and atomic types 502, which has been transformed into an embedding 504 of a given atomic system. The latent space representation 526 then refers to a representation with specific dimensions. A restricted latent space is constructed, in which the core features, information, and / or relevances of the input data are processed and then provided to the decoder 528. The task of the decoder 528 is then to generate auxiliary attributes based on the core features learned within the restricted latent space.

[0077] For example Figure 5B As shown, the auxiliary state 508, learned by the autoencoder 506, realizes discontinuities and / or transitions within the potential energy surface. Figure 5B In the example shown, the vertical dashed line within line 532 illustrates bond breaking because the atomic charge changes abruptly with increasing bond length. Line 530 illustrates the same type of transition without learning the auxiliary state 508 using the autoencoder 506. The absence of abrupt transitions and the increased variability of the auxiliary properties lead to instability in the multidimensional potential energy surface (PES).

[0078] Figure 6 This diagram illustrates another workflow for autoencoder-assisted energy determination in the context of machine learning of interatomic potentials in atomic systems, according to some embodiments.

[0079] Similar to Figure 5A and 5B The process 500 illustrates this, while process 600 demonstrates the use of atomic positions and types to determine the total energy of a given atomic system. Atom descriptors 602 are embedded as input to the interatomic potential during embedding 604 and are subsequently provided to the autoencoder 606. Similar to process 500 above, the autoencoder 606 is configured as a latent space representation with constrained dimensions.

[0080] like Figure 6 As shown, the output of autoencoder 606 is a learned auxiliary property defined by a finite set of discrete states. This is also referred to as auxiliary state 608 in the figure. The set of discretized states is equal to the number of selected dimensions of the latent space of autoencoder 606. In some embodiments, the set of discretized states within the latent space representation 526 is then further transformed into the auxiliary state set 608 by decoder 528.

[0081] Then, one or more auxiliary properties are used to determine the auxiliary Hamiltonian description of the atomic system. As shown in the figure, the auxiliary Hamiltonian description encompasses the analysis of both short-range and long-range effects, while also taking into account discontinuities and / or transitions associated with the given atomic system.

[0082] In parallel, embedded atomic descriptors are also provided to learning 618, as indicated by atomic descriptors 614 and embeddings 616. Figure 6 As depicted, the sequences 602, 604, 606, and 608 can occur in parallel with the embeddings of the atoms described by the sequences 614 and 616. However, auxiliary state 608 is also provided as input before the model is executed in learning 618. This may be advantageous in certain embodiments, where both the embedded atomic descriptors and the auxiliary states ensure a more robust model for learning local energies.

[0083] Similar to Figure 5A and 5B The contents shown, the determined auxiliary Hamiltonian description 610 and the learned local energy 620 are then used to determine the total energy 612 of the atomic system, and in some embodiments, they can also be used to determine forces, stresses or some other physically meaningful value.

[0084] Figure 7The illustration shows an example implementation of applying autoencoder-assisted energy determination to a scenario of dissolving salt in water, according to some embodiments.

[0085] exist Figure 7 In the given scenario depicted, process 700 describes the overall process of receiving a request from a client to determine properties of an atomic system that are considered to simulate the dissolution of a salt in water. As shown in box 702, in this scenario, the problem statement received from the client requests the determination of the total energy of a given system in which a certain concentration of NaCl is dissolved in water.

[0086] In some embodiments, the customer may additionally provide atomic positions (as shown in the lattice of NaCl and water molecules in box 702 of the figure) and atomic types, which are understood to be sodium, chlorine, oxygen, and hydrogen according to the problem statement.

[0087] In other embodiments, the customer provides only a request to determine the total energy of a given atomic system, and methods and systems such as those described herein are configured to determine the atomic positions and types.

[0088] Subsequently, atomic descriptions, including atomic positions and types, are provided to those with, for example... Figure 5A , 5B Or a computational system with the architecture shown in Figure 6. Therefore, box 704 includes embedding atomic locations and types into atomic descriptors, providing atomic descriptors to an autoencoder, learning given auxiliary properties based on those atomic descriptors, and determining the resulting auxiliary Hamiltonian description of the atomic system. Box 704 also includes providing the embedded atomic descriptions to a deep neural network or a Gaussian-based model to determine the local energy of a given atomic system.

[0089] In some embodiments, and as Figure 6 As shown, in addition to the embedded atomic descriptors provided as input, auxiliary properties learned by the autoencoder can also be provided as input to the deep neural network or Gaussian-based model.

[0090] The auxiliary Hamiltonian, described and learned from the local energy, can then be used to determine the client's request, such as the determination of the total energy of the atomic system. As shown in box 706, the contribution from the auxiliary Hamiltonian can be performed via Ewald summation.

[0091] According to some embodiments, the results of block 706 can then be provided to the customer. Block 704 may also include two or more iterations of autoencoder-assisted energy determination, and thus the customer can receive information about the results of one or more of these iterations.

[0092] Given scenario 700, the generality of the autoencoder is also demonstrated. For example, depending on the completed embedding, the autoencoder can be provided with rotational symmetry and / or exchange symmetry. Then, in the first example, if the restricted-dimensional latent space of the autoencoder is fixed to have a dimension of 4, the autoencoder can be configured to learn that the shielding charge of sodium ions is always +0.9, chloride ions are always -0.9, hydrogen molecules of water molecules have a partial charge of 0.5, and oxygen molecules have a partial charge of -1.0.

[0093] In the second example, if the limited-dimensional latent space of the autoencoder is fixed to have dimensions 5, 6, 7, 8, 9, or 10, the autoencoder can be additionally configured to learn the differences between water, protons, hydroxyl groups, and hydrated hydrogen ions.

[0094] Furthermore, autoencoders are also generalizable by incorporating or not incorporating considerations of charge neutrality. For example, if an autoencoder is provided with information indicating the presence of 5 sodium ions and 5 chloride ions, and if the dimension of the latent space is fixed at 2, the autoencoder learns that the total charge prediction is zero.

[0095] Figure 8 This is a flowchart illustrating a process, according to some embodiments, of performing an autoencoder to learn auxiliary properties of an atomic system and applying the learned auxiliary properties to determine long-range and short-range effects of the atomic system.

[0096] Process 800 is provided in a context where a specific problem statement is received from a client and specific properties of a given atomic system are learned. In some embodiments, process 800 may occur on one or more processors of a computing system, such as regarding... Figure 1 and 2 The aforementioned. A user interface can also be provided via such a computing system, allowing one or more clients to submit requests for MLIP-based simulations to be run on the computing system and to receive the results of those requests.

[0097] As shown in box 802, the client can provide an atomic description of the atomic system, which includes at least the atomic positions and types known to exist within the atomic system. The problem statement can further define certain objectives, such as an interest in using machine learning to determine an auxiliary Hamiltonian description of the atomic system, and / or an interest in a description of the total energy of the atomic system.

[0098] In box 804, the atomic position and type are embedded into an atomic descriptor, which may be invariant or covariant with respect to certain symmetries of the system. The embedding is then provided to an autoencoder in box 806, where the atomic descriptor is mapped through a restricted-dimensional latent space to learn auxiliary properties of the atomic system. These auxiliary properties correspond to a set of discretized states, such as charge states, oxidation states, or magnetic states.

[0099] In box 808, the learned auxiliary properties are used to generate an auxiliary Hamiltonian description for a given atomic system. This is due to the use of atomic positions and types, and because a fixed atomic cutoff radius is not required. This auxiliary Hamiltonian description is configured to describe both long-range and short-range effects of atomic systems.

[0100] In box 810, the embedded atomic descriptors are also provided to the machine learning model simultaneously or sequentially to determine the local energy of the atomic system. In some embodiments, the machine learning model may be similar to a deep neural network, a Gaussian-based model, or any other MLIP-based model configured to learn the local energy of the atomic system. Furthermore, according to some embodiments, the learned auxiliary properties described in box 806 may also be provided as input to the machine learning model.

[0101] In box 812, the total energy of the atomic system is determined using the auxiliary Hamiltonian description and the learned local energy.

[0102] After determining the total energy of the atomic system, the process can be iterated again from start to finish (800 iterations). The number of iterations above the initial iteration can be determined based on specific properties intended to be learned by autoencoders and machine learning models, or based on the complexity of the given problem statement.

[0103] Once the total energy has been determined and / or convergence within a given threshold has been achieved, the results of the autoencoder-assisted energy determination are provided to the client via the client interface.

[0104] In some embodiments, process 800 can be analogous to a subprocess in a larger context. For example, once an auxiliary Hamiltonian description is determined using process 800, the auxiliary Hamiltonian can be used as input to another technique to determine the ground state of the atomic system. In another example, once the total energy of the atomic system is determined using process 800, backpropagation can be applied to an autoencoder-assisted energy determination architecture, such as... Figure 5A , 5B And those shown in 6, so as to also determine other properties, such as the relevant forces of the atomic system. In yet another example, energy and force calculations using process 800 can be iteratively incorporated into molecular dynamics (MD) simulations.

[0105] Figure 9 This is a flowchart illustrating an iterative molecular dynamics-based process according to some embodiments. As indicated by the arrows between updating position 910 and atomic position 902, process 900 can be calculated more than once. Furthermore, and as also shown in "Update Partition," "Update Neighbor List," and "Update Charge," one or more steps within process 900 can be performed during each iteration, every other iteration, every N iterations, etc. The following paragraphs illustrate an example embodiment of the first run of process 900.

[0106] In box 902, atomic positions are enumerated for the corresponding atoms within a given atomic system. As described above, a problem statement provided by the customer may include atomic descriptions, such as information about the positions and types of atoms within the atomic system that are the focus of the problem statement.

[0107] In box 904, those atomic locations are partitioned across two or more processors, such as two or more processors 204 accessing the memory 208 storing the MLIP model. In some embodiments, processors 204 are configured to partition the corresponding atomic locations such that neighboring atoms are partitioned onto the same processor. This can reduce the amount of Message Passing Interface (MPI) communication that needs to occur during and / or between iterations of process 900. As indicated by the arrows, this partitioning may not need to be repartitioned at every time step of the simulation.

[0108] Create an atom in box 906. i All atoms in the neighborhood j A set of atomic neighbors. For example, the neighbor list can be included in the set of atoms. i Cutoff radius All atoms within the system. As described above, for each atom within the atomic system... j It can be found in atomic descriptors The atom locations are defined within (such as in atom descriptors 502, 514, 602, and 614). As the arrows indicate, this neighbor list may not need to be regenerated at every time step of the simulation.

[0109] In box 908, a charge list can be created based on an autoencoder, such as in Figure 5A , 5B In the architecture described in section 6, as indicated by the arrows, these charges may not need to be regenerated at every time step of the simulation because they may be relatively stable. In some embodiments, a charge rebalancing step is further performed here to ensure... ,in It is the total charge distributed in the system.

[0110] In box 910, an autoencoder-assisted energy determination is used to determine the total energy of the atomic system. Such as in this article Figure 5A , 5B In the architectures described in section 6, as introduced above, energy calculations provide atomic positions, types, charges, and / or other properties, and feed them to autoencoders and machine learning models. Auxiliary Hamiltonian descriptions and local energies are learned separately and then applied to calculate the total energy of the atomic system. Additionally, forces... Alternatively, it can be calculated, for example, via backpropagation and using the value of the local energy already learned by neural network 518 or 618.

[0111] In box 912, the calculated energy and force are used as inputs to update the atom positions, such as by using an integration scheme, like a jump integral.

[0112] As indicated by the arrows between boxes 912 and 902, MPI then transfers the results between the corresponding processors in the processors used in the partitioning to achieve updated atomic positions and / or updated total energies based on that particular iteration of process 900.

[0113] As described above, process 900 can iterate more than once, and boxes 904, 906, 908, and / or 910 can be updated during at least some subsequent iterations of process 900. For example, and after the updated atomic positions are determined via boxes 912 and 902, the atomic positions can be updated to the partitions on the corresponding processors before continuing to create the neighbor list in box 906. In some embodiments, the partitions can be updated every N iterations, where N can be equal to a value such as 1000. In another example, and after the atomic position partitions in box 904, the atomic neighbor list in box 906 can be updated. In some embodiments, the neighbor list can be updated every M iterations, where M can be equal to a value such as 100. In yet another example, and after the neighbor list is created in box 906, the charge can be updated. Similarly, the charge may or may not be updated in each iteration, depending on the integration done for updating position 912 during previous iterations.

[0114] It should be understood that process 900 can be repeated any given number of times based on pre-set convergence criteria, time limits, computational capacity constraints, or any other number of implementation methods and / or customer-specific criteria.

[0115] While exemplary embodiments have been described above, these embodiments are not intended to describe all possible forms covered by the claims. The terms used in this specification are descriptive rather than restrictive, and it should be understood that various changes may be made without departing from the spirit and scope of this disclosure. As previously stated, features of various embodiments may be combined to form further embodiments of the invention that may not be explicitly described or illustrated. While various embodiments may have been described as providing advantages or superiority over other embodiments or prior art implementations in one or more desired characteristics, those skilled in the art will recognize that one or more features or characteristics may be compromised to achieve desired overall system properties, depending on the specific application and implementation. These properties may include, but are not limited to, cost, strength, durability, lifecycle cost, marketability, appearance, packaging, size, serviceability, weight, manufacturability, ease of assembly, etc. Therefore, any embodiment described as less desirable than other embodiments or prior art implementations in one or more characteristics is not outside the scope of this disclosure and may be desirable for a particular application.

Claims

1. A computer-implemented method for performing machine learning networks on inter-atomic potentials for machine learning, comprising: Receive data indicating an atomic description of an atomic system, wherein the atomic description includes the atomic position and atom type of the corresponding atom in the atomic system; The data indicating the atom position and the atom type is embedded into the atom descriptor; Atom descriptors embedded by a restricted-dimensional latent space mapping of an autoencoder are used to learn the discretized auxiliary state set of the atomic system; Auxiliary Hamiltonian descriptions are generated based on the learned auxiliary states; The embedded atomic descriptors and the learned auxiliary states are provided as input to the machine learning model; The machine learning model is executed to learn the local energy of the atomic system; as well as The total energy of the atomic system is output based on the auxiliary Hamiltonian description and the learned local energy.

2. The computer-implemented method according to claim 1 further includes: Based on the total energy output by the atomic system, the relevant forces of the atomic system are determined through backpropagation. as well as Output the relevant forces.

3. The computer-implemented method according to claim 2, wherein: The total energy and the associated forces of the atomic system's output are provided for integration within a given iteration of the molecular dynamics simulation; as well as The method further includes: Receive an indication that one or more of the atomic positions have been updated relative to the atomic positions within the atomic description during subsequent iterations of the molecular dynamics simulation; Embed the updated atom positions and atom types into the updated atom descriptors; and The embedded updated atomic descriptors are remapped and the machine learning model is re-executed to output the updated total energy of the atomic system.

4. The computer-implemented method according to claim 1, Based on the type of auxiliary state to be learned, determine whether to force the charge neutrality of the atomic system during mapping the embedded atomic descriptors through the restricted-dimensional latent space of the autoencoder; and Provide the required charge neutrality indication to the automatic encoder.

5. The computer-implemented method according to claim 1, Based on the type of auxiliary states to be learned, determine that the charge neutrality of the atomic system is not enforced during the mapping of the embedded atomic descriptors through the restricted-dimensional latent space of the autoencoder; and The automatic encoder is provided with an indication that does not restrict charge neutrality.

6. The computer-implemented method according to claim 1, further comprising: Additionally, it receives an indication of the type of auxiliary state to be learned; as well as The dimension of the restricted-dimensional potential space to be applied is determined at least in part based on the complexity of the atomic system or the type of the auxiliary state.

7. The computer-implemented method according to claim 1, wherein, The set of discretized auxiliary states is one or more of the following: Charge state; Oxidized state; or Magnetic state.

8. The computer-implemented method according to claim 1, wherein the autoencoder is a variational autoencoder, a regularized autoencoder, or a sparse autoencoder.

9. The computer-implemented method according to claim 1, wherein the machine learning model is a deep neural network or one or more Gaussian processes.

10. A computer-implemented method for performing machine learning networks on inter-atomic potentials for machine learning, comprising: Receive data indicating a request from a client for the total energy of a defined atomic system, wherein the request includes the atomic position and atom type of the corresponding atom in the atomic system; The data indicating the atom position and the atom type is embedded into the atom descriptor; Atom descriptors embedded by a restricted-dimensional latent space mapping of an autoencoder are used to learn the discretized auxiliary state set of the atomic system; Auxiliary Hamiltonian descriptions are generated based on the learned auxiliary states; A machine learning model is executed based on the embedded atomic descriptors to learn the local energy of the atomic system; The total energy of the atomic system is output based on the auxiliary Hamiltonian description and the learned local energy. as well as The total energy is provided to the customer.

11. The computer-implemented method according to claim 10, wherein: The atomic descriptor is an input describing the interatomic potential of the atomic system; and The atomic descriptor is invariant or covariant with respect to the symmetry set of the atomic system.

12. The computer-implemented method according to claim 10, wherein: The learned auxiliary states are provided as input to the machine learning model; as well as Based on the embedded atomic descriptors and the learned auxiliary states, the machine learning model is executed to learn the local energy of the atomic system.

13. The computer-implemented method according to claim 10, wherein, The set of discretized auxiliary states is one or more of the following: Charge state; Oxidized state; or Magnetic state.

14. The computer-implemented method according to claim 10, wherein: The request also includes an indication of the type of the set of discretized auxiliary states to be learned; and The method also includes determining the dimension of the restricted dimensional potential space to be applied, at least in part, based on the complexity of the atomic system or the type of the auxiliary state.

15. The computer-implemented method according to claim 14, further comprising: Based on the request, it is determined that the charge neutrality of the atomic system is enforced during the mapping of the embedded atomic descriptors through the restricted dimensional potential space of the autoencoder; as well as Provide the required charge neutrality indication to the automatic encoder.

16. The computer-implemented method according to claim 14, further comprising: Based on the request, it is determined that the charge neutrality of the atomic system is not enforced during the mapping of the embedded atomic descriptors through the restricted-dimensional potential space of the autoencoder; as well as The automatic encoder is provided with an indication that does not restrict charge neutrality.

17. A non-transitory computer-readable medium storing program instructions that, when executed on or across one or more processors, cause the one or more processors to: Receive data indicating an atomic description of an atomic system, wherein the atomic description includes the atomic position and atom type of the corresponding atom in the atomic system; The data indicating the atom position and the atom type is embedded into the atom descriptor; The embedded atomic descriptors are mapped through the restricted-dimensional latent space of the autoencoder to learn the discretized auxiliary state set of the atomic system; Auxiliary Hamiltonian descriptions are generated based on the learned auxiliary states; Execute a machine learning model to learn the local scalar vector or tensor properties of the atomic system based on the embedded atomic descriptors; as well as The total properties of the atomic system are output based on the auxiliary Hamiltonian description and the learned local scalar vector or tensor properties.

18. The non-transitory computer-readable medium of claim 17, wherein the program instructions further cause the one or more processors to: The learned auxiliary states are provided as input to the machine learning model; and Based on the embedded atomic descriptors and the learned auxiliary states, the machine learning model is executed to learn the local scalar vector or tensor properties of the atomic system.

19. The non-transitory computer-readable medium according to claim 17, wherein, The set of discretized auxiliary states is one or more of the following: Charge state; Oxidized state; or Magnetic state.

20. The non-transitory computer-readable medium of claim 17, wherein: The local scalar vector or tensor property is local energy, and the total property is total energy; or The local scalar vector or tensor property is a related force, and the total property is a total force.

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