Physical property estimation system, physical property estimation method, and program

Abstract

A physical property estimation system (100) comprises an acquisition unit (11), an estimation unit (14), and an output unit (15). The acquisition unit (11) acquires structure information related to a structure including the arrangement of a plurality of atoms in a three-dimensional space, and first spin information related to the initial values of the plurality of atoms in a spin state in the structure. The estimation unit (14) estimates physical property information related to the physical properties of the structure on the basis of the structure information and the first spin information acquired by the acquisition unit (11). The output unit (15) outputs the physical property information estimated by the estimation unit (14).

Description

Physical property estimation system, physical property estimation method, and program

[0001] The present disclosure relates to a physical property estimation system for estimating the physical properties of a material.

[0002] Calculating the physical properties of crystal structures or molecules is important in many fields of science and engineering. However, the high computational cost of conventional first-principles calculations using density functional theory (DFT) and other methods poses a challenge. Therefore, in recent years, methods have been proposed that use machine learning techniques such as neural networks to predict physical properties with high accuracy and efficiency. These methods, called neural network potentials (NNPs), are constructed as regression models that predict physical properties such as energy or force from inputs such as atomic coordinates or chemical species.

[0003] For example, Patent Document 1 discloses a method for predicting the energy of a crystal structure calculated by first-principles calculation using NNP. Non-Patent Document 1 discloses a method for predicting spin information (atomic magnetic moment) in addition to the energy of a crystal structure. For example, Non-Patent Document 2 discloses a method for predicting the energy of a crystal structure using spin information calculated by DFT calculation and the crystal structure as input.

[0004] International Publication No. 2020 / 203922

[0005] DENG, Bowen, et al. CHGNet as a pretrained universal neural network potential for charge-informed atomic modeling. Nature Machine Intelligence, 2023, 5.9: 1031-1041. YU, Hongyu, et al. Spin-Dependent Graph Neural Network Potential for Magnetic Materials. arXiv preprint arXiv:2203.02853, 2022.

[0006] The present disclosure provides a physical property estimation system and the like that can easily improve the accuracy of estimating the physical properties of a material.

[0007] A physical property estimation system according to one aspect of the present disclosure includes an acquisition unit that acquires structural information about a structure including an arrangement of multiple atoms in three-dimensional space and first spin information about initial values ​​of spin states of the multiple atoms in the structure, an estimation unit that estimates physical property information about the physical properties of the structure based on the structural information and the first spin information acquired by the acquisition unit, and an output unit that outputs the physical property information estimated by the estimation unit.

[0008] According to the present disclosure, it is easy to improve the accuracy of estimating the physical properties of materials.

[0009] FIG. 1 is a block diagram showing an overall configuration including a physical property estimation system according to embodiment 1. FIG. 2 is a flowchart showing an outline of the operation of the physical property estimation system according to embodiment 1. FIG. 3 is a diagram showing an example of generating a spin estimation value from first spin information. FIG. 4 is a diagram showing another example of generating a spin estimation value from the first spin information. FIG. 5 is a diagram showing yet another example of generating a spin estimation value from the first spin information. FIG. 6 is a diagram showing an example of generating model input information. FIG. 7 is a diagram showing an example of information displayed on a display unit by an output unit of the physical property estimation system according to embodiment 1. FIG. 8 is a flowchart showing an outline of the operation of a physical property estimation system according to embodiment 2. FIG. 9 is a flowchart showing an outline of the operation when second spin information is output using intermediate spin information. FIG. 10 is a block diagram showing an overall configuration including a physical property estimation system according to embodiment 3. FIG. 11 is a flowchart showing an outline of the operation of the physical property estimation system according to embodiment 3. FIG. 12 is a flowchart showing an outline of the operation of a physical property estimation system according to comparative example 1. FIG. 13 is a flowchart showing an outline of the operation of a physical property estimation system according to comparative example 2.

[0010] (Findings that led to the present disclosure) The inventors of the present application have focused on the fact that the spin state of a material significantly affects the physical properties of the material. For example, a crystal structure containing one or more transition metal atoms is classified into a ferromagnetic, antiferromagnetic, or ferrimagnetic state depending on the magnitude and direction of the magnetic moment of each transition metal atom, and these states have different physical properties. In DFT calculations, an initial estimated value of the magnetic moment is set so that the material converges to one of the above states, and then the calculation is performed to calculate the physical properties of the material in the target state.

[0011] On the other hand, many NNPs do not take spin information into account. Here, spin information is information that represents the spin state of a material. For example, spin information may be a set of values ​​describing the magnetic moment value and its direction for each atom contained in the material, or it may represent the overall spin state of a crystal structure or molecule, such as ferromagnetic, antiferromagnetic, singlet, or triplet.

[0012] For example, the method disclosed in Patent Document 1 predicts energy using structural information that does not include spin information of the material, so the same predicted energy value is obtained for any spin state, making it difficult to accurately predict the physical properties of the material.

[0013] Non-Patent Document 1 discloses a method for predicting the magnetic moment of atoms in addition to the energy of a crystal structure. However, in this method, spin information is not included in the input to the NNP, and it is not possible to calculate the physical properties for each of multiple spin states. Furthermore, in this method, which spin state is obtained depends on the training data during NNP training and is uncontrollable during prediction, making it difficult to accurately predict the physical properties of a material for a desired spin state.

[0014] On the other hand, Non-Patent Document 2 discloses a method for predicting the energy of a crystal structure by inputting spin information and a crystal structure to an NNP. However, the spin information used in Non-Patent Document 2 is calculated by DFT calculation. Therefore, in this method, in order to predict the energy of a crystal structure, it is necessary to perform a DFT calculation each time, which has a very high calculation cost, making it difficult to predict the physical properties of a material quickly.

[0015] The inventors of the present application have discovered that the physical properties of a material can be estimated with high accuracy by using a prediction model to estimate the physical properties of a material from simple input data, namely, structural information about the material and a spin estimate value that does not require pre-calculation. Furthermore, they have discovered that by not only using spin information as input to the prediction model but also outputting spin information estimated from the prediction model, the physical properties of the material can be estimated with even higher accuracy using the output spin information. Here, the spin estimate value is an estimate of the spin state.

[0016] A physical property estimation system according to a first aspect of the present disclosure includes an acquisition unit that acquires structural information regarding a structure including an arrangement of multiple atoms in three-dimensional space and first spin information regarding initial values ​​of spin states of the multiple atoms in the structure, an estimation unit that estimates physical property information regarding the physical properties of the structure based on the structural information and the first spin information acquired by the acquisition unit, and an output unit that outputs the physical property information estimated by the estimation unit.

[0017] This has the advantage that it becomes possible to distinguish between structures that have the same structural information but different spin states, making it easier to improve the accuracy of estimating the physical properties of materials.

[0018] For example, in a physical property estimation system according to a second aspect of the present disclosure, in the first aspect, the acquisition unit may acquire, as the first spin information, at least one of the valence and spin state of an element of one or more atoms among the plurality of atoms (at least one selected from the group consisting of).

[0019] This has the advantage that the user's prior knowledge about the spin state of each atom can be easily introduced into the estimation section.

[0020] For example, in the property estimation system according to the third aspect of the present disclosure, in the first or second aspect, the acquisition unit may acquire, as the first spin information, a method for generating the initial value of each of the plurality of atoms.

[0021] This has the advantage that when a user does not have prior knowledge about the spin state of each atom but has prior knowledge about the spin state of the entire material, this prior knowledge can be easily introduced into the estimation unit.

[0022] For example, in the property estimation system according to the fourth aspect of the present disclosure, in any one of the first to third aspects, the acquisition unit may acquire, as the first spin information, a constraint that limits the initial value of each of the plurality of atoms to within a specified range.

[0023] This has the advantage that, when estimating the physical properties of a structure, it is easy to avoid each atom taking on an unrealistic spin state that deviates from the constraints.

[0024] For example, in a physical property estimation system according to a fifth aspect of the present disclosure, in any one of the first to fourth aspects, the estimation unit may estimate the physical property information using a prediction model having isovariance that returns isovariant output in response to a change in input.

[0025] This makes it possible to enforce the physical validity of output changes in response to input changes, which not only improves estimation accuracy but also has the advantage of making it easier to reduce the amount of data required for learning if the prediction model is a machine learning model.

[0026] For example, in a physical property estimation system according to a sixth aspect of the present disclosure, in the fifth aspect, the prediction model may have a variance according to the physical property information of the estimation target.

[0027] For example, in the physical property estimation system according to the seventh aspect of the present disclosure, in the fifth aspect, the prediction model may have the same modification as the first spin information.

[0028] This has the advantage that the prediction model can estimate a physically appropriate output in response to a change in the first spin information.

[0029] For example, in a physical property estimation system according to the eighth aspect of the present disclosure, in the seventh aspect, the prediction model may have a denaturation that combines a denaturation for the structural information and a denaturation for the first spin information.

[0030] This has the advantage that the prediction model can estimate a physically appropriate output for a combined change in the structural information and the first spin information.

[0031] For example, in a physical property estimation system according to a ninth aspect of the present disclosure, in any one of the first to fifth aspects, the estimation unit may further estimate second spin information regarding spin states that are different from the initial values ​​of the spin states of the multiple atoms in the first spin information.

[0032] This has the advantage of making it easier to understand the physical properties of materials based on more accurate spin states.

[0033] For example, in a physical property estimation system according to a tenth aspect of the present disclosure, in the eighth aspect, the estimation unit may output intermediate spin information regarding spin states that are different from the initial values ​​of the spin states of the plurality of atoms in the first spin information, and output the second spin information by further using the intermediate spin information at least once or more as input to the estimation unit instead of the first spin information.

[0034] This has the advantage that since further physical property information is estimated based on the intermediate spin information, it is easy to further improve the accuracy of estimating the physical properties of the material.

[0035] For example, the physical property estimation system according to an eleventh aspect of the present disclosure, in any one of the first to fifth aspects, may further include an atomic position optimization unit that optimizes positions of the plurality of atoms in the structure based on the physical property information estimated by the estimation unit.

[0036] This has the advantage that by optimizing the position of each atom taking into account the spin state, it is easier to improve the accuracy of estimating the physical properties of the material.

[0037] For example, in a physical property estimation system according to a twelfth aspect of the present disclosure, in any one of the first to fifth aspects, the physical property information may include information on the energy possessed by the structure.

[0038] This allows the physical properties of the material to be confirmed while referring to the energy of the structure, which has the advantage that it becomes easier to understand the physical properties of the material, for example, with respect to the most stable structure.

[0039] For example, a physical property estimation method according to a thirteenth aspect of the present disclosure includes the steps of acquiring structural information regarding a structure including an arrangement of a plurality of atoms in three-dimensional space; acquiring first spin information regarding initial values ​​of spin states of the plurality of atoms in the structure; estimating physical property information regarding the physical properties of the structure by inputting the acquired structural information and the first spin information into a prediction model; and outputting the estimated physical property information, wherein the prediction model is constructed to receive the structural information and the first spin information as input and to output the physical property information.

[0040] This has the advantage that it becomes possible to distinguish between structures that have the same structural information but different spin states, making it easier to improve the accuracy of estimating the physical properties of materials.

[0041] For example, in the physical property estimation method according to the fourteenth aspect of the present disclosure, in the thirteenth aspect, the prediction model is constructed to further output second spin information regarding spin states that are different from the initial values ​​of the spin states of the plurality of atoms in the first spin information, and the step of estimating the physical property information may further estimate the second spin information.

[0042] This has the advantage of making it easier to understand the physical properties of materials based on more accurate spin states.

[0043] For example, a program according to a fifteenth aspect of the present disclosure causes a computer to execute the following steps: acquiring structural information regarding a structure including an arrangement of a plurality of atoms in three-dimensional space; acquiring first spin information regarding initial values ​​of spin states of the plurality of atoms in the structure; estimating physical property information regarding physical properties of the structure by inputting the acquired structural information and the first spin information into a prediction model; and outputting the estimated physical property information; the prediction model is constructed to receive the structural information and the first spin information as input and output the physical property information.

[0044] This has the advantage that it becomes possible to distinguish between structures that have the same structural information but different spin states, making it easier to improve the accuracy of estimating the physical properties of materials.

[0045] The physical property estimation method of the present disclosure can also be realized as a computer program that causes a computer to execute characteristic processes. Needless to say, such a computer program can be distributed on a computer-readable non-transitory recording medium such as a CD-ROM or via a communication network such as the Internet.

[0046] Hereinafter, the embodiments will be specifically described with reference to the drawings.

[0047] Note that each embodiment described below shows a comprehensive or specific example of the present disclosure. The numerical values, shapes, materials, components, component placement and connection configurations, steps, step order, etc. shown in each embodiment below are examples and are not intended to limit the present disclosure. Among the components in each embodiment below, components that are not described in an independent claim that represents the highest concept are described as optional components. In all embodiments, the respective contents can be combined. Each figure is a schematic diagram and is not necessarily an exact illustration. In each figure, the same components are assigned the same reference numerals.

[0048] The physical property estimation system according to the embodiment of the present disclosure may be configured so that all components are included in one computer, or may be configured as a system in which multiple components are distributed across multiple computers.

[0049] In the present disclosure, "at least one selected from the group consisting of A1 and A2" may be interpreted as "A1," "A2," or "A1 and A2."

[0050] First Embodiment Hereinafter, a physical property estimation system 100 (physical property estimation method or program) according to a first embodiment of the present disclosure will be described in detail with reference to the drawings.

[0051] [1. Configuration] First, the overall configuration including a physical property estimation system 100 according to the first embodiment will be described with reference to Fig. 1. Fig. 1 is a block diagram showing the overall configuration including the physical property estimation system 100 according to the first embodiment. The physical property estimation system 100 is configured as a computer such as a personal computer or a server. That is, the physical property estimation system 100 may be realized by cloud computing, for example. In the first embodiment, the physical property estimation system 100 will be described as being a stationary computer.

[0052] The physical property estimation system 100 includes a processing unit 10 and a storage unit 16. The processing unit 10 includes an acquisition unit 11, an initial spin generation unit 12, a model input information generation unit 13, an estimation unit 14, and an output unit 15. The physical property estimation system 100 is connected to an input unit 2, a display control unit 30, and a display unit 3. The input unit 2, the display control unit 30, and the display unit 3 are configured by an information terminal used by a user, such as a smartphone, a tablet terminal, or a personal computer.

[0053] The input unit 2 is an input interface that accepts user input and is configured, for example, with a keyboard, a touch sensor, a touchpad, or a mouse. The input unit 2 accepts an input operation by the user and outputs a signal corresponding to the input operation to the physical property estimation system 100. In the present disclosure, the display unit 3 and the input unit 2 are configured independently of each other, but they may be configured integrally like a touch panel. In the present disclosure, the physical property estimation system 100 does not include the display unit 3 or the input unit 2, but may include these.

[0054] The input unit 2 receives input of structural information relating to a structure including the arrangement of a plurality of atoms in a three-dimensional space, and first spin information relating to the initial values ​​of the spin states of a plurality of atoms in the structure.

[0055] The acquisition unit 11 acquires structural information regarding a structure including the arrangement of multiple atoms in three-dimensional space, and first spin information regarding the initial values ​​of the spin states of multiple atoms in the structure. Details of the structural information and the first spin information will be described later. The acquisition unit 11 is an entity that executes the step of acquiring structural information and the step of acquiring first spin information in the physical property estimation method disclosed herein. Specifically, the acquisition unit 11 acquires the structural information and the first spin information input by the user via the input unit 2.

[0056] The initial spin generator 12 generates spin estimates for each atom in the structure indicated by the structural information, based on the structural information and the first spin information acquired by the acquirer 11. The initial spin generator 12 is the entity that executes the step of generating spin estimates in the physical property estimation method of the present disclosure. Details of the processing executed by the initial spin generator 12 will be described later.

[0057] The model input information generation unit 13 generates information to be input to the prediction model using the structural information acquired by the acquisition unit 11 and the spin estimation value generated by the initial spin generation unit 12. The model input information generation unit 13 is the entity that executes the step of generating model input information in the physical property estimation method of the present disclosure. Details of the processing executed by the model input information generation unit 13 will be described later.

[0058] The estimation unit 14 estimates physical property information related to the physical properties of the structure indicated by the structural information, using the model input information generated by the model input information generation unit 13 and the prediction model. The estimation unit 14 is the entity that executes the step of estimating physical property information in the physical property estimation method of the present disclosure. Details of the processing executed by the estimation unit 14 will be described later.

[0059] The output unit 15 outputs the image etc. to the display control unit 30, thereby displaying the image etc. on the display unit 3. The output unit 15 outputs the physical property information estimated by the estimation unit 14. The output unit 15 is an entity that executes the step of outputting the physical property information in the physical property estimation method of the present disclosure.

[0060] The storage unit 16 is a recording medium that stores the structural information and first spin information acquired by the acquisition unit 11, the spin estimation values ​​generated by the initial spin generation unit 12, the model input information generated by the model input information generation unit 13, and the physical property information estimated by the estimation unit 14. The recording medium is, for example, a hard disk drive, a RAM (Random Access Memory), a ROM (Read Only Memory), or a semiconductor memory. Note that such a recording medium may be volatile or non-volatile.

[0061] The display control unit 30 causes the display unit 3 to display an image or the like based on information output from the output unit 15 of the physical property estimation system 100. The display unit 3 displays an image or the like under the control of the display control unit 30. The display unit 3 is, for example, a liquid crystal display, a plasma display, an organic EL (Electro-Luminescence) display, or the like, but is not limited to these.

[0062] 2. Operation The following describes the operation (i.e., the property estimation method) of the physical property estimation system 100 according to Embodiment 1. Fig. 2 is a flowchart showing an outline of the operation of the physical property estimation system 100 according to Embodiment 1.

[0063] (Step S101) The acquisition unit 11 acquires structural information regarding a structure including the arrangement of multiple atoms in three-dimensional space, and first spin information regarding the initial values ​​of the spin states of multiple atoms in the structure. The structural information is information describing, for example, a crystal structure, an organic molecule, a metal-organic framework (MOF), a polymer, or the like. In general, the structural information can be described by specifying the element and coordinates for each of multiple atoms included in the structure. Note that when the structural information describes a crystal structure, the structural information includes information on the repeating unit of the atomic arrangement, i.e., the unit cell.

[0064] The first spin information is information specifying the spin states of multiple atoms in the structure represented by the structural information. The initial values ​​of the spin states of the multiple atoms are user-specified or arbitrarily set. For example, the first spin information may include information indicating the magnitude and direction of the magnetic moment for each of the multiple atoms in the structure represented by the structural information. The first spin information does not need to indicate the spin states of all atoms in the structure represented by the structural information. In other words, the first spin information may be information specifying the spin states of some atoms included in the multiple atoms in the structure represented by the structural information. The first spin information may be information indicating the spin state of the entire structure represented by the structural information. For example, the first spin information may be magnetic information possessed by a crystalline structure such as ferromagnetic, antiferromagnetic, or ferrimagnetic, or may be information on the spin state of a molecule such as a singlet or triplet. The physical property estimation system 100 of the present disclosure can handle either colllinear or non-colllinear spin directions.

[0065] In the physical property estimation system 100 of the present disclosure, the first spin information does not need to be an accurate value of the spin states of multiple atoms calculated by DFT calculation, but may be an estimate of the spin states of multiple atoms estimated by the user. The estimate of the spin states of multiple atoms estimated by the user can be referred to as an initial value. For example, if the direction of the magnetic moment of each atom in a crystal structure is known but the magnitude is unknown, the magnitude of the magnetic moment of each atom in the first spin information may be an estimate. Even in this case, the physical property estimation system 100 of the present disclosure can distinguish multiple structures with different magnetic moment directions as different structures and estimate different physical properties for each. This is a unique feature of the physical property estimation system 100 of the present disclosure that is not available in conventional physical property estimation systems using NNPs.

[0066] (Step S102) The initial spin generator 12 generates a spin estimate (e.g., a magnetic moment) for each atom in the structure indicated by the structural information based on the structural information and first spin information acquired by the acquisition unit 11. Hereinafter, the spin estimate generated by the initial spin generator 12 will also be referred to as an "initial spin estimate." FIG. 3 is a diagram showing an example of generating a spin estimate from the first spin information. The left side of the arrow in FIG. 3 represents the structural information and first spin information acquired by the acquisition unit 11, and the right side of the arrow in FIG. 3 represents the spin estimate (initial spin estimate) generated by the initial spin generator 12. In FIG. 3, the magnitude of the numerical value represents the magnitude of the magnetic moment, and the positive and negative values ​​of the numerical value represent the direction of the magnetic moment in the case of collinear. The same applies to FIGS. 4 and 5 described below.

[0067] In the example shown in FIG. 3 , the acquisition unit 11 acquires structural information in which element species and coordinates are assigned to each atom, and first spin information in which spin states are assigned to some atoms. In this example, the spin state is defined for one atom and includes information indicating the magnitude and direction (sign) of the magnetic moment of the atom. Specifically, the acquisition unit 11 acquires the spin state for one of two Li atoms, but not for the other Li atom (see “null” in FIG. 3 ). The acquisition unit 11 acquires the spin state for one of two Ni atoms, but only acquires the spin state direction for the other Ni atom (see “null(-)” in FIG. 3 ). The initial spin generation unit 12 generates spin estimates for atoms with no spin state (see “null” in FIG. 3 ) or atoms with a spin state that is only directional (see “null(-)” in FIG. 3 ).

[0068] In this case, the initial spin generator 12 may generate a spin estimate value for the element to be generated by, for example, duplicating the spin state imparted to the same element as the element to be generated in the structure. The initial spin generator 12 may generate a spin estimate value for the element to be generated by, for example, referring to a preset correspondence relationship between elements and the magnitude of the magnetic moment. The correspondence relationship is not particularly defined, but, for example, experimental values ​​of the magnetic moment for each atom can be used for the correspondence relationship.

[0069] In this way, if spin states are assigned to only some atoms in the first spin information, the initial spin generator 12 complements the first spin information by generating spin states for the other atoms. Therefore, if spin states are assigned to all atoms in the first spin state and there are no constraints described below, the initial spin generator 12 will regard the first spin information as the initial spin generation value.

[0070] The first spin information may include the valence of the element. This is because the spin state can be estimated based on the valence of the element, since the expected value of the magnetic moment varies depending on the valence of the element. In this case, the initial spin generator 12 may refer to the correspondence between the element type, including the valence, and the magnetic moment.

[0071] The first spin information may include a method for generating a spin estimated value. Fig. 4 is a diagram showing another example of generating a spin estimated value from the first spin information. In the example shown in Fig. 4, the acquisition unit 11 acquires, as the first spin information, the magnetism of the entire structure indicated by the structural information and information on the target element that exhibits the magnetism (i.e., the method for generating a spin estimated value). Based on these conditions, the initial spin generator 12 generates a spin estimated value that indicates the appropriate magnitude and direction of the magnetic moment for each atom.

[0072] 4, when the spin generation value generation method is set to "ferromagnetism" and the target element is set to "Ni," the initial spin generator 12 generates a spin estimation value indicating the direction of the magnetic moment of each Ni atom, assuming that the magnetic moments of all Ni atoms in the structure indicated by the structural information are oriented in the same direction. The initial spin generator 12 generates a spin estimation value indicating the magnitude of the magnetic moment of each atom by referring to the above correspondence relationship.

[0073] The method for generating the spin estimation value may use, for example, ferromagnetism, antiferromagnetism, ferrimagnetism, etc., but is not limited to these. For example, in the method for generating the spin estimation value, a specific element A may be set to be "ferromagnetic" and other elements may be set to have "magnetic moments in the opposite direction to that of element A."

[0074] The first spin information may include a constraint that limits the spin estimate value of each of the multiple atoms within a specified range. Figure 5 is a diagram showing yet another example of generating a spin estimate value from the first spin information. In the example shown in Figure 5, the acquisition unit 11 acquires, as in the example shown in Figure 4, the magnetism of the entire structure indicated by the structural information and the method for generating the spin estimate value as the first spin information, and further acquires the magnitude of the magnetic moment that can be taken for each element as a constraint. If the magnitude of the magnetic moment obtained by referring to the above correspondence does not satisfy the constraint, the initial spin generation unit 12 sets the magnitude of the magnetic moment to the boundary value of the range specified by the constraint.

[0075] In the example shown in Figure 5, the acquisition unit 11 acquires the constraints that the magnitude of the magnetic moment of Ni is "4.0" or less and the magnitude of the magnetic moment of Li is "0.1" or less. Therefore, although the magnitude of the magnetic moment of Ni obtained by referring to the above correspondence is "5.0", the initial spin generation unit 12 determines the magnitude of the magnetic moment of Ni to be "4.0" in accordance with the constraints. Although the magnitude of the magnetic moment of Li obtained by referring to the above correspondence is "0.6", the initial spin generation unit 12 determines the magnitude of the magnetic moment of Li to be "0.1" in accordance with the constraints.

[0076] The first spin information may be a combination of the above-mentioned pieces of information. For example, in the case of a structure including Li, Ni, and O, the first spin information may be such that only Li and O specify the magnitude and direction of the magnetic moment, and Ni specifies a method for generating a spin estimation value such as ferromagnetism.

[0077] (Step S103) The model input information generation unit 13 generates model input information to be input to the prediction model based on the structural information acquired by the acquisition unit 11 and the spin estimates (initial spin estimates) generated by the initial spin generation unit 12. For example, the model input information generation unit 13 vectorizes the structural information and the spin estimates to generate information to be input to the prediction model, i.e., feature quantities. The generation of feature quantities may be performed, for example, for each atom or each bond between atoms, and may be expressed as a directed or undirected graph. This generation method is particularly effective when using a graph neural network, which will be described later.

[0078] Fig. 6 is a diagram showing an example of generating model input information. In the example shown in Fig. 6, the model input information is generated as an undirected graph. "Element" and "Coordinate" on the left side of Fig. 6 represent structural information acquired by the acquisition unit 11, and "Spin Estimate" represents the spin estimate generated by the initial spin generation unit 12. On the right side of Fig. 6, each element is represented by a node, and bonds between elements are represented by edges.

[0079] The feature (node ​​feature) of each atom can be, for example, a vector combining a one-hot vector indicating the element type and a magnetic moment. If the spin information is a scalar, it can be expanded using basis functions such as Gaussian functions and made multidimensional, which can be used as the feature of each atom.

[0080] The feature of the bond between atoms (edge ​​feature) can be, for example, a multidimensional feature obtained by expanding the distance between atoms using a basis function such as a Gaussian function. Whether or not atoms are bonded can be determined, for example, by whether or not two atoms exist within a specific cutoff radius.

[0081] (Step S104) The estimation unit 14 estimates physical property information related to the physical properties of the structure indicated by the structural information (i.e., the physical properties of the material) using the prediction model and the model input information generated by the model input information generation unit 13. For example, the estimation unit 14 uses a machine learning model trained in advance by machine learning as a prediction model to estimate the energy of the structure as the physical property information.

[0082] The machine learning model is not particularly limited, and may be a linear model, a support vector machine, a decision tree, a random forest, a gradient boosting regression tree, a Gaussian process regression, a neural network, etc. The prediction model may be a combination of these machine learning models.

[0083] The prediction model can be obtained by training a machine learning model using a training dataset that includes, for example, structural information, spin estimates, and physical property information. That is, the machine learning model learns the correspondence between the structural information and spin estimates as inputs and the physical property information as output. In this case, the physical property information can be, for example, physical property values ​​obtained by DFT calculations or physical property values ​​obtained through experiments.

[0084] Among machine learning models, neural networks can effectively represent nonlinearity or higher-order interactions and are easy to learn complex correspondences. In particular, graph neural networks, a type of neural network, are a suitable method when input data is provided as a graph structure. A graph structure is a data structure whose elements contain information about multiple nodes and one or more edges connecting them. By regarding nodes as atoms and edges as bonds between atoms, it is possible to represent molecular or crystalline structures while retaining their structural information. Graph neural networks use graph structures as input and can represent the three-dimensional arrangement of multiple atoms, making it easy to estimate physical property information with relatively high accuracy.

[0085] Here, examples of the physical properties include the energy of a structure, the force acting on an atom, the stress acting on a crystal lattice, the charge of an atom, or the band gap energy. Note that the physical properties are not limited to these. For example, the prediction model may be constructed to estimate any physical property for each structure, each atom, or each crystal lattice. As in the second embodiment described below, the prediction model may estimate second spin information as the physical property information. As in the third embodiment described below, the prediction model may estimate a result derived from the physical property of the structure as the physical property information.

[0086] (Step S105) The output unit 15 outputs the physical property information estimated by the estimation unit 14. Here, the output unit 15 outputs the physical property information estimated by the estimation unit 14 by displaying the physical property information on the display unit 3. At this time, the output unit 15 may output not only the physical property information but also structural information and a spin estimation value (initial spin estimation value). The output unit 15 may further output second spin information output in the second embodiment described below and structural information corresponding to the second spin information.

[0087] FIG. 7 is a diagram illustrating an example of information displayed on the display unit 3 by the output unit 15 of the physical property estimation system 100 according to the first embodiment. In the graph illustrated in FIG. 7 , the vertical axis represents the energy of the structure (i.e., physical property information), and the horizontal axis represents the setting information. The setting information includes structural information and first spin information acquired by the acquisition unit 11. In FIG. 7 , "Setting 1," "Setting 2," "Setting 3," and "Setting 4" each have the same structural information but different first spin information. In the balloon area illustrated in FIG. 7 , "initial spin" represents the initial spin estimate generated by the initial spin generation unit 12, and "final spin" represents the second spin information (see the second embodiment described below). The balloon area displays the structure indicated by the structural information (here, the positional relationship between Li, Ni, and O) and the spin state of each atom. Here, the magnitude and direction of the magnetic moment of each atom are represented by the size and direction of the arrow. Note that in the first embodiment, the "final spin" and structural information corresponding to the final spin are not displayed on the display unit 3.

[0088] By viewing the graph displayed on the display unit 3, the user can visually grasp the energy of the structure for each set information, in other words, the energy of the structure for each spin state. By selecting a point on the graph using a pointing device such as a mouse, the user can visually grasp the structural information and initial spin estimation value (and second spin information if displayed) corresponding to the point. In this way, by viewing the display unit 3, the user can easily and efficiently determine the atomic arrangement and spin state of an energetically stable structure.

[0089] (Embodiment 2) A physical property estimation system (physical property estimation method or program) according to embodiment 2 of the present disclosure will be described below. The physical property estimation system according to embodiment 2 differs from physical property estimation system 100 according to embodiment 1 in that estimation unit 14 estimates physical property information including second spin information. In addition, in the physical property estimation system according to embodiment 2, output unit 15 outputs physical property information including second spin information estimated by estimation unit 14, making it easier for the user to understand the physical properties of the material based on a more accurate spin state. Note that a block diagram of the physical property estimation system according to embodiment 2 is the same as the block diagram of physical property estimation system 100 according to embodiment 1 (see FIG. 1 ), and therefore a description thereof will be omitted here.

[0090] The operation of the physical property estimation system according to embodiment 2 will be described below. Fig. 8 is a flowchart showing an outline of the operation of the physical property estimation system according to embodiment 2. Note that steps S201 to S203 are similar to steps S101 to S103 (see Fig. 2) of the physical property estimation system 100 according to embodiment 1, respectively, and therefore will not be described here.

[0091] (Step S204) Unlike step S104 (see FIG. 2) of the physical property estimation system 100 according to the first embodiment, the estimation unit 14 estimates physical property information including second spin information using the model input information generated by the model input information generation unit 13 and a prediction model. Here, the second spin information, like the first spin information, is information regarding estimated values ​​of the spin states of multiple atoms in the structure indicated by the structural information. For example, the second spin information includes estimated values ​​such as the magnitude and direction of the magnetic moment of each atom. Hereinafter, in the description of step S204, the first spin information may be read as an initial spin estimation value.

[0092] The second spin information may be the same as or different from the first spin information. When the second spin information has information different from the first spin information, the second spin information may differ, for example, in at least one of the magnetic moment and direction of each atom in the first spin information. In this case, the relationship between the first spin information and the second spin information can be said to be similar to the relationship between the input information of the spin state and the output information of the calculated spin state in a DFT calculation.

[0093] That is, in the DFT calculation, for example, structural information and the magnetic moment and direction of each atom are used as input information, and the energy of the structure indicated by the structural information and the magnetic moment and direction of each atom in a state where the electronic state has converged are calculated as output information. Here, the magnetic moment in the input information and the magnetic moment in the output information are generally different, and the magnetic moment in the input information is optimized in the DFT calculation. The estimation unit 14 in the second embodiment is similar to the DFT calculation in that it outputs second spin information based on the input first spin information (or initial spin estimate value). Although the processing is different from the DFT calculation, it performs an optimization process for the input information of the spin state. Therefore, even if the spin state of each atom indicated by the first spin information is an estimated value different from the actual value, the estimation unit 14 can output the second spin information using a prediction model, thereby obtaining the spin state of each atom with higher accuracy than the first spin information, or even with the same accuracy as when performing a DFT calculation.

[0094] As with the prediction model used in embodiment 1, any model can be used as the prediction model used in embodiment 2. In particular, a neural network or graph neural network, which can describe complex input-output relationships and easily obtain multiple outputs, may be used as the prediction model.

[0095] The prediction model used in the second embodiment can be obtained by training a machine learning model using a training data set including, for example, structural information, input spin information, output spin information, and energy (physical property information) so as to optimize the parameters of the machine learning model so that the energy and output spin information match the correct values ​​of the training data. Here, the input spin information can be a spin estimated value (initial spin estimated value), and the output spin information can be second spin information.

[0096] In this case, the predictive model may have equivariance. Equivariance is a property in which the output values ​​are subjected to a similar operation when an operation is applied to input data, and plays an important role in fields such as image recognition, physics, and chemistry. Mathematically, a transformation Φ having equivariance satisfies the property shown in Equation 1 below.

[0097]

[0098] In other words, if the result obtained by applying an operation g to an input x and then executing a transformation Φ is the same as the result obtained by applying the transformation Φ to the input x and then applying an operation π(g) corresponding to the operation g in the transformed vector space, then the transformation Φ is equivariant to the operation g.

[0099] In this case, if the operation π(g) represents an identity transformation, the transformation Φ has invariance. In other words, this refers to the case where the output of the transformation Φ is the same regardless of the presence or absence of the operation g. Invariance is a special case of isovariance and is included in isovariance.

[0100] Here, in estimating the physical properties of a material, it is extremely important that the prediction model has isovariance in order to obtain physically reasonable output. For example, consider how a transformation (prediction model) that calculates the energy of an input structure and the forces acting on atoms should change with respect to the rotation of the input structure. For example, even if the entire structure is rotated, the energy of the structure does not change. Therefore, a prediction model that estimates energy may be invariant with respect to the rotation of the input structure. On the other hand, when viewed in the same coordinate system, the forces acting on atoms rotate in the same way with respect to the rotation of the input structure. Therefore, a prediction model that estimates the forces acting on atoms may have isovariance with respect to the rotation of the input structure. In this way, a prediction model may have isovariance according to the physical properties to be estimated.

[0101] A predictive model with homogeneity can process multiple data sets that are identical when rotated, for example, using the same parameters. Therefore, data efficiency is high when generating predictive models with homogeneity through machine learning. In particular, in a physical property estimation system such as that disclosed herein, the inputs are variables in three-dimensional space, providing a high degree of freedom, and it is therefore important to improve data efficiency when generating predictive models through machine learning.

[0102] The prediction model may use the three-dimensional special Euclidean group SE(3) to incorporate the isovariance for rotation and translation operations on the input structure, or may further use the three-dimensional Euclidean group E(3) to incorporate the isovariance for reflection operations, thereby enabling efficient construction of the prediction model.

[0103] Furthermore, the prediction model may have a homovariant with respect to the input first spin information. Here, homovariant includes not only rotation, translation, and mirroring operations, but also sign (direction) inversion operations. For example, if an operation that inverts only the direction of the magnetic moment without changing the magnitude of the magnetic moment is performed simultaneously on all atoms, the state before the operation and the state after the operation will be physically equivalent. Therefore, when estimating energy, the prediction model may be invariant with respect to the inversion of the first spin information. On the other hand, the second spin information may be homovariant because it undergoes a similar inversion with respect to the inversion of the first spin information. Note that the inversion homovariant of the first spin information is sometimes referred to as time-reversal homovariant.

[0104] The prediction model may have a variance that combines the variance of the input structure and the variance of the first spin information. That is, the prediction model may have a variance for an operation that combines the E(3) operation for the input structure and the inversion operation for the first spin information. This makes it possible to generate a prediction model that satisfies the property that, for example, the second spin information is invariant to the translation of the structure but is equivariant to the inversion of the first spin information.

[0105] (Step S205) The output unit 15 outputs the physical property information estimated by the estimation unit 14. Here, the output unit 15 outputs the physical property information by displaying the physical property information estimated by the estimation unit 14 on the display unit 3. At this time, the output unit 15 may output not only the physical property information but also structural information and a spin estimation value (initial spin estimation value). The output unit 15 may further output second spin information and structural information corresponding to the second spin information.

[0106] Here, the estimation unit 14 may estimate the second spin information through multiple processes. Specifically, intermediate spin information may be estimated instead of the second spin information output in step S204, and the model input information generation unit 13 may generate the model input information again using the intermediate spin information as input instead of the initial spin estimation value. The estimation unit 14 may then estimate the intermediate spin information again based on the regenerated model input information. This series of processes may be executed any number of times, for example, until a first convergence condition (described later) is satisfied. Then, the output unit 15 outputs the intermediate spin information when the first convergence condition is satisfied as the second spin information.

[0107] 9 is a flowchart showing an outline of the operation when the second spin information is output using the intermediate spin information. Note that steps S301 to S303 are the same as steps S201 to S203 (see FIG. 8), respectively, and therefore their explanation will be omitted here.

[0108] (Step S304) The estimation unit 14 estimates intermediate spin information using the model input information generated in step S303 and the prediction model. The intermediate spin information can be estimated using the same method as that used to estimate the second spin information. The intermediate spin information is not particularly limited, but may take the same format as the second spin information. Here, the intermediate spin information is assumed to be the magnetic moment and direction of each atom. Note that the intermediate spin information is different from the first spin information, but may be different from or the same as the second spin information. As will be described later, the intermediate spin information becomes the second spin information when the first convergence condition is satisfied.

[0109] (Step S305) The estimation unit 14 determines whether a first convergence condition is satisfied based on the intermediate spin information estimated in step S304, etc. Here, the first convergence condition is a condition for determining whether to further repeatedly estimate the intermediate spin information.

[0110] The first convergence condition may be, for example, a condition that does not use intermediate spin information, such as "a specified number of iterations has been reached," or a condition that uses intermediate spin information, such as "the difference from the intermediate spin information in the previous estimation is equal to or less than a threshold." Here, the first convergence condition is a condition that uses intermediate spin information. In this case, the first convergence condition may be, for example, a condition that calculates the difference between the magnitude of the magnetic moment estimated previously and the magnitude of the magnetic moment estimated this time for all atoms, and that the sum of the calculated differences is equal to or less than 0.1 μB.

[0111] If the first convergence condition is satisfied (step S305: Yes), step S307 is executed. In this case, the second spin information is set to the intermediate spin information estimated in the last executed step S304. On the other hand, if the first convergence condition is not satisfied (step S305: No), step S306 is executed.

[0112] (Step S306) The model input information generation unit 13 acquires the intermediate spin information estimated by the estimation unit 14 in step S304. Then, the model input information generation unit 13 executes step S303 again using the acquired intermediate spin information instead of the initial spin estimation value. In other words, the intermediate spin information has information similar to the initial spin estimation value, and the model input information generation unit 13 generates the model input information again using the structure information and the intermediate spin information.

[0113] At this time, because the intermediate spin information is different from the first spin information, the model input information is also different from the information obtained when the first spin information is used. Therefore, when the intermediate spin information is estimated again in step S304, information different from the intermediate spin information estimated using the first spin information is obtained. Then, based on the difference between these intermediate spin information, a determination is made again in step S305 as to whether the first convergence condition is satisfied. The above series of processes is executed until the first convergence condition is satisfied in step S305.

[0114] (Step S307) The output unit 15 outputs the final intermediate spin information as second spin information. The output method is the same as in step S205, and therefore will not be described here.

[0115] (Embodiment 3) A physical property estimation system 200 (physical property estimation method or program) according to embodiment 3 of the present disclosure will be described below. The physical property estimation system 200 according to embodiment 3 differs from the physical property estimation system 100 according to embodiment 1 in that it estimates an optimized structure based on the forces acting on each atom, etc.

[0116] Generally, multiple structures having different spin states have different stable structures. Here, a stable structure refers to a structure when the force acting on each atom converges to a value equal to or less than a certain value. In order to obtain a stable structure including the spin state for a certain structure, it is necessary to prepare multiple structures with different spin states, calculate all of the multiple stable structures for these multiple structures, and adopt the structure and spin state with the lowest energy among the multiple stable structures. In the property estimation system 200 according to the third embodiment, a stable structure including the spin state can be obtained by performing an optimization process on each of multiple structures having different spin states.

[0117] 10 is a block diagram showing the overall configuration including a physical property estimation system 200 according to embodiment 3. The physical property estimation system 200 according to embodiment 3 differs from the physical property estimation system 100 according to embodiment 1 in that the processing unit 10 further includes an atomic position optimization unit 17 and sequentially updates structural information. Note that, in the following, a description of the configuration common to the physical property estimation system 100 according to embodiment 1 will be omitted.

[0118] The atomic position optimization unit 17 updates the atomic positions in the structure based on the forces acting on each of the multiple atoms in the structure. The atomic position optimization unit 17 is the main body that executes the step of updating the atomic positions in the physical property estimation method of the present disclosure. Details of the processing executed by the atomic position optimization unit 17 will be described later.

[0119] The following describes the operation of the physical property estimation system 200 according to embodiment 3. Fig. 11 is a flowchart showing an outline of the operation of the physical property estimation system 200 according to embodiment 3. Note that steps S401 to S403 are similar to steps S101 to S103 (see Fig. 2) of the physical property estimation system 100 according to embodiment 1, respectively, and therefore will not be described here.

[0120] (Step S404) Unlike step S104 (see FIG. 2 ) of the physical property estimation system 100 according to embodiment 1, the estimation unit 14 estimates, as physical property information, the forces acting on each of the multiple atoms included in the structure, using the prediction model and the model input information generated by the model input information generation unit 13. To estimate the forces acting on each atom, for example, a method similar to the method used in step S104 can be used.

[0121] The force acting on each atom can be described as a vector acting on each atom in any coordinate system. For example, in a three-dimensional Cartesian coordinate system, each atom can be assigned a vector consisting of three components of forces along the coordinate axes.

[0122] If the structure is a crystalline structure, the estimation unit 14 may estimate the stress acting on the unit cell in addition to the force acting on each atom. In this case, it is possible to optimize the shape of the unit cell in addition to the position of each of the multiple atoms in the structure.

[0123] (Step S405) The estimation unit 14 determines whether a second convergence condition is satisfied based on the forces acting on each atom estimated in step S404. Here, the second convergence condition is a condition for determining whether to update the atomic positions. The second convergence condition may be, for example, that the maximum value of the magnitude of the vector of the forces acting on each atom is equal to or less than a threshold value.

[0124] If the second convergence condition is satisfied (step S405: Yes), step S407 is executed. On the other hand, if the second convergence condition is not satisfied (step S405: No), step S406 is executed.

[0125] (Step S406) The atomic position optimization unit 17 updates the atomic positions based on the forces acting on each atom estimated in step S404 by the estimation unit 14. At this time, if the structure is a crystalline structure, the atomic position optimization unit 17 may also update the shape of the unit cell, i.e., the lattice constant.

[0126] Here, the force acting on each atom is the gradient of the position of each atom relative to the energy of the structure. Therefore, the atom position optimization unit 17 can optimize the position of each atom using gradient information so as to minimize the energy. As an optimization algorithm, for example, the steepest descent method, Newton's method, quasi-Newton's method, conjugate gradient method, or derivatives of these methods can be used. For example, a moving average of the gradient may be used, or an algorithm such as Adagrad, Adadelta, or Adam, which adaptively changes the learning rate in accordance with changes in the gradient, may be used.

[0127] When the positions of multiple atoms are updated by the atomic position optimization unit 17, the structural information changes. The changed structural information is then used to generate model input information in step S403. At this time, the spin estimate used in step S403 may be the same value as before the structural information was changed, or may be changed in accordance with the changed structural information. Changing the spin estimate in the latter manner can be employed, for example, when the estimation unit 14 estimates intermediate spin information in step S404 as in the physical property estimation system according to embodiment 2 and uses the estimated intermediate spin information as the spin estimate. Then, using the newly generated model input information, the estimation unit 14 again estimates the force acting on each atom in step S404. Then, based on the estimated force acting on each atom, a determination is again made in step S405 as to whether the second convergence condition is satisfied. The above series of processes is executed until the second convergence condition is satisfied in step S305.

[0128] (Step S407) The output unit 15 outputs the final structural information as structural information. The output method is the same as that of step S105, and therefore a description thereof will be omitted here. Note that the output unit 15 may further output physical property information and spin estimation values ​​(initial spin estimation values ​​or second spin information) in addition to the structural information.

[0129] (Examples) Below, an example (Example 1) of the physical property estimation system 100 according to embodiment 1 and an example (Example 2) of the physical property estimation system according to embodiment 2 will be described, along with comparisons with an example (Comparative Example 1) of the physical property estimation system according to Comparative Example 1 and an example (Comparative Example 2) of the physical property estimation system according to Comparative Example 2.

[0130] 12 is a flowchart showing an outline of the operation of the physical property estimation system according to Comparative Example 1. The physical property estimation system according to Comparative Example 1 differs from the physical property estimation system 100 according to Embodiment 1 in that it does not include first spin information as an input.

[0131] 12, step S501 is the same as step S101 except that the first spin information is not acquired. Steps S502, S503, and S504 are the same as steps S103, S104, and S105, respectively, except that no processing is performed on the first spin information.

[0132] 13 is a flowchart showing an outline of the operation of the physical property estimation system according to Comparative Example 2. The physical property estimation system according to Comparative Example 2 differs from the physical property estimation system according to Embodiment 2 in that it estimates second spin information using only structural information as input without using first spin information.

[0133] 13, step S601 is the same as step S201 except that the first spin information is not acquired. Steps S602, S603, and S604 are the same as steps S203, S204, and S205, respectively, except that no processing is performed on the first spin information.

[0134] Example 1 First, an example (Example 1) of the physical property estimation system 100 according to the first embodiment will be described.

[0135] [Structure Generation] Seventeen structures composed of Ni and O and with a decomposition energy of 0.2 eV / atom or less were obtained from the Materials Project database. Random changes in atomic positions or random deformations of the unit cell were applied to each obtained structure, resulting in up to 100 structures for each. DFT calculations were performed on these structures in a ferromagnetic configuration and one or more antiferromagnetic configurations, and energy and DFT spin information were calculated. In other words, the energy in two or more spin states was calculated for one structure (three-dimensional atomic configuration). The DFT calculations were performed with the magnitudes of the initial magnetic moments of Ni and O set to "5.0" and "0.6," respectively. Through these processes, a total of 5,000 sets of structures, energy, and DFT spin information were created.

[0136] Here, in each of Example 1 and Comparative Example 1, the structures and energies of each set were used, and in each of Example 2 and Comparative Example 2, the structures, energies, and DFT spin information of each set were used.

[0137] [Assignment of First Spin Information (Initial Spin Estimate)] As in the DFT calculation, first spin information (initial spin estimate) was assigned to each structure. That is, an initial estimate of the magnetic moment (Ni: 5.0, O: 0.6) and its direction were assigned to each atom in each structure.

[0138] [Generation of model input information] For each atom, each structure was graphed using the element's one-hot vector and the displacement vector between neighboring atoms. Furthermore, model input information was generated for each structure by combining the first spin information with the node feature. To perform machine learning, the energy calculated by DFT calculation was prepared for each structure as a ground truth label.

[0139] [Construction of Prediction Model] A graph neural network was used as a machine learning model to learn the correspondence between the above model input information and the correct label (energy), and a prediction model used in the property estimation system 100 according to the first embodiment was constructed.

[0140] Next, a description will be given of an example (Example 2) of the physical property estimation system according to the embodiment 2. First, a structure was generated and first spin information (initial spin estimation value) was generated in the same manner as in Example 1.

[0141] [Generation of Model Input Information] Model input information was generated using the same process as in Example 1. To perform machine learning, energy calculated by DFT calculation and DFT spin information were prepared for each structure as ground truth labels.

[0142] [Construction of a Prediction Model] A graph neural network was used as a machine learning model to learn the correspondence between the above model input information and the correct labels (energy and DFT spin information), and a prediction model to be used in the property estimation system according to the second embodiment was constructed.

[0143] Comparative Example 1 Next, an example of a physical property estimation system according to Comparative Example 1 (Comparative Example 1) will be described. First, a structure was generated using the same process as in Example 1.

[0144] [Generation of model input information] For each atom, each structure was characterized using the element's one-hot vector and the displacement vector between neighboring atoms to generate model input information. To perform machine learning, the energy calculated by DFT calculation was prepared for each structure as a ground truth label.

[0145] [Construction of Prediction Model] A prediction model used in the physical property estimation system according to Comparative Example 1 was constructed by performing the same process as in Example 1 using the model input information and the correct label (energy).

[0146] Comparative Example 2 Next, an example of a physical property estimation system according to Comparative Example 2 (Comparative Example 2) will be described. First, a structure was generated using the same process as in Example 2.

[0147] [Generation of Model Input Information] Model input information was generated using the same process as in Comparative Example 1. To perform machine learning, energy calculated by DFT calculation and DFT spin information were prepared for each structure as ground truth labels.

[0148] [Construction of Prediction Model] A prediction model used in the property estimation system according to Comparative Example 2 was constructed by performing the same processing as in Example 2 using the model input information and the correct labels (energy and DFT spin information).

[0149] <Results> The following Table 1 compares the estimation errors of physical properties in each Example and each Comparative Example. Here, Mean Absolute Error (MAE) was used as an index of estimation error.

[0150]

[0151] From Table 1, it can be seen that the energy estimation errors in Example 1 and Example 2 are smaller than the energy estimation errors in Comparative Example 1 and Comparative Example 2. This is because Comparative Example 1 and Comparative Example 2 do not use the first spin information (initial spin estimation value) as input, and therefore the same energy is estimated for multiple structures that have the same atomic arrangement but different spin states. On the other hand, in Example 1 and Example 2, by using the first spin information as input, different energies can be estimated for each of the multiple structures, and therefore the energies of the structures can be estimated with high accuracy.

[0152] In Example 2, second spin information is further estimated. Here, the graph neural network used as a prediction model in Example 2 is updated with parameters so that DFT spin information can be estimated in addition to energy. That is, variables within the graph neural network have information on spin information corresponding to the DFT spin information and information on energy corresponding to the spin information. Therefore, in Example 2, even if the first spin information is an estimated value rather than an accurate value, the energy can be estimated with high accuracy.

[0153] Here, it can be seen that the estimation error of the second spin information is smaller in Example 2 than in Comparative Example 2. This is because Comparative Example 2 does not use the first spin information as an input, and therefore the user's prior knowledge regarding the spin state of each atom cannot be introduced into the prediction model. On the other hand, in Example 2, the user's prior knowledge regarding the spin state of each atom can be introduced into the prediction model via the first spin information, and therefore the second spin information can be estimated with high accuracy. Here, the first spin information is an estimated value regarding the magnitude and direction of the magnetic moment, and is a value that can be easily estimated, so the barriers to implementation are extremely small.

[0154] The execution time of the physical property estimation system in the present disclosure is extremely short, completing within approximately one second, depending on the scale of the structure. On the other hand, since DFT calculations require computational costs of several hours to several days, using DFT spin information as the first spin information (initial spin estimate) presents a significant barrier to implementation. The physical property estimation system in the present disclosure is characterized in that the first spin information can be an estimate, which eliminates the need for DFT calculations when estimating physical properties, enabling high-speed physical property estimation.

[0155] From the above results, it is difficult to improve the accuracy of estimating the physical properties of a material in a physical property estimation system that does not use the first spin information, as in Comparative Example 1 and Comparative Example 2. On the other hand, it is easy to improve the accuracy of estimating the physical properties of a material in a physical property estimation system that uses the estimated value of the spin information as the first spin information (initial spin estimated value), as in Example 1 and Example 2.

[0156] (Modifications) A physical property estimation system (physical property estimation method) according to one or more aspects of the present disclosure has been described above based on Embodiments 1 to 3, but the present disclosure is not limited to the above-mentioned Embodiments 1 to 3. Various modifications that would occur to those skilled in the art may be made to the above-mentioned Embodiments 1 to 3 without departing from the spirit of the present disclosure.

[0157] In the above first to third embodiments, each component may be configured with dedicated hardware, or may be realized by executing a software program suitable for each component. Each component may be realized by a program execution unit such as a CPU (Central Processing Unit) or a processor reading and executing a software program recorded on a recording medium such as a hard disk or semiconductor memory.

[0158] The following cases are also included in this disclosure:

[0159] (1) The at least one device is specifically a computer system comprising a microprocessor, a ROM (Read Only Memory), a RAM (Random Access Memory), a hard disk unit, a display unit, a keyboard, a mouse, etc. A computer program is stored in the RAM or hard disk unit. The at least one device achieves its function when the microprocessor operates in accordance with the computer program. Here, the computer program is composed of a combination of multiple instruction codes that indicate commands to a computer to achieve a predetermined function.

[0160] (2) Some or all of the components constituting at least one of the above devices may be configured as a single system LSI (Large Scale Integration). A system LSI is an ultra-multifunctional LSI manufactured by integrating multiple components on a single chip, and specifically, is a computer system configured to include a microprocessor, ROM, RAM, etc. A computer program is stored in the RAM. The system LSI achieves its functions by the microprocessor operating in accordance with the computer program.

[0161] (3) Some or all of the components constituting at least one of the above devices may be configured as an IC card or a standalone module that can be attached to the device. The IC card or module is a computer system configured from a microprocessor, ROM, RAM, etc. The IC card or module may include the above-mentioned ultra-multifunctional LSI. The IC card or module achieves its functions when the microprocessor operates in accordance with a computer program. This IC card or module may be tamper-resistant.

[0162] (4) The present disclosure may be embodied as the above-described methods, a computer program for implementing these methods on a computer, or a digital signal comprising the computer program.

[0163] The present disclosure may be a computer program or a digital signal recorded on a computer-readable recording medium, such as a flexible disk, a hard disk, a CD (Compact Disc)-ROM, a DVD, a DVD-ROM, a DVD-RAM, a BD (Blu-ray (registered trademark) Disc), or a semiconductor memory, or may be a digital signal recorded on such a recording medium.

[0164] The present disclosure may involve transmitting a computer program or a digital signal via a telecommunications line, a wireless or wired communication line, a network such as the Internet, or data broadcasting.

[0165] The program or digital signal may be recorded on a recording medium and transferred, or the program or digital signal may be transferred via a network or the like, so that the program or digital signal may be implemented by another independent computer system.

[0166] (Other) The aspects of the physical property estimation system, physical property estimation method, program, etc. in the present disclosure are not limited to the above-described embodiments. This disclosure also includes forms obtained by applying various modifications to each embodiment that a person skilled in the art would conceive, and forms realized by arbitrarily combining the components and functions of each embodiment within the scope of the present disclosure. Modifications of the embodiments of the present disclosure may be as follows.

[0167] (Variation a) A method executed by a computer, the method comprising: acquiring structural information including a plurality of sets of coordinates in a three-dimensional space that correspond one-to-one to a plurality of atoms included in a structure and elemental symbols of each of the plurality of atoms, and first spin information that indicates spin states corresponding to the plurality of atoms; determining a magnitude of a magnetic moment and a direction of the magnetic moment of each of the plurality of atoms based on the first spin information; determining physical property information regarding physical properties corresponding to the structure based on the structural information, the determined magnitude of the magnetic moment of each of the plurality of atoms, and the determined direction of the magnetic moment of each of the plurality of atoms; and outputting the determined physical property information, wherein the first spin information, the magnitude of the magnetic moment of each of the plurality of atoms, the direction of the magnetic moment of each of the plurality of atoms, and the physical property information are not determined using a density functional theory.

[0168] (Variation a) recites that "the first spin information, the magnitude of the magnetic moment of each of the plurality of atoms, the direction of the magnetic moment of each of the plurality of atoms, and the physical property information are not determined using density functional theory," thereby reducing unnecessary consumption of computer resources, i.e., reducing the amount of memory used and the amount of calculations performed by a computer.

[0169] (Variation b) A method according to (Variation a), wherein the plurality of atoms include a first atom represented by a first element symbol, a second atom represented by the first element symbol, a third atom represented by a second element symbol, and a fourth atom represented by the second element symbol, the first spin information includes information indicating a first magnitude of a first magnetic moment of the first atom, the first spin information includes information indicating a first direction of the first magnetic moment of the first atom, the first spin information does not include information indicating a second magnitude of a second magnetic moment of the second atom, the first spin information does not include information indicating a second direction of the second magnetic moment of the second atom, the first spin information includes information indicating a third magnitude of a third magnetic moment of the third atom, the first spin information includes information indicating a third direction of the third magnetic moment of the third atom, the first spin information does not include information indicating a fourth magnitude of a fourth magnetic moment of the fourth atom, and the first spin information includes information indicating a fourth direction of the fourth magnetic moment of the fourth atom, the determined magnitudes of the magnetic moments of each of the plurality of atoms include: a determined first magnitude of the magnetic moment of the first atom; a determined second magnitude of the magnetic moment of the second atom; a determined third magnitude of the magnetic moment of the third atom; and a determined fourth magnitude of the magnetic moment of the fourth atom; the determined directions of the magnetic moments of each of the plurality of atoms include: a determined first direction of the magnetic moment of the first atom; a determined second direction of the magnetic moment of the second atom; a determined third direction of the magnetic moment of the third atom; and a determined fourth direction of the magnetic moment of the fourth atom; the determined first magnitude is equal to the first magnitude; the determined second magnitude is equal to the first magnitude; the determined third magnitude is equal to the third magnitude; the determined fourth magnitude is equal to the third magnitude; and the determined first direction is equal to the first direction. the determined second direction is equal to the first direction, the determined third direction is equal to the third direction,The determined fourth direction is equal to the fourth direction, and the third direction is different from the fourth direction.

[0170] The above variant b is supported, for example, by FIG.

[0171] The present disclosure is useful for improving the accuracy of estimating the physical properties of materials.

[0172] REFERENCE SIGNS LIST 10 Processing unit 11 Acquisition unit 12 Initial spin generation unit 13 Model input information generation unit 14 Estimation unit 15 Output unit 16 Storage unit 17 Atomic position optimization unit 2 Input unit 3 Display unit 30 Display control unit 100, 200 Physical property estimation system

Claims

1. A physical property estimation system comprising: an acquisition unit that acquires structural information regarding a structure including the arrangement of multiple atoms in three-dimensional space and first spin information regarding the initial values ​​of the spin states of the multiple atoms in the structure; an estimation unit that estimates physical property information regarding the physical properties of the structure based on the structural information and the first spin information acquired by the acquisition unit; and an output unit that outputs the physical property information estimated by the estimation unit.

2. The physical property estimation system according to claim 1, wherein the acquisition unit acquires at least one of the valence and spin state of an element of one or more atoms among the plurality of atoms as the first spin information.

3. The physical property estimation system according to claim 1, wherein the acquisition unit acquires, as the first spin information, a method for generating the initial value for each of the plurality of atoms.

4. The physical property estimation system according to claim 1, wherein the acquisition unit acquires, as the first spin information, a constraint that limits the initial value of each of the plurality of atoms to within a specified range.

5. The physical property estimation system according to claim 1, wherein the estimation unit estimates the physical property information using a prediction model having isovariance that returns isovariant outputs in response to changes in inputs.

6. The physical property estimation system according to claim 5, wherein the prediction model has a variance corresponding to the physical property information of the estimation target.

7. The physical property estimation system according to claim 5, wherein the prediction model has the same degeneration as the first spin information.

8. The physical property estimation system according to claim 7, wherein the prediction model has a denaturation that combines a denaturation for the structural information and a denaturation for the first spin information.

9. A physical property estimation system according to any one of claims 1 to 5, wherein the estimation unit further estimates second spin information relating to spin states different from the initial values ​​of the spin states of the plurality of atoms in the first spin information.

10. The physical property estimation system according to claim 8, wherein the estimation unit outputs intermediate spin information relating to spin states that are different from the initial values ​​of the spin states of the plurality of atoms in the first spin information, and outputs the second spin information by further using the intermediate spin information at least once or more as input to the estimation unit in place of the first spin information.

11. A physical property estimation system according to any one of claims 1 to 5, further comprising an atomic position optimization unit that optimizes positions of the plurality of atoms in the structure based on the physical property information estimated by the estimation unit.

12. A physical property estimation system according to any one of claims 1 to 5, wherein the physical property information includes information on the energy of the structure.

13. A physical property estimation method comprising: a step of acquiring structural information regarding a structure including an arrangement of a plurality of atoms in three-dimensional space; a step of acquiring first spin information regarding initial values ​​of spin states of the plurality of atoms in the structure; a step of estimating physical property information regarding the physical properties of the structure by inputting the acquired structural information and the first spin information into a prediction model; and a step of outputting the estimated physical property information, wherein the prediction model is constructed to receive the structural information and the first spin information as input and to output the physical property information.

14. The physical property estimation method according to claim 13, wherein the prediction model is constructed to further output second spin information regarding spin states that are different from the initial values ​​of the spin states of the plurality of atoms in the first spin information, and the step of estimating physical property information further estimates the second spin information.

15. A program that causes a computer to execute the steps of: acquiring structural information regarding a structure including the arrangement of a plurality of atoms in three-dimensional space; acquiring first spin information regarding the initial values ​​of the spin states of the plurality of atoms in the structure; estimating physical property information regarding the physical properties of the structure by inputting the acquired structural information and the first spin information into a prediction model; and outputting the estimated physical property information, wherein the prediction model is constructed to receive the structural information and the first spin information as input and output the physical property information.

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