Discovering novel meta-stable materials using neural networks

Abstract

Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for meta-stable material discovery. In one aspect, a method comprises: obtaining data defining macroscopic properties for an initial material; generating a set of precursor materials, comprising: generating a simulated sample of the initial material through computational simulation; and identifying precursor materials within the simulated sample based on microscopic properties of regions within the simulated sample; for each precursor material: generating a simulated sample of an optimized precursor material through a computational simulation altering the microscopic properties of the precursor material to optimize a macroscopic property of the precursor material; and determining one or more quantities characterizing the simulated sample of the optimized precursor material.

Description

DISCOVERING NOVEL META-STABLE MATERIALS USING NEURALNETWORKSCROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. Provisional Application No. 63 / 541,264, filed on September 28, 2023. The disclosure of the prior application is considered part of and is incorporated by reference in the disclosure of this application.BACKGROUND

[0002] This specification relates to processing data using machine learning models.

[0003] Machine learning models receive an input and generate an output, e.g., a predicted output, based on the received input. Some machine learning models are parametric models and generate the output based on the received input and on values of the parameters of the model.

[0004] Some machine learning models are deep models that employ multiple layers of models to generate an output for a received input. For example, a deep neural network is a deep machine learning model that includes an output layer and one or more hidden layers that each apply a non-linear transformation to a received input to generate an output.SUMMARY

[0005] This specification generally describes a system implemented as computer programs on one or more computers in one or more locations that can discover novel meta-stable materials using neural networks.

[0006] According to one aspect, there is provided a method comprising: obtaining data defining macroscopic properties for an initial material; generating a set of precursor materials, comprising: generating a simulated sample of the initial material through computational simulation; and identifying precursor materials within the simulated sample based on microscopic properties of regions within the simulated sample; for each precursor material: generating a simulated sample of an optimized precursor material through a computational simulation altering the microscopic properties of the precursor material to optimize a macroscopic property of the precursor material; and determining one or more quantities characterizing the simulated sample of the optimized precursor material.

[0007] For example, the initial material can be an amorphous material, specified by a set of macroscopic properties (e.g., temperature, pressure, polarization, magnetization, etc.) that includes a chemical stoichiometry defining the respective fraction of multiple chemical elements within the initial material. The simulated sample can be obtained by a computational simulation of quenching the initial material from a suitable high temperature to a suitable lowertemperature at constant volume and pressure. The precursor materials can be collections of simulated atoms found within the simulated sample to have certain desired microscopic properties (e.g., the chemical elements and the configurations of particular atoms) for a metastable crystal. The optimized precursor materials can be determined by altering microscopic properties, such as the positions of atoms within the precursor material, so as to locally minimize the energy of a crystal of the precursor material. The returned candidate materials can be meta-stable crystals, identified as low energy crystals identified amongst the optimized precursor materials.

[0008] Particular embodiments of the subject matter described in this specification can be implemented so as to realize one or more of the following advantages.

[0009] The development of modem technologies requires the discovery of new materials, e.g., new photovoltaic materials for solar cells, new semiconductor materials for microchips, and new superconductor materials for fusion energy production. Significant effort has gone into exploring the combinatorial space of materials, including enumerating atomic compositions and producing catalogs of their properties. However, the rate of materials discovery has been bottlenecked by the pace of physical experiments and high-fidelity computational simulations.

[0010] Computational material discovery generally requires performing resource intensive optimizations and searches over material configurations to identify candidate materials (e.g., physically plausible candidate materials). Conventional methods for computational material discovery often identify candidate materials by simulating and optimizing large numbers of initial material configurations to identify physically plausible candidate materials (e.g., candidate materials that represent optima of material strains, potential energies, etc.). To simulate and optimize candidate materials, conventional methods can perform high-fidelity computational simulations (e.g., ab-initio simulations based on density functional theory) that directly simulate quantum mechanical processes within the candidate materials. Performing high-fidelity computational simulations can be computationally intensive (e.g., consuming significant quantities of computational resources such as memory' and computing power) and generating simulations of large numbers of candidate materials using high-fidelity computational simulations can be computationally infeasible. Conventional methods for computational material discovery can have particular difficulty discovering and determining the properties of meta-stable materials (e.g., materials whose molecular structure is a local optimum of potential energy), as local energy optima can be missed when optimizing molecular structures to identify potential energy minima.

[0011] The system described in this specification can efficiently identify candidate meta-stable materials by simulating a phase transition of an initial material. As the initial material undergoes the phase transition (e.g., at the start of the phase transition), multiple structures (e.g., phases of the initial material) can form within the initial material. The structures that form within the initial material during the phase transition can include various meta-stable materials. The system described in this specification can identify novel meta-stable materials by searching and testing the structures that form during the simulated phase transition of the initial material. The system can validate properties of the identified candidate meta-stable materials using high-fidelity computational simulations (e.g., ab-initio simulations based on density functional theory) and physical experiments of synthesizations of the identified candidate meta-stable materials. As part of identifying the candidate meta-stable materials, the described systems can perform simulations of materials using a graph neural network configured to predict atomic forces and energies to simulate and optimize simulated materials.

[0012] In comparison to conventional methods for computational material discovery' that optimize randomized initial materials (e.g., random initializations, random alterations of known stable materials, etc.) to identify possible material configurations, the described systems can circumvent much of the computationally costly search over material configurations by identify ing the candidate meta-stable materials as products of simulated phase transitions of initial materials. Additionally, the described systems can use graph neural networks to more efficiently (e.g., using fewer computational resources) predict forces and energies for simulated materials with a single pass through a sequence of neural network layers, as compared to high- fidelity computational simulations as used by conventional methods. By using machine learned force fields specified by graph neural networks, the described system can simulate a phase transition for a larger sample of the initial material and can optimize structures for more candidate meta-stable materials than would be possible using high-fidelity computational simulations. Therefore, the described systems can require significantly fewer computational resources (e.g., computational time, memory' usage, etc.) to identify' and predict properties for meta-stable materials compared to conventional methods for computational material discovery.

[0013] The resulting properties of the metastable materials can be compared to desired properties of a product or product component, and one or more of the metastable material selected for incorporation into the product based on the comparison, e.g., if the properties of the metastable material satisfy one or more threshold conditions. One or more of the selected metastable materials can be synthesized and incorporated into the product / product component. The use of the methods described herein can thus allow products containing metastablematerials to be prototyped and developed more efficiently when compared to conventional methods for computational material discovery.

[0014] The details of one or more embodiments of the subject matter of this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0015] FIG. 1 A is a block diagram of an example meta-stable material discovery system.

[0016] FIG. IB illustrates simulating a phase transition of an initial material.

[0017] FIG. 1C illustrates identifying precursor materials within a simulated sample of an initial material.

[0018] FIG. ID is a flow diagram of an example process of generating candidate materials by simulating a phase transition of an initial material.

[0019] FIG. 2 is a flow diagram of an example process for simulating a phase transition of an initial material using a molecular dynamics simulation.

[0020] FIG. 3 is a flow diagram for an example process for identifying precursor materials by searching regions of a simulated sample of an initial material.

[0021] FIG. 4A is a flow diagram for an example process for optimizing structures of precursor materials.

[0022] FIG. 4B illustrates optimizing a structure of an example precursor material.

[0023] FIG. 5A illustrates generating an input graph for a graph neural network configured to predict forces for atoms of simulated materials.

[0024] FIG. 5B is a flow chart for an example process for predicting force vectors for atoms within the simulated materials using a graph neural network.

[0025] FIG. 5C is a flow chart for an example process for training a graph neural network to predict properties of simulated materials.

[0026] FIG. 6 is a flow chart for an example process for identifying candidate materials within a set of optimized precursor materials.

[0027] FIG. 7A illustrates example meta-stable materials identified and validated using an implementation of a meta-stable material discovery system.

[0028] FIG. 7B illustrates formation energies for an example formation pathway for meta- stable materials identified using an implementation of a meta-stable material discovery system.

[0029] FIG. 7C illustrates chemical structures from an example formation pathway for meta- silable materials identified using an implementation of a meta-stable material discovery system.

[0030] Like reference numbers and designations in the various drawings indicate like elements.DETAILED DESCRIPTION

[0031] FIG. 1 A shows an example meta-stable matenal discovery system 100. The meta-stable material discovery system 100 is an example of a system implemented as computer programs on one or more computers in one or more locations in which the systems, components, and techniques described below are implemented.

[0032] The meta-stable material discovery system 100 can receive material property data 104 specifying an initial material and generate one or more novel candidate materials 102 by simulating a phase transition of the initial material. As the initial material undergoes the phase transition (e.g., at the start of the phase transition), multiple structures (e.g., phases of the initial material) can form within the initial material. The meta-stable material discovery system 100 can identify the novel candidate materials 102 by searching and testing structures that form during the simulated phase transition of the initial material.

[0033] For example, for an example application of identifying meta-stable cry stals, the initial material can be an amorphous material and the meta-stable discovery system 100 can simulate a crystallization of the initial material. During the crystallization of the initial material, multiple different structures can crystalize within the initial material, including meta-stable structures (e.g., meta-stable crystals). The meta-stable material discovery' system 100 can identify candidate meta-stable crystals by searching and testing structures that form during the crystallization of the initial material.

[0034] For illustrative purposes, the example application of identifying meta-stable crystals by simulating a crystallization of an amorphous initial material will be referenced throughout this specification. However, the meta-stable material discovery system 100 can identify novel candidate materials 102 by simulating any appropriate phase transition of any appropriate initial material. The initial material can therefore be, e.g., a crystalline material, a poly cry stalline material, an amorphous material, an inorganic material, an organic material, a hybrid material including organic and inorganic components, an alloy, and so on. The simulated phase transition of the initial material can be. e.g., a freezing of the initial material, a melting of the initial material, a sublimation of the initial material, a deposition of the initial material, a crystallization of the initial material, a decrystallization of the initial material, anelectromagnetic phase transition of the initial material, and so on. The candidate materials 102 can include any materials that form as a product of the simulated phase transition of the initial material, e.g., crystalline materials, polycrystalline materials, amorphous materials, inorganic materials, organic materials, hybrid materials including organic and inorganic components, alloys, and so on.

[0035] The meta-stable material discovery’ system 100 includes a molecular dynamics system 106, a precursor search system 108, a structure optimization system 110, and a validation system 112, which are each described next (and throughout this specification).

[0036] The molecular dynamics system 106 can receive the material property data 102 defining the initial material. The molecular dynamics system 106 can process the material property' data 102 generate a simulated sample of the initial material 114 as specified by the material property data 102 by performing a computational simulation of the initial material. In particular, the molecular dynamics system 106 can generate the simulated sample of the initial material 114 by performing a molecular dynamics simulation of a phase transition of the initial material.

[0037] The material property data 102 can define macroscopic properties for the initial material, e.g., a chemical composition of the initial material, a physical arrangement of the initial material, a polarization of the initial material, a magnetization of the initial material, and so on. For example, the material property’ data 102 can include a chemical stoichiometry’ for the initial material defining the respective fraction of multiple chemical elements within the initial material.

[0038] The material property data 102 can also specify properties of the phase transition for the initial material. For example, the material property’ data 102 can specify, e.g., initial and final temperatures, pressures, volumes, electric fields, magnetic fields, and so on for the phase transition of the initial material. Different candidate materials 104 can require different physical conditions to form. By simulating phase transitions with different physical properties as specified by the material property data, the molecular dynamics system 106 can simulate formation processes for candidate materials 104 within the initial material under different physical conditions.

[0039] For example, to simulate a crystallization of an amorphous initial material, the material property data 102 can specify simulating a phase transition from a suitable high initial temperature to a suitable lower temperature at constant volume and pressure. The molecular dynamics system 106 can simulate a quenching of the amorphous initial material as specified by the material property data 102 to generate the simulated sample of the amorphous initial material 114. By simulating the crystallization of the amorphous initial material under differentconditions (e g., different temperatures and pressures), the molecular dynamics system 106 can simulate the formation of crystals within the amorphous initial material 114 that require particular physical conditions to form.

[0040] As part of performing the molecular dynamics simulation of the phase transition of the initial material, the molecular dynamics system 106 can determine forces between atoms of the simulated sample of the initial material 114 using machine learned force fields 116 stored by the system 100 for the molecular dynamics simulation. The machine learned force fields 116 can be specified by any appropriate machine learning model for predicting inter-atomic forces or energies. For example, the machine learned force fields 116 can be specified by a graph neural network configured to predict forces for configurations of atoms by processing input graphs representing the configurations of atoms, as described by Batzner et al. in '’E(3)- Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials”.

[0041] The process of generating the simulated sample of the initial material 114 by simulating a phase transition using the molecular dynamics system 106 is described in more detail below with reference to FIG. IB and FIG. 2.

[0042] The precursor search system 108 can identify precursor structures of precursor materials within the simulated sample of the initial material 114. The precursor structures can be groups of atoms within the simulated sample of the initial material 114 that represent particular products of the phase transformation of the initial material. The identified precursor structures can include precursor structures of the candidate materials 102. The precursor search system 108 can output data specifying precursor materials 1 18 defined by the identified precursor structures. For example, the precursor materials 118 can be materials with physical structures and chemical compositions defined the physical structures and chemical compositions of the identified precursor structures.

[0043] In particular, the precursor search system 108 can search sub-cells (e.g., regions) of the simulated sample of the initial material 114 and can identify the precursor structures as being sub-cells of the simulated sample of the initial material 114 that satisfy' certain search criteria for precursor materials. The search criteria can include criteria for microscopic properties of the sub-cells of the simulated sample of the initial material 114. such as criteria regarding a physical arrangement of atoms within the sub-cells, chemical composition of the sub-cells, a polarization of the sub-cell, a magnetization of the sub-cell, and so on. The precursor materials 118 can be defined as periodic replications of the sub-cells of the precursor structures identified by the precursor search system.

[0044] For example, the precursor search system 108 can identify precursor crystal structures for crystal materials forming within a simulated sample of an amorphous material undergoing crystallization. The precursor search system 108 can identify the precursor crystal structures based on search criteria that include criteria regarding, e.g., the chemical composition of the precursor crystal structures. The precursor search system 108 can then output specifying precursor materials 118 defined as periodic replications of the identified precursor crystal structures (e.g., using the identified precursor crystal structures as unit cells of the precursor materials 1 18).

[0045] The process of identifying precursor materials 118 within the simulated sample of the initial material 114 using the precursor search system 108 is described in more detail below with reference to FIG. 1C and FIG. 3.

[0046] For each of the identified precursor materials 118, the structure optimization system 110 can generate a simulated sample of an optimized precursor material 120. In particular, the structure optimization system 110 can perform computational simulations altering microscopic properties of the precursor materials to optimize a macroscopic property of the precursor materials 1 18. For example, the structure optimization system 110 can generate the optimized precursor materials 120 by altering properties of the sub-cells of the identified precursor structures such as, e.g., arrangements of atoms within the sub-cells, geometries of the sub-cells, and so on, to optimize properties such as. e.g., energies of the optimized precursor materials 120, strains of the optimized precursor materials 120, and so on.

[0047] As an example, the structure optimization system 1 10 can generate optimized crystal materials by optimizing properties of the identified precursor cr stal structures as unit-cells for the optimized crystal materials. For example, the structure optimization system 110 can alter the arrangement of atoms within the precursor cry stal structures and the geometries of the precursor crystal structures as unit-cells for the optimized crystal materials to optimize (e.g., to minimize) energies of the optimized crystal materials.

[0048] As part of optimizing properties of the optimized precursor materials 120, the structure optimization system 110 can determine energies and forces between atoms for the simulated samples of optimized precursor materials 120 using the machine learned force fields 1 16 stored by the system 100 for the precursor structure optimization. In particular, to determine energies and forces between atoms for the simulated samples of optimized precursor materials 120, the structure optimization system 110 can use the same machine learning model (e.g., the same graph neural network) as the molecular dynamics system 106 used to perform the molecular dynamics simulation of the phase transition of the initial material.

[0049] The process of optimizing structures of precursor materials 118 using the structure optimization system 110 is described in more detail below with reference to FIG. 1C, FIG. 4A., and FIG. 4B.

[0050] The validation system 112 can determine one or more predicted material properties (e.g., quantities) characterizing the simulated samples of the optimized precursor materials 120. The validation system 112 can use the predicted material properties to validate the optimized precursor materials 120. In particular, the validation system 112 can use the predicted material properties to select optimized precursor materials 120 to output as candidate materials 102.

[0051] The validation system 112 can validate the optimized precursor materials 120 by any of a variety of methods. As an example, the validation system 112 can validate and predict material properties for the optimized precursor materials 120 by performing simulations of samples of the optimized precursor materials 120 using machine learned force fields 1 16 stored by the system 100 for material validation. In particular, to validate and predict material properties for the optimized precursor materials 120, the validation system 112 can use the same machine learning model (e.g., the same graph neural network) as the molecular dynamics system 106, the structure optimization system 110, or both. As another example, the validation system 112 can validate the optimized precursor materials by performing ab-initio simulations (e.g., following density7functional theory7) to predict material properties of the optimized precursor materials 120. As another example, the validation system 112 can request and receive results for experimental validations of the predicted material properties by. e.g., providing data characterizing the optimized precursor materials for synthesis and obtaining results from physical tests of the synthesized optimized precursor materials.

[0052] Ab-initio simulation and physical experimental validation of the candidate materials are generally resource-intensive compared to predicting material properties using the machine learned force fields 116. For example, an ab-initio simulation of a material can accurately predict material properties of the material by performing a computationally intensive direct simulation of the material as a quantum mechanical many-body system. Rather than performing a simulation of materials using operations that directly model physical interactions for the material (e.g., as performed within ab-initio simulations), the machine learned force fields 116 can be used to predict material properties following machine learned operations. The machine learned force fields 116 can be used generate predicted material properties for the optimized precursor materials that approximate corresponding predictions from ab-initio simulation of the optimized precursor materials while incurring a smaller computational cost compared to ab-initio simulations (e.g., by requiring fewer computational iterations, byenabling more parallelized computations, etc.). Additionally, the predicting material properties using the machine learned force fields 116 can be automated, which avoids the significant time, expertise, laboratory resources, etc., required to perform physical experimental tests of the optimized precursor materials.

[0053] The validation system 112 can therefore use the predicted material properties generated using the machine learned force fields 116 to initially validate and select the candidate materials 102 from among the optimized precursor materials 120. In some implementations, the validation system 112 can further validate and predict material properties for the candidate materials 102 using ab-initio simulation, physical experimentation, or both.

[0054] When the validation system 112 predicts materials for an optimized precursor material 120, the validation system 112 can store data specifying the optimized precursor material 120 and predicted material properties of the optimized precursor material 120 to a materials database 122 for the system 100. In general, the validation system can update the materials database 112 to include any optimized precursor material 120 generated by the system 100.

[0055] The validation system 112 can select optimized precursor materials 120 for inclusion within the candidate materials 102 using a variety of selection criteria for the candidate materials 102. As an example, the validation system 112 can determine whether to identify each optimized precursor material 120 as a candidate material 102 based on the predicted material properties of the optimized precursor material 120. As another example, the validation system 1 12 can determine whether to identify an optimized precursor material 120 as a candidate material 102 based whether the optimized precursor material 120 is already stored within the materials database 122 as a previously known material.

[0056] In some implementations, the validation system 112 can select one or more candidate materials 102 for physical synthesis by screening the candidate materials 102 based on the predicted material properties for the candidate materials 102. In particular, for each of the candidate materials 102, the validation system 112 can evaluate screening criteria for the candidate material based on the predicted material properties of the candidate material and can generate output data characterizing a decision to physically synthesize the candidate material based on the evaluated screening criteria for the candidate materials 102. In particular, the screening criteria can specify desired material properties for the candidate materials 102. The output data characterizing the decision to physically synthesize the candidate material can include data characterizing a request to physically synthesize the candidate material. Ingeneral, the validation system 112 can generate output data requesting physical synthesis of candidate materials 102 that satisfy the screening criteria.

[0057] After the validation system 112 selects one or more of the candidate materials 102 for physical synthesis, the validation system 112 can request physical synthesis of the selected candidate materials (e.g., by transmitting the request to a laboratory', a fabrication plant, etc.). The selected candidate materials can be physically synthesized for any of a variety of tasks. For example, the selected candidate materials can be physically synthesized perform a manufacturing process involving the selected candidate materials. As another example, the selected can be physically synthesized to perform experimental testing and validation of the predicted material properties of the selected candidate materials. When a candidate material is physically synthesized, the validation system 112 can receive data characterizing experimental results for the synthesized candidate materials and can update the materials database 122 using the experimental results (e.g., update the materials database 122 to include experimentally validated material properties of the candidate materials).

[0058] The candidate materials 102 identified by the system 100 can be synthesized and used for in any of a variety of applications. For example, the candidate materials 102 can be used as solid-state battery electrodes or electrolytes, electronic components, magnetic components, protective coatings, and so on.

[0059] The overall process of generating novel candidate materials 102 by simulating a phase transition of an initial material using the meta-material discovery system 100 is described in more detail below with reference to FIG. IB, 1 C, and I D.

[0060] By simulating the formation of meta-stable materials as products of phase transitions of initial materials, the meta-stable material discovery' system 100 can efficiently discover novel meta-stable materials. Additionally, the candidate materials 102 generated by the meta- stable material discovery system 100 can be used to determine properties of formation pathways of meta-stable materials within phase transitions of various materials. Example meta-stable materials identified and validated using an implementation of the meta-stable material discovery system 100 are illustrated in FIG. 7A. FIG. 7B and FIG. 7C illustrate an example formation pathway for meta-stable materials identified using the meta-stable material discovery' system 100.

[0061] By efficiently discovering and validating new meta-stable materials, the meta-stable material discovery system 100 can improve materials design for new devices. For example, the system 100 can be used to discover new semi-conductor materials that improve, e.g.. power efficiency, die size, and so on. As another example, the system 100 can be used todiscover new materials for use in batteries that improve, e.g., storage capacity, energy density, and so on.

[0062] FIG. IB illustrates simulating a phase transition of an initial material using a molecular dynamics system (e.g., the molecular dynamics system 106 of the meta-stable material discovery system 100 of FIG. 1). In particular, FIG. IB illustrates simulating cry stallization of an amorphous initial material.

[0063] The system can initialize a simulated sample of the initial material based on received material property data. The system can determine positions, velocities, and chemical elements for the initial material to the simulated sample as specified by the received material property7data. As an example, the system can determine the locations of atoms within the simulated sample based on a physical structure specified by the received material data (e.g., when the material property data specifies a crystal structure for the initial material). As another example, the system can generate a random initialization 130 for the atoms simulated sample (e.g., when the initial material is an amorphous material), as illustrated by FIG. IB. The system can generate the random initialization 130 for the simulated sample by randomly sampling positions and velocities for the atoms of the simulated sample. When the system samples random velocities for atoms of the simulated sample, the system can sample the velocities from a velocity distribution that initializes the simulated sample to have, e.g., a particular temperature, pressure, and so on.|0064| In some implementations, the system can perform a relaxation 132 of the simulated sample to generate a relaxed initialization 134 for the simulated sample. In some cases, a random initialization 130 for the simulated sample can include unphysical positions for atoms (e.g., randomly sampling positions for the atoms can result in atoms being placed too closely together). By performing the relaxation 132 of the simulated sample, the system can more quickly equilibrate the simulated sample and more accurately simulate the phase transition of the initial material. The system can perform the relaxation 132 of the simulated sample by performing a gradient descent of the atoms’ positions to minimize a potential energy' of the simulated sample. For example, the system can perform the gradient descent to minimize a potential energy of the simulated sample determined using a soft-sphere potential for each atom of the simulated sample.

[0065] The system can generate the simulated sample of the initial material 136 by performing a molecular dynamics simulation of the phase transition of the initial material. The material property data can specify properties of the phase transition for the initial material and the system can simulate the phase transition following the properties specified by the materialproperty data. For example, the material property' data can specify, e.g., initial and final temperatures, pressures, volumes, electric fields, magnetic fields, and so on for the phase transition of the initial material. As an example, as illustrated by FIG. IB, the system can simulate the crystallization of the amorphous initial material by simulating the phase transition from a suitable high initial temperature to a suitable lower temperature at constant volume and pressure. As described above with reference to FIG. 1 A, the system can perform the molecular dynamics simulation of the phase transition of the initial material by determining forces between atoms of the simulated sample of the initial material 136 using machine learned force fields specified by a machine learning model (e.g., a graph neural network) configured to predict inter-atomic forces or energies.

[0066] An example process for performing a molecular dynamics simulation to simulate a phase transition of the initial material is described in more detail below with reference to FIG. 2.

[0067] As described below, after simulating the phase transition of the initial material, the system can search the simulated sample of the initial material 136 to identify precursor structures of candidate meta-stable materials.

[0068] FIG. 1C illustrates identifying precursor materials within a simulated sample of an initial material.

[0069] As described above with reference to FIG. 1A, the system can identify precursor structures of precursor materials within the simulated sample of the initial material 136. In particular, the system can search sub-cells (e.g., regions) of the simulated sample of the initial material 136 and can identify' the precursor structures as being sub-cells of the simulated sample of the initial material 114 that satisfy certain search criteria for precursor materials, e.g., as criteria regarding a physical arrangement of atoms within the sub-cells, chemical composition of the sub-cells, a polarization of the sub-cell, a magnetization of the sub-cell, and so on. For example, as illustrated in FIG. 1C the system can identify precursor crystal structures 138-A, 138-B, and 138-C for cry stal materials forming within the simulated sample of the amorphous material 136 undergoing cry’ stall izati on.

[0070] An example process for identifying precursor structures within simulated samples of the initial material is described in more detail below' with reference to FIG. 3.

[0071] The system can then generate optimized precursor materials by altering properties of the sub-cells of the identified precursor structures such as, e.g., arrangements of atoms within the sub-cells, geometries of the sub-cells, and so on, to optimize, e.g., energies of the optimized precursor materials. For example, the structure optimization system can generate optimizedcrystal structures 140- A. 140-B, and 140-C that are unit cells for optimized crystal materials by altering the arrangement of atoms within the precursor crystal structures 138-A, 138-B, and 138-C and the geometries of the precursor crystal structures 138-A, 138-B, and 138-C to optimize (e.g., to minimize) energies of the optimized cry stal materials.

[0072] As described above with reference to FIG. 1A, the system can optimize the properties of the optimized precursor materials by determining energies and forces between atoms of simulated samples of the optimized precursor materials using machine learned force fields specified by a machine learning model (e g., a graph neural network) configured to predict inter-atomic forces or energies. In particular, the system can use the same machine learning model (e.g., the same graph neural network) to optimize the structures of the precursor materials as the system used to perform the molecular dynamics simulation of the phase transition of the initial material.

[0073] An example process for optimizing structures of precursor materials is described in more detail below with reference to FIG. 4A and FIG. 4B.

[0074] FIG. ID is a flow diagram of an example process of generating candidate materials by simulating a phase transition of an initial material. For convenience, the process 150 will be described as being performed by a system of one or more computers located in one or more locations. For example, a meta-material discovery system, e.g., the meta-material discovery7system 100 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 150.

[0075] The system can obtain material property7data specifying an initial material (step 152). The material property7data can define macroscopic properties for the initial material, e.g., a chemical composition of the initial material, a physical arrangement of the initial material, a polarization of the initial material, a magnetization of the initial material, and so on. For example, the material property data can include a chemical stoichiometry for the initial material defining the respective fraction of multiple chemical elements within the initial material.

[0076] The system can receive the material property data by a variety of methods. For example, the system can receive the material property data from a user of the system. As another example, the material property data can receive the material property data as transmitted by an application programming interface (API) of the system.

[0077] The initial material can be any of a variety7of materials, e.g., a cry stalline material, a poly cr stall ine material, an amorphous material, an inorganic material, an organic material, a hybrid material including organic and inorganic components, an alloy7, and so on.

[0078] The system can generate a simulated sample of the initial material by simulating a phase transition of the initial material (step 154). In particular, the system can simulate the phase transition of the initial material by performing a molecular dynamics simulation of the initial material. The simulated phase transition of the initial material can be any of a variety of phase transitions, e.g., a freezing of the initial material, a melting of the initial material, a sublimation of the initial material, a deposition of the initial material, a crystallization of the initial material, a decrystallization of the initial material, an electromagnetic phase transition of the initial material, and so on. An example process for generating a simulated sample of the initial material by simulating a phase transition of the initial material is described in more detail below with reference to FIG. 2.

[0079] The system can identify precursor materials based on regions of the simulated sample of the initial material (step 156). In particular, the system can identify the precursor materials based on microscopic properties of regions within the simulated sample. For example, the system can search sub-cells of the simulated sample of the initial material and can identify the precursor materials as being defined by sub-cells that satisfy certain search criteria for precursor materials. The search cnteria can include critena for microscopic properties of the sub-cells, such as criteria regarding a physical arrangement of atoms within the sub-cells, chemical composition of the sub-cells, a polarization of the sub-cell, a magnetization of the sub-cell, and so on. The precursor materials can be defined by the sub-cells as being periodic replications of the sub-cells that satisfy the search criteria for precursor materials. An example process for identify ing the precursor materials is described in more detail below with reference to FIG. 3.

[0080] The system can then optimize structures of the identified precursor materials (step 158). In particular, the system can generate a simulated sample of each optimized precursor material by altering microscopic properties of the corresponding precursor material to optimize a macroscopic property. For example, the system can generate the optimized precursor materials by altering properties of the sub-cells of the identified precursor structures such as, e.g., arrangements of atoms within the sub-cells, geometries of the sub-cells, and so on, to optimize properties of the optimized precursor materials, e.g.. energies of the optimized precursor materials, strains of the optimized precursor materials, and so on. An example process for optimizing the structures of the identified precursor materials is described in more detail below with reference to FIG. 4A and FIG. 4B.

[0081] The system can screen the optimized precursor materials to identify candidate materials (step 160). As part of screening the optimized precursor materials, the system can determineone or more quantities characterizing simulated samples of each of the optimized precursor materials. The system can determine whether to identify each optimized precursor material as a candidate material based on the one or more quantities determined for the simulated sample of the optimized precursor material. For example, the system can determine predicted physical properties (e.g., predicted physical structures, predicted energies, etc.) of the optimized precursor materials and can screen the optimized precursor materials to identify the candidate materials based on the predicted material properties. An example process for screening the optimized precursor materials to identify the candidate materials is described in more detail below with reference to FIG. 5.

[0082] The system can finally output the identified candidate materials (step 162)

[0083] FIG. 2 is a flow diagram of an example process for generating a simulated sample of an initial material by simulating a phase transition of the initial material. For convenience, the process 200 will be described as being performed by a system of one or more computers located in one or more locations. For example, ameta-stable material discovery system, e.g., the metastable material discovery system 100 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 200.

[0084] The system can receive material property data specifying macroscopic properties of the initial material (step 202). The material property' data can define macroscopic properties for the initial material, e.g., a chemical composition of the initial material, a physical arrangement of the initial material, a polarization of the initial material, a magnetization of the initial material, and so on. As an example, the material property data for the initial material can define a chemical stoichiometry for the initial material.

[0085] The material property' data can specify properties of the phase transition for the initial material. For example, the material property data can specify, e.g., initial and final temperatures, pressures, volumes, electric fields, magnetic fields, and so on for the phase transition of the initial material.

[0086] The system can initialize a simulated sample of the initial material (step 204). For example, the system can initialize the simulated sample by defining a respective spatial position, spatial velocity, and chemical element of each of a plurality of simulated atoms within the simulated sample. The system can process the material property data for the initial material to initialize the simulated sample as specified by the material property7data. For example, the system can determine a chemical element for each atom of the sample in accordance with the chemical stoichiometry defined for the initial material by the material property data.

[0087] In some implementations, the system can determine the positions of atoms within the simulated sample by randomly assigning a position for each atom within the simulated sample. Similarly, the system can determine the velocities of atoms within the simulated sample by randomly assigning a velocity for each atom within the simulated sample (e.g., as sampled from a distribution of velocities for an initial temperature and pressure of the simulated sample).

[0088] In some implementations, the system can perform a relaxation of the simulated sample of the initial material (step 206). The system can perform the relaxation of the simulated sample by optimizing a relaxation potential energy that depends on the positions of the atoms within the simulated sample. For example, at each of a sequence of relaxation update steps, the system can compute the relaxation potential energy for the simulated sample and update the position of each atom within the sample by performing gradient descent of the computed relaxation potential energy. The relaxation potential energy can be determined by any appropriate interatomic potential, e.g., a soft shell potential, a Lennard-Jones potential, a Morse potential, and so on.

[0089] In some implementations, the system can perform an initial equilibration of the simulated sample of the initial material (step 208). The system can perform the initial equilibration of the simulated sample by performing a molecular dynamics simulation of the simulated sample in accordance with a set of starting equilibrium properties (e.g., an initial equilibration temperature, pressure, volume, electric field, magnetic field, and so on). The set of starting equilibrium properties can be specified by the received material property data for the initial material. For example, the starting equilibrium properties can include an initial equilibration temperature and the system can perform the molecular dynamics simulation in accordance with a thermostat (e.g., a Nose-Hoover thermostat) fixed at the initial equilibration temperature.

[0090] An example process for performing the molecular dynamics simulation is described in more detail below with reference to steps 210 through 214.

[0091] The system can perform the molecular dynamics simulation for the initial equilibration using machine learned force fields determined by a machine learning model (e.g.. a neural network, such as a graph neural network). The system can use the same machine learning model for the molecular dynamics simulation of the initial equilibration as the system uses for the molecular dynamics simulation of the phase transition of the initial material (e.g., the same machine learning model as described below in step 210).

[0092] The system can simulate the phase transition of the initial material by performing a molecular dynamics simulation over a sequence of molecular dynamics steps. At each molecular dynamics step, the system can perform steps 210 through 214.

[0093] At each molecular dynamics step, the system can update the positions and velocities of the atoms within the simulated sample following force fields computed for the atoms (step 210).

[0094] In particular, the system can generate a respective force vector (e.g., a three dimensional force vector that characterizes component forces along x-, y-, and z- directions) for each atom of the simulated material. The system can generate the force vectors for the atoms of the simulated material processing data characterizing the positions of the atoms using machine learned force fields determined by a machine learning model (e.g., a neural network, such as a graph neural network). An example graph neural network configured to predict forces for atoms of the simulated material is described in more detail below with reference to FIG. 5A, FIG. 5B, and FIG. 5C.

[0095] The system can update the spatial position of each atom in simulated sample based on the predicted force vector for the node representing the atom. For example, the system can update the positions of the atoms by performing a simulation of the atoms moving in response to the predicted forces for the atoms. As a further example, the system can update the positions of a 7 -th atom at the i-th molecular dynamics step, x]:ifollowing:

[0096] Whereis a velocity7of the y-th atom at the i-th molecular dynamics step (e.g., as tracked by the system during the molecular dynamics simulation), F^- is the predicted force on the y-th atom at the i-th molecular dynamics step, and Ax and Av are update rules for performing numerical integration of the atomic positions based on the predicted forces (e.g., Ax and Av can implement Euler integration. Verlet integration, etc., for the atomic positions).

[0097] At each molecular dynamics step, the system can update macroscopic properties of the simulated sample to simulate the phase transition (step 212). The system can update, e.g., a temperature, pressure, volume, applied electric field, applied magnetic field, and so on of the simulated sample to simulate the phase transition. In some implementations, the material property data for the initial material can specify macroscopic properties of the simulated sample for each molecular dynamics step for simulating the phase transition and the system can update the macroscopic properties of the simulated sample as specified by the material property data.

[0098] In some cases, the system can update the positions and velocities of the atoms of the simulated sample as part of updating the macroscopic properties of the simulated sample. For example, as part of updating a volume of the simulated sample, the system can update positions of the atoms of the simulated sample. As another example, as part of updating properties such as a temperature, pressure, or volume of the simulated sample, the system can update the velocities of the atoms of the simulated sample. In particular, the system can update the properties of the simulated sample to simulate a quenching of the initial material, e.g.. by updating the properties of the simulated sample in accordance with a thermostat transitioning from an initial quenching temperature to a final quenching temperature (e.g., as specified by the material property data).

[0099] At each step, the system can determine whether the molecular dynamics simulation is complete (step 214). For example, the system can determine that the molecular dynamics simulation is complete after a pre-determined number of molecular dynamics steps. If the system determines that the molecular dynamics simulation is not complete, the system can continue the molecular dynamics simulation (e.g., return to step 210). Otherwise, the system can terminate the molecular dynamics simulation (e.g., proceed to step 216).

[0100] In some implementations, the system can perform a final equilibration of the simulated sample of the initial material (step 216). The system can perform the final equilibration of the simulated sample by performing a molecular dynamics simulation of the simulated sample in accordance with a set of final equilibrium properties (e.g.. a final equilibration temperature, pressure, volume, electric field, magnetic field, and so on). The set of final equilibrium properties can be specified by the received material property data for the initial material. For example, the starting equilibrium properties can include a final equilibration temperature and the system can perform the molecular dynamics simulation in accordance with a thermostat (e.g., a Nose-Hoover thermostat) fixed at the final equilibration temperature.

[0101] An example process for performing the molecular dynamics simulation is described in more detail above with reference to steps 210 through 214.

[0102] The system can perform the molecular dynamics simulation for the final equilibration using machine learned force fields determined by a machine learning model (e.g.. a neural network, such as a graph neural network). The system can use the same machine learning model for the molecular dynamics simulation of the final equilibration as the system uses for the molecular dynamics simulation of the phase transition of the initial material (e.g., the same machine learning model as described above in step 210).

[0103] The system can finally output the simulated sample of the initial material (step 218).

[0104] FIG. 3 is a flow diagram for an example process for identifying precursor materials by searching regions of a simulated sample of an initial material. For convenience, the process 300 will be described as being performed by a system of one or more computers located in one or more locations. For example, a meta-stable material discovery system, e.g., the meta-stable material discovery system 100 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 300.

[0105] The system can divide the simulated sample of the initial material into a plurality of sub-cells (step 302). In particular, the plurality of sub-cells includes all sub-cells that can be generated by partitioning the simulated sample along a predetermined grid for the simulated sample.

[0106] The system can identify sub-cells that represent precursor materials based on certain precursor search criteria (step 304). The system can determine whether the sub-cell represents a precursor material based on whether the sub-cell satisfies the precursor search criteria. The precursor search criteria can include criteria regarding, e.g., the chemical elements of the atoms contained within the sub-cells, the physical arrangements of the atoms contained within the sub-cells, polarizations of the sub-cells, magnetizations of the sub-cells, and so on.

[0107] The system can output data specifying the identified precursor materials (step 306). In particular, for each sub-cell the system identifies as representing a precursor material, the system can output data specifying the precursor material as specified by a periodic replication of the sub-cell along one or more spatial dimensions.

[0108] FIG. 4A is a flow diagram for an example process for optimizing structures of precursor materials. For convenience, the process 400 will be described as being performed by a system of one or more computers located in one or more locations. For example, a meta-stable material discovery’ system, e.g.. the meta-stable material discovery system 100 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 400.

[0109] The system can receive data specifying the precursor material (step 402). For example, the data specifying the precursor material can specify the precursor material as a periodic replication of a sub-cell of atoms and can specify positions and chemical elements for each atom within the sub-cell for the precursor material.

[0110] The system can optimize the structure of the precursor material over a sequence of optimization steps. At each optimization step, the system can perform steps 404 and 406.

[0111] The system can update the structure of the precursor material to optimize a macroscopic property of the precursor material (step 404). The optimized macroscopic property can be anyof a variety of properties of the precursor material, e.g., an estimated potential energy of the precursor material, an estimated strain of the precursor material, and so on.

[0112] In some implementations, as part of updating the structure of the precursor material, the system can compute a gradient of the macroscopic property with respect to the position of each atom within the sub-cell representing the precursor material. The system can update the position of each atom within the sub-cell in accordance with the computed gradient. For example, the system can update the position of each atom within the sub-cell by performing gradient descent of the optimized macroscopic property using the computed gradient.

[0113] In some implementations, as part of updating the structure of the precursor material, the system can compute a gradient of the macroscopic property with respect to each of a set of parameters determining the size and shape of the sub-cell representing the precursor material. The system can update the parameters determining the size and shape of the sub-cell in accordance with the computed gradient. For example, the system can update the parameters determining the size and shape of the sub-cell by performing gradient descent of the optimized macroscopic property using the computed gradient.

[0114] The system can determine the gradients of the optimized macroscopic property using data characterizing the positions of the atoms within the sub cell using machine learned force fields determined by a machine learning model (e.g., a neural network, such as a graph neural network). An example graph neural network configured to predict forces and energies for atoms of the sub-cell is described in more detail below with reference to FIG. 5 A. FIG. 5B, and FIG. 5C. In particular, the system can determine the gradients of the optimize macroscopic property using the same machine learning model used to simulate the phase transition of the initial material (e.g., as described in step 210 of FIG. 2).

[0115] The system can determine whether the optimization is complete (step 406). The system can determine whether the optimization is complete by any of a variety of criteria. For example, the system can determine that the optimization is complete after a predetermined number of optimization steps. As another example, the system can determine that the optimization is complete if difference between values of the optimized macroscopic property computed at the current optimization step and a previous optimization step falls below a predetermined threshold.

[0116] If the system determines that the optimization is not complete, the system can continue a next optimization step (e.g., return to step 404). Otherwise, the system can terminate the optimization (e.g., proceed to step 408).

[0117] The system can finally output data specifying the optimized precursor material (408). For example, the data specifying the precursor material can specify the precursor material as a periodic replication of a sub-cell of atoms and can specify positions and chemical elements for each atom within the sub-cell for the precursor material.

[0118] FIG. 4B illustrates optimizing a structure of an example precursor material.

[0119] In particular, FIG. 4B illustrates optimizing the structure of a sub-cell of the example precursor material 410 (e.g.. as obtained using the process 300 of FIG. 3) identified within a simulated sample of an initial material 412 (e g., as generated using the process 200 of FIG. 2).

[0120] The system updates the structure of the sub-cell of precursor material 410 to optimize an energy 414 of the precursor material (e.g., an energy of the precursor material defined as a periodic replication of the sub-cell 410).

[0121] As the system optimizes the energy 414, the system updates the structure of the subcell of precursor material 410 from an initial structure 416 to a final, optimized structure 416. It should be noted that to generate the optimized structure 416, the system alters both the position of atoms within the sub-cell 410 and the geometry of the sub-cell 410.

[0122] FIG. 5A illustrates generating an input graph for a graph neural network configured to predict properties of a simulated material 502. In particular, the input graph can be a graph representation 504 of the simulated material 502.

[0123] The simulated material 502 is composed of and can include atoms of different elements. The simulated material 502 can be, e.g., a crystalline material, a poly crystalline material, an amorphous material, an inorganic material, an organic material, a hybrid material that includes both inorganic and organic components, and so on. For example, the simulated material 502 can include atoms 508-A through 508-E.

[0124] The simulated material 502 can be a periodic replication of a unit cell 509 for the simulated material 502, and configuration of the simulated material 502 can be determined by specifying configurations (e.g., positions, orientations, chemical elements, etc.) for atoms within the unit cell 509. For example, a configuration of the simulated material 502 can be determined by specifying positions, orientations, chemical elements, etc. for the atoms 508-A through 508-E within the unit cell 509.

[0125] The system can generate the graph representation 504 of the simulated material 502 that represents a particular configuration of the simulated material 502. The graph representation 504 can include respective graph nodes representing each atom of the simulated material 502. For example, as illustrated, the graph representation 504 includes graph nodes 510-A through 510-E that correspond to the atoms 508-A through 508-E.

[0126] Each graph node can include a node embedding. The node embeddings for the graph nodes 510- A through 510-E can be based on the chemical element of the corresponding atoms 508-A through 508-E. The node embeddings for the graph nodes 510-A through 510-E can include data characterizing positions and orientations of the corresponding atoms 508-A through 508-E within the simulated material 502. When the simulated material 502 is a defined as a periodic replication of a unit cell 509, the node embeddings for the graph nodes 510-A through 510-E can include data characterizing positions and orientations of the corresponding atoms 508-A through 508-E within the unit cell 509.

[0127] The graph representation 504 can include graph edges between pairs of the graph nodes 510-A through 510-E representing interactions between the atoms 508-A through 508-E. In some implementations, the graph representation 504 can include graph edges between a pair of graph nodes 510-A through 510-E only when the corresponding pair of atoms 508-A through 508-E are spatially separated by less than a threshold distance. The graph edges can include edge embeddings that characterize the relative positions of the pairs of atoms for the graph edge.

[0128] The system can process the graph representation 504 using an appropriately configured graph neural network (to predict properties (e.g., energies, atomic forces, etc.) of the candidate material 502.

[0129] The graph neural network can include one or more update layers and can process an input graph to the network by performing message passing between graph nodes over a sequence of update iterations. At each update iteration, the graph neural network can process the input graph using one of the update layers to determine updated values for the node embeddings of the nodes for the input graph.

[0130] The graph neural network can include decoder layers that can process graphs resulting from the message passing updates to generate the predicted material properties for the input graph, e.g., energy decoder layers that can generate predicted energies for the input graph, force decoder layers that can generate predicted forces for atoms represented by the input graph, and so on. In some implementations, the decoder layers can receive, as network inputs, combined node embeddings for the nodes of the graphs resulting from the message passing updates (e.g.. as generated by pooling, averaging, concatenating, etc., the node embeddings for the nodes). For example, the graph neural network can generate combined node embeddings based on the graphs resulting from the message passing updates and processing the combined node embeddings using the decoder layers to predict the associated material property of the candidate material.

[0131] Each decoder layer of the graph neural network can be any appropriate ty pe of neural network layer (e.g., fully connected layers, attentional layers, etc.).

[0132] An example process of predicting properties for a simulated material using the graph neural network is described in more detail below with reference to FIG. 5B.

[0133] The graph neural network can be trained to reproduce computationally or experimentally determined properties for a training set of example materials. In particular, the graph neural network can be trained on material property data obtained by ab-initio simulation for a training set of example materials. The architecture of the graph neural network can be chosen to encourage certain symmetries (e.g., rotational symmetry, translational symmetry, etc.) for the outputs of the graph neural network.

[0134] An example process of training the graph neural network to predict properties for simulated materials is described in more detail below with reference to FIG. 5C.

[0135] As a particular example, the graph neural network can be a Neural Equivariant Interatomic Potentials graph neural network as described by Batzner et al. in “E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials”.

[0136] FIG. 5B is a flow chart for an example process for predicting force vectors for atoms within the simulated materials using a graph neural netw ork. For convenience, the process 520 will be described as being performed by a system of one or more computers located in one or more locations. For example, a material discovery system, e.g., the meta-stable material discovery’ system 100 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 520.

[0137] As described above with reference to FIG. 5A, as part of predicting material properties for the simulated material using the graph neural network, the system can process the graph data for the simulated material by performing message passing over a sequence of update iterations.

[0138] To predict force vectors for atoms in the simulated material, the system can, at each update iteration, generating a combined edge embedding for each node in the graph (step 522). The system can generate the combined edge embedding for each node by combining (e.g., pooling, averaging, etc.) edge embeddings corresponding to each edge connected to the node.

[0139] The system can then generate normalized edge embeddings for each node in the graph based on the combined edge embeddings (step 524). For example, the system can generate the normalized edge embedding by normalizing the combined edge embedding by a normalization factor. The normalization factor can be based on a measure of dispersion of a set of values that includes a value for each node of the graph that defines a number of edges connected to thenode. As a particular example, the system can generate the normalized edge embedding for a node to be an average edge embedding for the node as scaled by the number of edges connected to the node.

[0140] The system can then process the graph data using one or more update neural network layers of the graph neural network to update the node embeddings (step 526). In particular, the system can process, as network inputs for the update layers, the normalized edge embedding and the node embedding for each node. In general, the system can update the node embeddings following message passing operations, in which the embedding for each node is updated based on the embeddings of the neighboring nodes.

[0141] The system can determine whether message passing is complete (step 528). In particular, the system can determine that message passing is complete after a pre-determined number of update iterations. If the system determines that the message passing is not complete, the system can proceed to a next update iteration (e.g., return to step 522 for the next update iteration).

[0142] The system can then process the graph data to predict the force vectors for the atoms of the simulated material (step 530). In particular, when the system determines that the message passing is complete, the system can then process the graph data, as updated by the message passing, to predict the force vectors for the atoms of the simulated material. As described above with reference to FIG. 5A, the system can generate a predicted force vector for each node in the graph by processing the node embedding for the node using one or more force decoder neural network layers of the graph neural network.

[0143] FIG. 5C is a flow chart for an example process for training a graph neural network to predict properties of simulated materials. For convenience, the process 540 will be described as being performed by a system of one or more computers located in one or more locations. For example, a material discovery system, e.g., the meta-stable material discovery system 100 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 540.

[0144] The system can obtain training data for the graph neural network (step 542). The training data for the graph neural network can include a plurality of training examples. Each training example can include data characterizing an example material for the training example and target properties for the example material. The target properties for the training examples for the training examples can be determined by ab-initio simulation (e.g., following density functional theory calculations) of the example materials for the example materials.

[0145] The system can train the graph neural network using the training data to optimize an objective function for the graph neural network (step 544). The objective function can be any appropriate objective function for training the graph neural network to predict properties of simulated materials. For example, the objective function can include a per-atom Huber loss, defined following:

[0146] Where N is the number of simulated atoms, A is a force loss coefficient, F^ is a force for the i-th atom along the 7 -th dimension as predicted by the graph neural network, F*j is a target force for the i-th atom along the 7 -th dimension, SFis a force loss threshold, B is an energy loss coefficient, Etis an energy for the i-th atom by the graph neural network, E* is a target energy for the i-th atom, and 8Eis an energy loss threshold.

[0147] The system can use any appropriate machine learning technique to train the graph neural network. For example, the system can compute gradients of the objective function and update parameters of the graph neural network using the computed gradients (e.g., using stochastic gradient descent, ADAM, etc.) to optimize the objective function.

[0148] Finally, the system can return the trained graph neural network (step 546).

[0149] FIG. 6 is a flow chart for an example process for identifying candidate materials within a set of optimized precursor materials. For convenience, the process 600 will be described as being performed by a system of one or more computers located in one or more locations. For example, a material discovery system, e.g., the meta-stable material discovery system 100 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 600.

[0150] The system can determine material properties of each of the set of optimized precursor materials (step 602). The material properties for the optimized precursor materials can include, e.g., predicted potential energies of the optimized precursor materials, electrical conductivities of the optimized precursor materials, polarizations of the optimized precursor materials, magnetizations of the optimized precursor materials, and so on.

[0151] As part of determining the material properties of the optimized precursor materials, the system can use machine learned force fields determined by a machine learning model (e.g.. a neural network, such as a graph neural network). An example graph neural network configured to predict forces and energies for atoms of the sub-cell is described in more detail below with reference to FIG. 5A, FIG. 5B, and FIG. 5C. In particular, the system can determine thematerial properties of the optimized precursor materials using the same machine learning model used to simulate the phase transition of the initial material (e.g., as described in step 210 of FIG. 2).

[0152] When the system predicts material properties for an optimized precursor material, the system can store data specifying the optimized precursor material and validated material properties of the optimized precursor material within a materials database for the system.

[0153] The system can identify the candidate materials within the set of optimized precursor materials based on candidate material selection criteria (step 604). The identify optimized precursor materials as candidate materials using a variety of candidate material selection criteria. As an example, the system can determine whether to identify each optimized precursor material as a candidate material based on the predicted material properties of the optimized precursor material. For example, the candidate material selection criteria can include one or more constraints on estimated potential energies for the optimized precursor materials. As a further example, the candidate material selection criteria can require that candidate materials have estimated potential energies smaller than a predefined threshold. As another example, the candidate material selection criteria can require that candidate materials have estimated potential energies smaller than a predefined fraction of the set of optimized precursor materials.

[0154] As another example, the system can determine whether to identify an optimized precursor material as a candidate material based whether the optimized precursor material has already stored within the materials database as a previously known material.

[0155] In some implementations the system can validate the material properties of the identified candidate materials (step 606). For example, the system can validate the candidate materials by performing ab-initio simulations (e g., following densify functional theory) to predict material properties of the candidate materials. As another example, the system can request and receive results for experimental validations of the predicted material properties by, e.g., providing data characterizing the candidate materials for synthesis and obtaining results from physical tests of the synthesized candidate materials.

[0156] When the system validates material properties for a candidate material, the system can store data specifying the candidate material and validated material properties of the candidate material within the materials database for the system.

[0157] In some implementations, the system can request physical synthesis and experimental validation of one or more of the candidate materials (step 608). The system can select candidate materials for physical synthesis by screening the candidate materials based on the predicted material properties for the candidate materials. In particular, for each of the candidate materials,the system can evaluate screening criteria based on the predicted material properties of the candidate material and can generate output data characterizing a decision to physically synthesize the candidate material based on the evaluated screening criteria for the candidate materials. In particular, the screening criteria can specify desired material properties for the candidate materials. The output data characterizing the decision to physically synthesize the candidate material can include data characterizing a request to physically synthesize the candidate material. In general, the system can generate output data requesting physical synthesis of candidate materials that satisfy the screening criteria.

[0158] After the system selects one or more of the candidate materials for physical synthesis, the system can request physical synthesis of the selected candidate materials (e.g., by transmitting the request to a laboratory, a fabrication plant, etc.). The selected candidate materials can be physically synthesized for any of a variety of tasks. For example, the selected candidate materials can be physically synthesized perform a manufacturing process involving the selected candidate materials. As another example, the selected can be physically synthesized to perform experimental testing and validation of the predicted material properties of the selected candidate materials. When a candidate material is physically synthesized, the system can receive data characterizing experimental results for the synthesized candidate materials and can update the materials database using the experimental results (e.g., update the materials database to include experimentally validated material properties of the candidate materials).

[0159] The system can finally output data characterizing the identified candidate materials (step 610).

[0160] FIG. 7 A illustrates example meta-stable materials identified and validated using an implementation of a meta-stable material discovery system. As illustrated, the meta-stable material discovery system configured as described by this specification can be used to identify meta-stable materials resulting from phase transitions of a variety of initial materials.

[0161] FIG. 7B illustrates formation energies for an example formation pathway for meta- stable materials identified using an implementation of a meta-stable material discovery system. In particular. FIG. 7B illustrates formation energies for a formation pathway of meta-stable materials during a crystallization of amorphous Fe80B20. The formation energies of meta- stable materials within a formation pathway can indicate an ordering of when meta-stable materials form during a phase transition of an initial material (e.g., meta-stable crystals with higher formation energies can form first during a crystallization of an amorphous material). For example, as illustrated in FIG. 7B, during the crystallization of amorphous Fe80B20, meta-stable Fe^B can form before other meta-stable products, such as meta-stable Fe3B. which themselves can form before stable crystals of Fe2B and Fe.

[0162] FIG. 7C illustrates chemical structures from an example formation pathway for meta- stable materials identified using an implementation of a meta-stable material discovery system. In particular, FIG. 7C illustrates chemical structures meta-stable materials identified by an implementation of a meta-stable material discovery system simulating a crystallization of amorphous Fe80B20.

[0163] As illustrated by FIG. 7B and 7C, the meta-stable material discover}' system configured as described by this specification can be used to determine a variety' of properties regarding formation pathways for meta-stable materials.

[0164] This specification uses the term “configured” in connection with systems and computer program components. For a system of one or more computers to be configured to perform particular operations or actions means that the system has installed on it software, firmware, hardware, or a combination of them that in operation cause the system to perform the operations or actions. For one or more computer programs to be configured to perform particular operations or actions means that the one or more programs include instructions that, when executed by data processing apparatus, cause the apparatus to perform the operations or actions.

[0165] Embodiments of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly-embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e.. one or more modules of computer program instructions encoded on a tangible non-transitory storage medium for execution by, or to control the operation of, data processing apparatus. The computer storage medium can be a machine- readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them. Alternatively or in addition, the program instructions can be encoded on an artificially-generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus.

[0166] The term “data processing apparatus” refers to data processing hardware and encompasses all kinds of apparatus, devices, and machines for processing data, including byway of example a programmable processor, a computer, or multiple processors or computers. The apparatus can also be, or further include, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit). The apparatus can optionally include, in addition to hardware, code that creates an execution environment for computer programs, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0167] A computer program, which may also be referred to or described as a program, software, a software application, an app, a module, a software module, a script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages; and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, e.g., files that store one or more modules, sub-programs, or portions of code. A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a data communication network.|0168| In this specification the term “engine” is used broadly to refer to a software-based system, subsystem, or process that is programmed to perform one or more specific functions. Generally, an engine will be implemented as one or more software modules or components, installed on one or more computers in one or more locations. In some cases, one or more computers will be dedicated to a particular engine; in other cases, multiple engines can be installed and running on the same computer or computers.

[0169] The processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by special purpose logic circuitry, e.g., an FPGA or an ASIC, or by a combination of special purpose logic circuitry and one or more programmed computers.

[0170] Computers suitable for the execution of a computer program can be based on general or special purpose microprocessors or both, or any other kind of central processing unit. Generally, a central processing unit will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a centralprocessing unit for performing or executing instructions and one or more memory devices for storing instructions and data. The central processing unit and the memory can be supplemented by, or incorporated in, special purpose logic circuitry. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device, e.g., a universal serial bus (USB) flash drive, to name just a few.

[0171] Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks.

[0172] To provide for interaction with a user, embodiments of the subject matter described in this specification can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user’s device in response to requests received from the web browser. Also, a computer can interact with a user by sending text messages or other forms of message to a personal device, e.g., a smartphone that is running a messaging application, and receiving responsive messages from the user in return.

[0173] Data processing apparatus for implementing machine learning models can also include, for example, special-purpose hardware accelerator units for processing common and computeintensive parts of machine learning training or production, i.e., inference, workloads.

[0174] Machine learning models can be implemented and deployed using a machine learning framework, e.g., a TensorFlow framework, or a Jax framework.

[0175] Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back-end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front-end component, e.g., a client computer having a graphical user interface, a web browser, or an app through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication, e g., a communication network. Examples of communication networks include a local area network (LAN) and a wide area network (WAN), e.g., the Internet.

[0176] The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. In some embodiments, a server transmits data, e.g., an HTML page, to a user device, e.g.. for purposes of displaying data to and receiving user input from a user interacting with the device, which acts as a client. Data generated at the user device, e.g., a result of the user interaction, can be received at the server from the device.

[0177] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any invention or on the scope of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially be claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

[0178] Similarly, while operations are depicted in the drawings and recited in the claims in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system modules andcomponents in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0179] Innovative aspects of the present disclosure are also set out in the following numbered clauses:Clause 1. A method comprising: obtaining data defining macroscopic properties for an initial material; generating a set of precursor materials, comprising: generating a simulated sample of the initial material through computational simulation; and identifying precursor materials within the simulated sample based on microscopic properties of regions within the simulated sample; and for each precursor material: generating a simulated sample of an optimized precursor material through a computational simulation altering the microscopic properties of the precursor material to optimize a macroscopic property of the precursor material; and determining one or more quantities characterizing the simulated sample of the optimized precursor material.Clause 2. The method of clause 1, further comprising: generating a set of candidate materials, comprising, for each precursor material: determining whether to identify the optimized precursor material as a candidate material based on the one or more quantities determined for the simulated sample of the optimized precursor material.Clause 3. The method of clause 1 or 2, wherein the data defining the macroscopic properties for the initial material defines a chemical stoichiometry for the initial material. Clause 4. The method of clause 3, wherein generating the simulated sample of the initial material through computational simulation comprises generating data defining a respective spatial position, spatial velocity, and chemical element of each of a plurality of simulated atoms within the simulated sample.Clause 5. The method of clause 4, wherein the data defining the macroscopic properties for the initial material defines a set of starting equilibrium properties and generating the simulated sample of the initial material further comprises: generating an unequilibrated sample of the initial material;generating an equilibrated sample of the initial material from the unequilibrated sample, comprising, for each of one or more equilibration steps: updating the positions and velocities of the atoms within the sample following an initial molecular dynamics simulation of the sample computed in accordance with the set of starting equilibrium properties.Clause 6. The method of clause 5, wherein the data defining the macroscopic properties for the initial material defines a set of final equilibrium properties and generating the simulated sample of the initial material further comprises: generating a quenched sample of the initial material from the equilibrated sample, comprising, for each of one or more quenching steps: updating the positions and velocities of the atoms within the sample following a quenching molecular dynamics simulation of the sample computed in accordance with the set of starting equilibrium properties and the set of final equilibrium properties.Clause 7. The method of clause 6, wherein generating the simulated sample of the initial material further comprises: generating a final equilibrated sample of the initial material from the quenched sample, comprising, for each of one or more equilibration steps: updating the positions and velocities of the atoms within the sample following a final molecular dynamics simulation of the sample computed in accordance with the set of final equilibrium properties.Clause 8. The method of any preceding clause when dependent on clause 5, wherein: the set of starting equilibrium properties specifies an initial equilibration temperature; and the initial molecular dynamics simulation is computed in accordance with a thermostat fixed at the initial equilibration temperature.Clause 9. The method of any preceding clause when dependent on clause 6, wherein: the set of starting equilibrium properties specifies an initial quenching temperature and a final quenching temperature; and the quenching molecular dynamics simulation is computed in accordance with a thermostat transitioning from the initial quenching temperature to the final quenching temperature.Clause 10. The method of any preceding clause when dependent on clause 7, wherein: the set of starting equilibrium properties specifies a final equilibration temperature; andthe final molecular dynamics simulation is computed in accordance with a thermostat fixed at the final equilibration temperature.Clause 11. The method of any preceding clause when dependent on clause 5, wherein the initial molecular dynamics simulation is computed based on force fields derived from a first neural network.Clause 12. The method of clause 11. wherein the first neural network is a graph neural network.Clause 13. The method of clause 11 or 12, wherein the first neural network is trained to replicate potential energies of atoms of a dataset of example materials.Clause 14. The method of clause 13. wherein the first neural netw ork is trained to minimize a per-atom Huber loss over the dataset of example materials.Clause 15. The method of clause 13 or 14, wherein the potential energies of atoms within the dataset of example materials include potentials computed using density functional theory calculations.Clause 16. The method of any preceding clause when dependent on clause 6, wherein the quenching molecular dynamics simulation is computed based on force fields derived from a second neural network.Clause 17. The method of clause 16 when dependent on clause 11, wherein the second neural netw ork is the first neural network.Clause 18. The method of any preceding clause when dependent on clause 7. wherein the final molecular dynamics simulation is computed based on force fields derived from a third neural network.Clause 19. The method of clause 18 when dependent on clause 11, wherein the third neural network is the first neural network.Clause 20. The method of any preceding clause when dependent on clause 5, wherein generating the unequilibrated sample comprises, for each simulated atom in the simulated sample: determining a chemical element for the atom, in accordance w ith the chemical stoichiometry defined for the initial material; and randomly assigning a position for the atom within the sample.Clause 21. The method of clause 20, wherein generating the simulated sample of the initial material further comprises relaxing the unequilibrated initial sample, comprising, for each of one or more update steps: computing a relaxation potential energy based on the position of the atoms within thesample; and updating the position of each atom within the sample by performing gradient descent of the computed relaxation potential.Clause 22. The method of clause 21, wherein the computed relaxation potential is a soft shell potential.Clause 23. The method of any preceding clause, wherein identifying precursor materials within the simulated sample based on microscopic properties of regions within the simulated sample comprises: dividing the simulated sample into a plurality of sub-cells, and, for each sub-cell: determining whether the sub-cell represents a precursor material based on at least the chemical elements of the atoms contained within the sub-cell.Clause 24. The method of clause 23, wherein the plurality’ of sub-cells includes all subcells that can be generated by partitioning the initial sample along a predetermined grid.Clause 25. The method of clause 23 or 24, wherein each identified precursor material is a periodic replication of the sub-cell representing the precursor material along one or more spatial dimensions.Clause 26. The method of clause 25, wherein the altering microscopic properties of the precursor material to optimize the macroscopic property of the precursor material comprises, for each of one or more optimization steps: computing a gradient of the macroscopic property with respect to the position of each atom within the sub-cell representing the precursor material; and updating the position of each atom w ithin the sub-cell in accordance with the computed gradient.Clause 27. The method of clause 26. wherein altering the microscopic properties of the precursor material further comprises: computing a gradient of the macroscopic property with respect to each of a set of parameters determining the size and shape of the sub-cell representing the precursor material; and updating the parameters determining the size and shape of the sub-cell in accordance with the computed gradient.Clause 28. The method of any preceding clause, w herein the optimized macroscopic property of the precursor material is an estimated potential energy of the precursor material . Clause 29. The method of clause 28. wherein the estimated potential energy of the precursor material is determined by a fourth neural network.Clause 30. The method of clause 29, when dependent on clause 11, wherein the fourth neural network is the first neural network.Clause 31. The method of any preceding clause when dependent on clause 28, wherein the set of candidate materials comprises the set of optimized precursor materials satisfying one or more constraints on the estimated potential energies.Clause 32. The method of clause 31. wherein the set of candidate materials are constrained to have estimated potential energies smaller than a predefined threshold. Clause 33. The method of clause 31 or 32, wherein the set of candidate materials are constrained to have estimated potential energies smaller than a predefined fraction of the set of optimized precursor materials.Clause 34. The method of any preceding clause, wherein one or more candidate materials in the set of candidate materials are crystalline materials.Clause 35. The method of any preceding clause, wherein one or more of the candidate materials in the set of candidate materials are poly crystalline materials.Clause 36. The method of any preceding clause, wherein one or more candidate materials in the set of candidate materials are amorphous materials.Clause 37. The method of any preceding clause, wherein one or more of the candidate materials are inorganic materials.Clause 38. The method of any preceding clause, wherein one or more of the candidate materials are organic materials.Clause 39. The method of any preceding clause, wherein one or more of the candidate materials are hybrid materials comprising inorganic and organic components.Clause 40. The method of any preceding clause, further comprising synthesizing one or more of the candidate materials.Clause 41. One or more non-transitory computer storage media storing instructions that when executed by one or more computers cause the one or more computers to perform operations of the respective method of any one of clauses 1-39.Clause 42. A system comprising: one or more computers; and one or more storage devices communicatively coupled to the one or more computers, wherein the one or more storage devices store instructions that, when executed by the one or more computers, cause the one or more computers to perform operations of the respective method of any one of clauses 1-39.

[0180] Particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some cases, multitasking and parallel processing may be advantageous.

[0181] What is claimed is:

Claims

CLAIMS1. A method comprising: obtaining data defining macroscopic properties for an initial material; generating a set of precursor materials, comprising: generating a simulated sample of the initial material through computational simulation; and identifying precursor materials within the simulated sample based on microscopic properties of regions within the simulated sample; and for each precursor material: generating a simulated sample of an optimized precursor material through a computational simulation altering the microscopic properties of the precursor material to optimize a macroscopic property of the precursor material; and determining one or more quantities characterizing the simulated sample of the optimized precursor material.

2. The method of claim 1 , further comprising: generating a set of candidate materials, comprising, for each precursor material: determining whether to identify the optimized precursor material as a candidate material based on the one or more quantities determined for the simulated sample of the optimized precursor material.

3. The method of claim 1 or 2, wherein the data defining the macroscopic properties for the initial material defines a chemical stoichiometry7for the initial material.

4. The method of claim 3, wherein generating the simulated sample of the initial material through computational simulation comprises generating data defining a respective spatial position, spatial velocity, and chemical element of each of a plurality of simulated atoms within the simulated sample.

5. The method of claim 4, wherein the data defining the macroscopic properties for the initial material defines a set of starting equilibrium properties and generating the simulated sample of the initial material further comprises: generating an unequilibrated sample of the initial material; generating an equilibrated sample of the initial material from the unequilibrated sample, comprising, for each of one or more equilibration steps:updating the positions and velocities of the atoms within the sample following an initial molecular dynamics simulation of the sample computed in accordance with the set of starting equilibrium properties.

6. The method of claim 5, wherein the data defining the macroscopic properties for the initial material defines a set of final equilibrium properties and generating the simulated sample of the initial material further comprises: generating a quenched sample of the initial material from the equilibrated sample, comprising, for each of one or more quenching steps: updating the positions and velocities of the atoms within the sample following a quenching molecular dynamics simulation of the sample computed in accordance with the set of starting equilibrium properties and the set of final equilibrium properties.

7. The method of claim 6, wherein generating the simulated sample of the initial material further comprises: generating a final equilibrated sample of the initial material from the quenched sample, comprising, for each of one or more equilibration steps: updating the positions and velocities of the atoms within the sample following a final molecular dynamics simulation of the sample computed in accordance with the set of final equilibrium properties.

8. The method of any preceding claim when dependent on claim 5, wherein: the set of starting equilibrium properties specifies an initial equilibration temperature; and the initial molecular dynamics simulation is computed in accordance with a thermostat fixed at the initial equilibration temperature.

9. The method of any preceding claim when dependent on claim 6, wherein: the set of starting equilibrium properties specifies an initial quenching temperature and a final quenching temperature; and the quenching molecular dynamics simulation is computed in accordance with a thermostat transitioning from the initial quenching temperature to the final quenching temperature.

10. The method of any preceding claim when dependent on claim 7, wherein: the set of starting equilibrium properties specifies a final equilibration temperature;and the final molecular dynamics simulation is computed in accordance with a thermostat fixed at the final equilibration temperature.

11. The method of any preceding claim when dependent on claim 5, wherein the initial molecular dynamics simulation is computed based on force fields derived from a first neural network.

12. The method of claim 11, wherein the first neural network is a graph neural network.

13. The method of claim 1 1 or 12, wherein the first neural network is trained to replicate potential energies of atoms of a dataset of example materials.

14. The method of claim 13, wherein the first neural network is trained to minimize a per- atom Huber loss over the dataset of example materials.

15. The method of claim 13 or 14, wherein the potential energies of atoms within the dataset of example materials include potentials computed using density functional theorycalculations.

16. The method of any preceding claim when dependent on claim 6, wherein the quenching molecular dynamics simulation is computed based on force fields derived from a second neural network.

17. The method of claim 16 when dependent on claim 11, wherein the second neural network is the first neural network.

18. The method of any preceding claim when dependent on claim 7, wherein the final molecular dynamics simulation is computed based on force fields derived from a third neural network.

19. The method of claim 18 when dependent on claim 11, wherein the third neural network is the first neural network.

20. The method of any preceding claim when dependent on claim 5, wherein generating the unequilibrated sample comprises, for each simulated atom in the simulated sample: determining a chemical element for the atom, in accordance with the chemicalstoichiometry defined for the initial material; and randomly assigning a position for the atom within the sample.

21. The method of claim 20, wherein generating the simulated sample of the initial material further comprises relaxing the unequilibrated initial sample, comprising, for each of one or more update steps: computing a relaxation potential energy based on the position of the atoms within the sample; and updating the position of each atom within the sample by performing gradient descent of the computed relaxation potential.

22. The method of claim 21, wherein the computed relaxation potential is a soft shell potential.

23. The method of any preceding claim, wherein identifying precursor materials within the simulated sample based on microscopic properties of regions within the simulated sample comprises: dividing the simulated sample into a plurality of sub-cells, and, for each sub-cell: determining whether the sub-cell represents a precursor material based on at least the chemical elements of the atoms contained within the sub-cell.

24. The method of claim 23, wherein the plurality of sub-cells includes all sub-cells that can be generated by partitioning the initial sample along a predetermined grid.

25. The method of claim 23 or 24, wherein each identified precursor material is a periodic replication of the sub-cell representing the precursor material along one or more spatial dimensions.

26. The method of claim 25, wherein the altering microscopic properties of the precursor material to optimize the macroscopic property of the precursor material comprises, for each of one or more optimization steps: computing a gradient of the macroscopic property with respect to the position of each atom within the sub-cell representing the precursor material; and updating the position of each atom w ithin the sub-cell in accordance with the computed gradient.

27. The method of claim 26, wherein altering the microscopic properties of the precursor material further comprises: computing a gradient of the macroscopic property with respect to each of a set of parameters determining the size and shape of the sub-cell representing the precursor material; and updating the parameters determining the size and shape of the sub-cell in accordance with the computed gradient.

28. The method of any preceding claim, wherein the optimized macroscopic property of the precursor material is an estimated potential energy of the precursor material .

29. The method of claim 28, wherein the estimated potential energy of the precursor material is determined by a fourth neural network.

30. The method of claim 29. when dependent on claim 11, wherein the fourth neural network is the first neural network.

31. The method of any preceding claim when dependent on claim 28, wherein the set of candidate materials comprises the set of optimized precursor materials satisfying one or more constraints on the estimated potential energies.

32. The method of claim 31, wherein the set of candidate materials are constrained to have estimated potential energies smaller than a predefined threshold.

33. The method of claim 31 or 32, wherein the set of candidate materials are constrained to have estimated potential energies smaller than a predefined fraction of the set of optimized precursor materials.

34. The method of any preceding claim, wherein one or more candidate materials in the set of candidate materials are crystalline materials.

35. The method of any preceding claim, w herein one or more of the candidate materials in the set of candidate materials are polycrystalline materials.

36. The method of any preceding claim, wherein one or more candidate materials in the set of candidate materials are amorphous materials.

37. The method of any preceding claim, wherein one or more of the candidate materials are inorganic materials.

38. The method of any preceding claim, wherein one or more of the candidate materials are organic materials.

39. The method of any preceding claim, wherein one or more of the candidate materials are hybrid materials comprising inorganic and organic components.

40. The method of any preceding claim, further comprising synthesizing one or more of the candidate materials.

41. One or more non-transitory computer storage media storing instructions that when executed by one or more computers cause the one or more computers to perform operations of the respective method of any one of claims 1-39.

42. A system comprising: one or more computers; and one or more storage devices communicatively coupled to the one or more computers, wherein the one or more storage devices store instructions that, when executed by the one or more computers, cause the one or more computers to perform operations of the respective method of any one of claims 1-39.

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