Estimation device, estimation method, training device, training method, program, and model generation method

Abstract

To construct an energy prediction model of a material system.SOLUTION: An estimate device comprises one or more memories, and one or more processors. The one or more processors input a vector about an atom, to a first network which extracts an atomic feature in a latent space from a vector about an atom, and estimate the feature of the atom in the latent space, via the first network.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to an estimation device, a training device, an estimation method, and a training method. [Background technology]

[0002] Quantum chemical calculations, such as first-principles calculations such as DFT (Density Functional Theory), are relatively reliable and easy to interpret because they calculate physical properties such as the energy of electronic systems from a chemical background. On the other hand, they take a long time to calculate and are difficult to apply to comprehensive material searches, so they are currently used for analysis to understand the characteristics of discovered materials. In response to this, the development of models to predict the physical properties of materials using deep learning technology has progressed rapidly in recent years.

[0003] However, as mentioned above, DFT requires a long calculation time. On the other hand, while models using deep learning technology can predict physical properties, existing models that allow input of coordinates have difficulty in increasing the number of atomic types, and also in simultaneously handling different states such as molecules and crystals, and their coexisting states. DISCLOSURE OF THEINVENTION

[0004] One embodiment provides an estimation apparatus and method that improves the accuracy of estimating physical properties of a material system, and a training apparatus and method thereof.

[0005] According to one embodiment, the estimation device includes one or more memories and one or more processors, which input vectors related to atoms to a first network that extracts features of the atoms in a latent space from the vectors related to the atoms, and estimate the features of the atoms in the latent space via the first network. [Brief description of the drawings]

[0006] [Figure 1] FIG. 1 is a schematic block diagram of an estimation device according to an embodiment. [Diagram 2]FIG. 2 is a schematic diagram of an atom feature acquisition unit according to an embodiment. [Diagram 3] FIG. 2 is a diagram showing an example of setting coordinates of molecules and the like according to an embodiment. [Figure 4] FIG. 2 is a diagram showing an example of obtaining graph data of molecules or the like according to an embodiment. [Diagram 5] FIG. 4 is a diagram showing an example of graph data according to an embodiment. [Figure 6] 4 is a flowchart showing a process of an estimation device according to an embodiment. [Figure 7] FIG. 1 is a schematic block diagram of a training device according to an embodiment. [Figure 8] FIG. 2 is a schematic diagram of a configuration for training an atom feature acquirer according to an embodiment. [Figure 9] FIG. 4 is a diagram showing an example of teacher data of physical properties according to an embodiment. [Figure 10] FIG. 13 is a diagram showing a state in which physical properties of atoms are trained according to an embodiment. [Figure 11] FIG. 2 is a schematic block diagram of a structural feature extraction unit according to an embodiment. [Figure 12] 1 is a flow chart illustrating a general training process according to one embodiment. [Figure 13] 1 is a flowchart showing a process for training a first network according to an embodiment. [Figure 14] FIG. 11 is a diagram showing an example of physical property values ​​based on the output of the first network according to an embodiment. [Figure 15] 11 is a flowchart showing a process for training the second, third, and fourth networks according to one embodiment. [Figure 16] FIG. 13 is a diagram showing an example of output of physical property values ​​according to an embodiment. [Figure 17] 1 illustrates an example implementation of an estimation device or a training device according to an embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0007] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. The drawings and the description of the embodiment are given by way of example only and are not intended to limit the present invention.

[0008] [Estimation device] 1 is a block diagram showing the functions of an estimation device 1 according to this embodiment. The estimation device 1 of this embodiment estimates and outputs physical property values ​​of an estimation target, which is a molecule or the like (hereinafter, molecules, molecules, and crystals are all referred to as molecules, etc.), from information on the type of atom, etc., coordinate information, and boundary condition information. This estimation device 1 includes an input unit 10, a storage unit 12, an atomic feature acquisition unit 14, an input information configuration unit 16, a structural feature extraction unit 18, a physical property prediction unit 20, and an output unit 22.

[0009] Necessary information such as the type and coordinates of atoms, which are estimation target information such as molecules, and boundary conditions, is input to the estimation device 1 via the input unit 10. In this embodiment, for example, information on the type, coordinates, and boundary conditions of atoms is described as being input, but the present invention is not limited to this and any information that defines the structure of a substance whose physical property values ​​are to be estimated may be used.

[0010] The coordinates of an atom are, for example, three-dimensional coordinates of the atom in absolute space or the like. For example, they may be coordinates in a coordinate system using a translationally invariant and rotationally invariant coordinate system. However, they are not limited to this, and may be coordinates using a coordinate system that can appropriately express the structure of an atom in an object such as a molecule to be estimated. By inputting the coordinates of the atom, it is possible to define the relative position of the atom in the molecule or the like.

[0011] The boundary condition is, for example, when obtaining the physical properties of a crystal to be estimated, the coordinates of atoms in a unit lattice or a supercell in which unit lattices are repeatedly arranged are input, and in this case, the input atoms are set as boundary surfaces with a vacuum, or the same atomic arrangement is repeated adjacently. For example, when a molecule is brought close to a crystal that serves as a catalyst, a boundary condition may be assumed in which the crystal surface in contact with the molecule is a boundary with a vacuum, and the crystal structure is otherwise continuous. In this way, the estimation device 1 is capable of estimating not only physical properties of molecules, but also physical properties of crystals, physical properties related to both crystals and molecules, etc.

[0012] The storage unit 12 stores information required for the estimation. For example, data used for the estimation input via the input unit 10 may be temporarily stored in the storage unit 12. Parameters required in each unit, such as parameters required to form a neural network provided in each unit, may also be stored. In addition, when the estimation device 1 specifically realizes information processing by software using hardware resources, programs, executable files, etc. required for this software may be stored.

[0013] The atomic feature acquisition unit 14 generates a quantity indicating the atomic feature. The quantity indicating the atomic feature may be expressed in a one-dimensional vector format, for example. The atomic feature acquisition unit 14 includes a neural network (first network) such as an MLP (Multilayer Perceptron) that converts a one-hot vector indicating an atom into a vector in a latent space when the vector is input, and outputs the vector in the latent space as the atomic feature.

[0014] Alternatively, the atomic feature acquisition unit 14 may receive other information, such as a tensor or vector, indicating an atom, instead of a one-hot vector. The other information, such as a one-hot vector, tensor, or vector, may be, for example, a code indicating an atom of interest, or information similar thereto. In this case, the input layer of the neural network may be formed as a layer having a dimension different from that using the one-hot vector.

[0015] The atomic feature acquisition unit 14 may generate a feature for each estimation, or as another example, may store the estimation results in the storage unit 12. For example, features may be stored in the storage unit 12 for frequently used atoms such as hydrogen atoms, carbon atoms, and oxygen atoms, and features may be generated for other atoms for each estimation.

[0016] When the input information construction unit 16 receives the input atomic coordinates, boundary conditions, and atomic features generated by the atomic feature acquisition unit 14 or features that distinguish similar atoms, it converts the structure of the molecule, etc. into a graph format and makes it compatible with the input of a network that processes graphs provided in the structural feature extraction unit 18.

[0017] The structural feature extraction unit 18 extracts structural features from the graph information generated by the input information configuration unit 16. The structural feature extraction unit 18 includes a graph-based neural network such as a GNN (Graph Neural Network) or a GCN (Graph Convolutional Network).

[0018] The physical property prediction unit 20 predicts and outputs physical property values ​​from the structural features of the estimation target, such as molecules, extracted by the structural feature extraction unit 18. The physical property prediction unit 20 includes a neural network, such as an MLP. The characteristics of the neural network may differ depending on the physical property value to be obtained. For this reason, a plurality of different neural networks may be prepared, and one of them may be selected according to the physical property value to be obtained.

[0019] The output unit 22 outputs the estimated physical property values. Here, the term "output" is a concept that includes both outputting to the outside of the estimation device 1 via an interface and outputting to the inside of the estimation device 1, such as the storage unit 12.

[0020] Each component will now be described in more detail.

[0021] (Atom Feature Acquisition Unit 14) As described above, the atomic feature acquisition unit 14 includes a neural network that outputs a vector in a latent space when, for example, a one-hot vector indicating an atom is input. The one-hot vector indicating an atom is, for example, a one-hot vector indicating information on atomic nucleus information. More specifically, for example, the number of protons, the number of neutrons, and the number of electrons are converted into a one-hot vector. For example, by inputting the number of protons and the number of neutrons, isotopes can also be subject to feature acquisition. For example, by inputting the number of protons and the number of electrons, ions can also be subject to feature acquisition.

[0022] The input data may include information other than the above. For example, information such as atomic number, group in the periodic table, period, block, and half-life between isotopes may be provided as an input in addition to the one-hot vector. Also, the one-hot vector and another input may be combined as a one-hot vector in the atomic feature acquisition unit 14. For example, a discrete value may be stored in the one-hot vector, and a quantity (scalar, vector, tensor, etc.) in which a continuous value represents the quantity may be added as the input.

[0023] The one-hot vector may be generated separately by the user. As another example, a one-hot vector generating unit may be provided separately, which receives input such as an atomic name, an atomic number, and an ID indicating another atom, and generates a one-hot vector from this information by referring to a database in the atomic feature acquiring unit 14. When a continuous value is also given as an input, an input vector generating unit may be further provided, which generates a vector different from the one-hot vector.

[0024] The neural network (first network) provided in the atomic feature acquisition unit 14 may be, for example, an encoder part of a model trained by a neural network forming an encoder and a decoder. The encoder and decoder may be configured by, for example, a Variational Encoder Decoder that imparts variance to the encoder output in the same manner as a VAE (Variational Autoencoder). An example in which a Variational Encoder Decoder is used will be described below, but the present invention is not limited to the Variational Encoder Decoder, and any model such as a neural network that can appropriately acquire vectors in a latent space for atomic features, i.e., feature quantities, may be used.

[0025] 2 is a diagram showing the concept of the atomic feature acquisition unit 14. The atomic feature acquisition unit 14 includes, for example, a one-hot vector generation unit 140 and an encoder 142. The encoder 142 and a decoder described later are part of a network using the above-mentioned Variational Encoder Decoder. Although the encoder 142 is shown, other networks, calculators, and the like for outputting features may be inserted after the encoder 142.

[0026] The one-hot vector generating unit 140 generates a one-hot vector from a variable indicating an atom. When a value to be converted into a one-hot vector, such as the number of protons, is input, the one-hot vector generating unit 140 generates a one-hot vector using the input data.

[0027] When the input data is an indirect value such as an atomic number or an atomic name, the one-hot vector generation unit 140 generates a one-hot vector by acquiring a value such as the number of protons from, for example, a database inside or outside the estimation device 1. In this way, the one-hot vector generation unit 140 performs appropriate processing based on the input data.

[0028] In this way, when input information to be converted into a one-hot vector is directly input, the one-hot vector generation unit 140 converts each of the variables into a format suitable for a one-hot vector and generates a one-hot vector. On the other hand, when only the atomic number is input, the one-hot vector generation unit 140 may automatically obtain data required for conversion into a one-hot vector from the input data and generate a one-hot vector based on the obtained data.

[0029] In the above description, a one-hot vector is used for input, but this is described as an example, and the present embodiment is not limited to this. For example, a vector, matrix, tensor, etc. that does not use a one-hot vector can be input.

[0030] In addition, when a one-hot vector is stored in the memory unit 12, it may be obtained from the memory unit 12, and when a user prepares a one-hot vector separately and inputs it to the estimation device 1, the one-hot vector generation unit 140 is not a required component.

[0031] The one-hot vector is input to the encoder 142. The encoder 142 derives a vector z μ and vector z μ A vector σ indicating the variance of 2 The output is sampled from this output result to produce vector z. For example, during training, this vector z μ Reconstructing atomic features from

[0032] The atomic feature acquisition unit 14 extracts the generated vector z μto the input information configuration unit 16. It is also possible to use the reparametrization trick, which is used as one method of VAE. In this case, the vector z may be obtained as follows using a vector ε of random values. The symbol odot (a dot in a circle) indicates the product of each element of a vector.

number

[0033] As another example, z with no variance may be output as an atomic feature.

[0034] As described later, the first network is trained as a network including an encoder that extracts features when an atomic one-hot vector or the like is input, and a decoder that outputs physical property values ​​from the features. By using the appropriately trained atomic feature acquisition unit 14, it becomes possible to extract information required for predicting physical property values ​​of molecules, etc., by the network without the user having to select it.

[0035] By using such an encoder and decoder, more information can be utilized compared to the case of directly inputting physical property values, and it is advantageous in that the physical property values ​​required for all atoms can be used even if they are unknown. Furthermore, since the mapping is performed in a continuous latent space, atoms with similar properties are transferred closer to each other in the latent space, and atoms with different properties are transferred farther away, making it possible to interpolate between the atoms. Therefore, it is possible to output results by interpolating between atoms even if all atoms are not included in the training data, and it is possible to generate features that can output physical property values ​​with high accuracy even when the training data for some atoms is insufficient.

[0036] In this way, the atomic feature acquisition unit 14 is configured to include, for example, a neural network (first network) capable of extracting features that can decode the physical property values ​​of each atom. 2It is also possible to convert the dimension of a one-hot vector of the order of 1 to a feature vector of about 16 dimensions. In this way, the first network is configured with a neural network whose output dimension is smaller than the input dimension.

[0037] (Input information configuration section 16) The input information construction unit 16 generates a graph relating to the atomic arrangement and connections in a molecule, etc., based on the input data and the data generated by the atomic feature acquisition unit 14. The input information construction unit 16 considers the boundary conditions together with the structure of the input molecule, etc., determines whether there are adjacent atoms, and if there are adjacent atoms, determines the coordinates of the adjacent atoms.

[0038] For example, in the case of a single molecule, the input information constructing unit 16 generates a graph using the atomic coordinates indicated in the input as adjacent atoms. In the case of a crystal, for example, the coordinates of atoms in a unit lattice are determined from the input atomic coordinates, and the coordinates of the outer adjacent atoms of atoms located on the periphery of the unit lattice are determined from the repeating pattern of the unit lattice. In the case of an interface in a crystal, for example, the adjacent atoms are determined without applying the repeating pattern to the interface side.

[0039] 3 is a diagram showing an example of coordinate setting according to this embodiment. For example, when generating a graph of only a molecule M, the graph is generated from the types of the three atoms constituting the molecule M and their relative coordinates.

[0040] For example, when generating a graph of only a crystal having repetition and having an interface I, the graph is generated assuming the unit lattice C of the crystal to have a repetition C1 to the right, a repetition C2 to the left, a repetition C3 to the bottom, a repetition C4 to the bottom left, a repetition C5 to the bottom right, ... and assuming adjacent atoms for each atom. In the figure, the dotted line indicates the interface I, the unit lattice indicated by the dashed line indicates the structure of the inputted crystal, and the area indicated by the dashed line indicates the area assuming the repetition of the unit lattice C of the crystal. In other words, the graph is generated assuming adjacent atoms for each atom that constitutes the crystal within a range not exceeding the interface I.

[0041] When estimating the physical properties of a molecule acting on a crystal, such as a catalyst, a graph is generated by calculating the coordinates of adjacent atoms from each atom constituting the molecule and adjacent atoms from the lattice atoms constituting the crystal, assuming an iteration that takes into account the molecule M and the interface I of the crystal described above.

[0042] Since there is a limit to the size of the graph to be input, for example, the interface I, unit lattice C, and repetition of unit lattice C may be set so that molecule M is at the center. In other words, the unit lattice C may be repeated an appropriate number of times to obtain coordinates and generate a graph. To generate a graph, for example, the unit lattice C closest to molecule M is set as the center, and repetition of unit lattice C up, down, left, and right is assumed so as not to exceed the number of atoms that can be expressed by the graph within a range that does not exceed the interface, and the coordinates of each adjacent atom are obtained.

[0043] 3, one unit cell C of a crystal having an interface I for one molecule M is input, but this is not limited thereto. For example, there may be a plurality of molecules M, and a plurality of crystals may exist.

[0044] The input information construction unit 16 may also calculate the distance between the two atoms constructed as above, and the angle between the three atoms when a certain atom is set as a vertex. The distance and angle are calculated based on the relative coordinates of each atom. The angle is obtained, for example, by using the inner product of vectors or the cosine theorem. For example, the calculation may be performed for all combinations of atoms, or the input information construction unit 16 may determine a cutoff radius Rc, search for other atoms within the cutoff radius Rc for each atom, and calculate the combinations of atoms present within this cutoff radius Rc.

[0045] An index may be assigned to each of the constituent atoms, and the calculated results may be stored together with the combination of the indexes in the storage unit 12. When calculating, the structural feature extraction unit 18 may read these values ​​from the storage unit 12 at the timing when they are to be used, or the input information construction unit 16 may output these values ​​to the structural feature extraction unit 18.

[0046] In addition, although it is shown in two dimensions for ease of understanding, molecules and the like exist in three-dimensional space, and therefore the repetition conditions may be applied to the front and back sides of the drawing.

[0047] In this way, the input information configuration unit 16 generates a graph to be input to the neural network from the input information on molecules, etc. and the characteristics of each atom generated by the atomic characteristic acquisition unit 14.

[0048] (Structural feature extraction unit 18) As described above, the structural feature extraction unit 18 of this embodiment includes a neural network that receives graph information and outputs features related to the structure of the graph. The input graph features may include angle information.

[0049] The structural feature extraction unit 18 is designed to maintain an output that is invariant to, for example, the replacement of atoms of the same kind in the input graph, and the translation and rotation of the input structure. This is because the physical properties of real substances do not depend on these quantities. For example, by defining adjacent atoms and angles between three atoms as shown below, it is possible to input graph information that satisfies these conditions.

[0050] First, for example, the structural feature extraction unit 18 determines the maximum number of neighboring atoms Nn and the cutoff radius Rc, and obtains neighboring atoms for the atom A of interest (atom of interest). By setting the cutoff radius Rc, it is possible to eliminate atoms whose mutual influence is so small that it can be ignored, and to prevent too many atoms from being extracted as neighboring atoms. In addition, by performing graph convolution multiple times, it is possible to incorporate the influence of atoms outside the cutoff radius.

[0051] If the number of adjacent atoms is less than the maximum number of adjacent atoms Nn, dummy atoms of the same type as atom A are randomly placed far enough away from the cutoff radius Rc. If the number of adjacent atoms is greater than the maximum number of adjacent atoms Nn, for example, Nn atoms are selected in order of closest distance from atom A to be candidates for adjacent atoms. Considering such adjacent atoms, the combination of three atoms is as follows: Nn There are C2 ways. For example, if Nn=12, 12 C2 = 66 ways.

[0052] The cutoff radius Rc is related to the interaction distance of the physical phenomenon to be reproduced. In the case of a dense system such as a crystal, the cutoff radius Rc is 4 ~ 8 × 10 -8 Using cm makes it possible to ensure sufficient accuracy in many cases. On the other hand, when considering interactions between the crystal surface and molecules, or between molecules, the two are not structurally connected, so even repeated graph convolution cannot take into account the effects of distant atoms, and the cutoff radius becomes the maximum direct interaction distance. Even in this case, a cutoff radius Rc of 8 × 10 -8 It is possible to apply this by considering the distance cm and starting the initial shape from that distance.

[0053] The maximum number of neighboring atoms Nn is set to about 12 from the viewpoint of calculation efficiency, but is not limited to this. It is also possible to take into account the influence of atoms within the cutoff radius Rc that are not selected as the Nn neighboring atoms by repeating the graph convolution.

[0054] For one atom of interest, for example, the concatenation of the feature of the atom, the features of the two adjacent atoms, the distance between the atom and the two adjacent atoms, and the angle between the atom and the two adjacent atoms is used as one input set. The feature of this atom is used as the feature of the node, and the distance and angle are used as the feature of the edge. The edge feature can be used as it is, or it can be processed in a predetermined manner. For example, it can be used after binning to a specific width, or a Gaussian filter can be applied.

[0055] FIG. 4 is a diagram for explaining an example of how to obtain graph data. Consider the atom of interest as atom A. As in FIG. 3, it is shown in two dimensions, but more precisely, the atoms exist in a three-dimensional space. In the following explanation, it is assumed that the neighboring atom candidates for atom A are atoms B, C, D, E, and F, but the number of atoms is determined by Nn, and the neighboring atom candidates change depending on the structure of the molecule and the state in which they exist, so it is not limited to this. For example, if atoms G, H, etc. are further present, the following feature extraction, etc. are similarly performed within a range not exceeding Nn.

[0056] The dotted arrow pointing from atom A indicates the cutoff radius Rc. The dotted circle indicates the range from atom A to the cutoff radius Rc. The neighboring atoms of atom A are searched within this dotted circle. If the maximum number of neighboring atoms Nn is 5 or more, the neighboring atoms of atom A are determined to be atoms B, C, D, E, and F. In this way, edge data is generated not only for atoms that are connected in the structural formula, but also for atoms that are not connected in the structural formula within the range formed by the cutoff radius Rc.

[0057] The structural feature extraction unit 18 extracts a combination of atoms to obtain angle data with atom A as the apex. Hereinafter, a combination of atoms A, B, and C will be described as ABC. There are 5C2=10 combinations for atom A: ABC, ABD, ABE, ABF, ACD, ACE, ACF, ADE, ADF, and AEF. The structural feature extraction unit 18 may, for example, assign an index to each of these. The index may be focused on only atom A, or may be uniquely assigned in consideration of multiple atoms or all atoms. By assigning an index in this way, it becomes possible to uniquely specify a combination of an atom of interest and an adjacent atom.

[0058] For example, the index of the combination of A, B, and C is assumed to be 0. Graph data in which the combination of adjacent atoms is atom B and atom C, that is, graph data with index 0, is generated for atom B and atom C, respectively.

[0059] For example, for atom A, which is the atom of interest, atom B is the first adjacent atom and atom C is the second adjacent atom. As data on the first adjacent atom, the structural feature extraction unit 18 combines information on the characteristics of atom A, the characteristics of atom B, the distance between atoms A and B, and the angle between atoms B, A, and C. As data on the second adjacent atom, it combines information on the characteristics of atom A, the characteristics of atom C, the distance between atoms A and B, and the angle between atoms C, A, and B.

[0060] The distance between atoms and the angle between the three atoms may be calculated by the input information construction unit 16, or if the input information construction unit 16 has not calculated them, they may be calculated by the structural feature extraction unit 18. The distance and angle can be calculated by a method similar to that described for the input information construction unit 16. Furthermore, the timing of calculation may be dynamically changed, for example, by calculating in the structural feature extraction unit 18 when the number of atoms is greater than a predetermined number, and by calculating in the input information construction unit 16 when the number of atoms is less than the predetermined number. In this case, it may be determined which one to use for calculation, based on the state of resources such as memory and processor.

[0061] Hereinafter, the feature of atom A when focusing on atom A will be referred to as the node feature of atom A. In the above case, the data of the node feature of atom A is redundant, so it may be stored together. For example, the graph data of index 0 may be configured with information on the node feature of atom A, the feature of atom B, the distance between atoms A and B, the angles of atoms B, A, and C, the feature of atom C, the distance between atoms A and C, and the angles of atoms C, A, and B.

[0062] The distance between atoms A and B and the angles between atoms B, A, and C are collectively referred to as the edge feature of atom B, and similarly, the distance between atoms A and C and the angles between atoms C, A, and B are collectively referred to as the edge feature of atom C. Since the edge feature includes angle information, the quantity differs depending on the atom it is paired with. For example, the edge feature of atom B when the adjacent atoms for atom A are B and C has a different value from the edge feature of atom B when the adjacent atoms are B and D.

[0063] The structural feature extraction unit 18 generates data on all combinations of two adjacent atoms for all atoms in the same manner as the graph data for atom A described above.

[0064] FIG. 5 shows an example of the graph data generated by the structural feature extraction unit 18.

[0065] For the node features of atom A, which is the first atom or atom of interest, atomic features and edge features are generated for each combination of adjacent atoms that exist within a cutoff radius Rc from atom A. The horizontal connections in the diagram may be linked by indexes, for example. In the same way as neighboring atoms of atom A, the first atom of interest, were selected and features were obtained, features are also obtained for the combinations of second, third and higher adjacent atoms for atoms B, C, ..., as second, third and higher atoms of interest, respectively.

[0066] In this way, node features, as well as atomic features and edge features related to adjacent atoms are obtained for all atoms. As a result, the feature of the atom of interest is a tensor of (n_site, site_dim), the feature of the adjacent atom is a tensor of (n_site, site_dim, n_nbr_comb, 2), and the edge feature is a tensor of (n_site, edge_dim, n_nbr_comb, 2). Note that n_site is the number of atoms, site_dim is the dimension of the vector indicating the atomic feature, and n_nbr_comb is the number of combinations of adjacent atoms for the atom of interest (= Nn C2), edge_dim is the dimension of the edge feature. The neighboring atom feature and edge feature are obtained for each neighboring atom by selecting two neighboring atoms for the target atom, so they are tensors with twice the dimensions of (n_site, site_dim, n_nbr_comb) and (n_site, edge_dim, n_nbr_comb), respectively.

[0067] The structural feature extraction unit 18 includes a neural network that updates and outputs the atomic features and edge features when these data are input. That is, the structural feature extraction unit 18 includes a graph data acquisition unit that acquires data related to a graph, and a neural network that updates when the data related to the graph is input. This neural network includes a second network that outputs (n_site, site_dim)-dimensional node features from input data having a dimension of (n_site, site_dim + edge_dim + site_dim, n_nbr_comb, 2), and a third network that outputs (n_site, edge_dim, n_nbr_comb, 2)-dimensional edge features.

[0068] The second network comprises a network that reduces the dimensionality of a tensor having the characteristics of two neighboring atoms of an atom of interest to a (n_site, site_dim, n_nbr_comb, 1)-dimensional tensor when a tensor having the characteristics of the dimension-reduced neighboring atoms of the atom of interest is input, and a network that reduces the dimensionality of a tensor having the characteristics of the dimension-reduced neighboring atoms of the atom of interest to a (n_site, site_dim, 1, 1)-dimensional tensor when a tensor having the characteristics of the dimension-reduced neighboring atoms of the atom of interest is input.

[0069] The first-stage network of the second network converts the features of each neighboring atom of atom A, which is the atom of interest, when atoms B and C are neighboring atoms, into features for the combination of neighboring atoms B and C for atom A, which is the atom of interest. This network makes it possible to extract the features of the combination of neighboring atoms. For atom A, which is the first atom of interest, all combinations of neighboring atoms are converted into this feature. Furthermore, for atom B, which is the second atom of interest, the features are converted in the same way for all combinations of neighboring atoms. This network converts the tensor indicating the features of neighboring atoms from (n_site, site_dim, n_nbr_comb, 2) dimensions to (n_site, site_dim, n_nbr_comb, 1) dimensions.

[0070] The second-stage network of the second network extracts node features of atom A that have the features of neighboring atoms from the combination of atoms B and C, the combination of atoms B and D, ..., and the combination of atoms E and F for atom A. This network makes it possible to extract node features that take into account the combinations of neighboring atoms for the atom of interest. Furthermore, for atoms B, ..., node features that take into account all combinations of neighboring atoms are extracted in the same way. This network converts the output of the second-stage network from dimensions (n_site, site_dim, n_nbr_comb, 1) to dimensions (n_site, site_dim, 1, 1), which are equivalent to the dimensions of the node features.

[0071] The structural feature extraction unit 18 of this embodiment updates the node feature based on the output of the second network. For example, the output of the second network and the node feature are added together to obtain an updated node feature (hereinafter, referred to as an updated node feature) via an activation function such as tanh(). This process does not need to be provided separately from the second network in the structural feature extraction unit 18, and this addition and activation function process may be provided as a layer on the output side of the second network. The second network, like the third network described later, can reduce information that may be unnecessary for the finally obtained physical property value.

[0072] The third network is a network that outputs updated edge features (hereinafter, referred to as updated edge features) when edge features are input. The third network converts a (n_site, edge_dim, n_nbr_comb, 2)-dimensional tensor into a (n_site, edge_dim, n_nbr_comb, 2)-dimensional tensor. For example, by using a gate or the like, information that is unnecessary for the physical property value that is ultimately to be obtained is reduced. The third network having this function is generated by training the parameters using a training device described later. In addition to the above, the third network may further include a network having the same input / output dimensions as a second stage.

[0073] The structural feature extraction unit 18 of this embodiment updates the edge feature based on the output of the third network. For example, the output of the third network and the edge feature are added together to obtain an updated edge feature via an activation function such as tanh(). In addition, when multiple features for the same edge are extracted, the average value of these may be calculated to obtain a single edge feature. These processes do not need to be provided in the structural feature extraction unit 18 separately from the third network, and the addition and activation function processes may be provided as a layer on the output side of the third network.

[0074] Each of the second network and the third network may be formed by a neural network that appropriately uses, for example, a convolution layer, batch normalization, pooling, gate processing, activation function, etc. It is not limited to the above, and may be formed by MLP, etc. Also, for example, it may be a network having an input layer that can further input a tensor obtained by squaring each element of an input tensor.

[0075] As another example, the second network and the third network may be formed as one network, rather than being formed separately. In this case, when a node feature, a feature of an adjacent atom, and an edge feature are input, the second network and the third network are formed as a network that outputs an updated node feature and an edge feature according to the above example.

[0076] In this way, the structural feature extraction unit 18 generates data on the nodes and edges of the graph taking adjacent atoms into consideration based on the input information constructed by the input information construction unit 16, and updates the generated data to update the node features and edge features of each atom. The updated node features are node features that take adjacent atoms into consideration. The updated edge features are edge features obtained by deleting information that may be redundant information regarding the physical property value to be obtained from the generated edge features.

[0077] (Physical property prediction unit 20) As described above, the physical property prediction unit 20 of this embodiment includes a neural network (fourth network) such as MLP that predicts and outputs a physical property value when it receives features related to the structure of molecules, for example, update node features and update edge features. The update node features and update edge features may not only be input as they are, but may also be processed in accordance with the physical property value to be obtained as described later.

[0078] The network used for predicting the physical property may be changed depending on the nature of the physical property to be predicted. For example, when it is desired to obtain energy, the features are input to the same fourth network for each node, the obtained output is set as the energy of each atom, and the sum of the outputs is output as the total energy value.

[0079] When predicting properties between specific atoms, the updated edge features are input to a fourth network to predict the desired property value.

[0080] When predicting a physical property value determined from the entire input, the average, sum, etc. of the update node features is calculated, and this calculated value is input to the fourth network to predict the physical property value.

[0081] In this manner, the fourth network may be configured as a different network for a desired physical property value, in which case at least one of the second network and the third network may be formed as a neural network that extracts a feature quantity used to acquire the physical property value.

[0082] As another example, the fourth network may be formed as a neural network that outputs a plurality of physical property values ​​at the same time as its output, in which case at least one of the second network and the third network may be formed as a neural network that extracts features used to obtain the plurality of physical property values.

[0083] In this way, the second network, the third network, and the fourth network may be formed as neural networks with different parameters and layer shapes, etc. depending on the physical property values ​​to be obtained, and trained based on each of the physical property values.

[0084] The physical property prediction unit 20 appropriately processes the output from the fourth network based on the physical property value to be obtained, and outputs the result. For example, when the total energy is to be obtained, if the energy for each atom is obtained by the fourth network, the energy is summed and output. In the case of other examples, similarly, the value output by the fourth network is processed appropriately for the physical property value to be obtained, and the result is the output value.

[0085] The amount output by the physical property value prediction unit 20 is output to the outside or inside of the estimation device 1 via the output unit 22.

[0086] 6 is a flowchart showing the flow of processing by the estimation device 1 according to this embodiment. The overall processing by the estimation device 1 will be described with reference to this flowchart. Detailed descriptions of each step are given above.

[0087] First, the estimation device 1 of this embodiment accepts input of data via the input unit 10 (S100). The input information includes boundary conditions of molecules, structural information of molecules, and information of atoms constituting the molecules. The boundary conditions of molecules and structural information of molecules may be specified by relative coordinates of atoms, for example.

[0088] Next, the atomic feature acquisition unit 14 generates features of each atom constituting the molecule, etc., from the input information of the atoms used in the molecule, etc. (S102). As described above, various atomic features may be generated in advance by the atomic feature acquisition unit 14 and stored in the storage unit 12, etc. In this case, they may be read from the storage unit 12 based on the type of atom used. The atomic feature acquisition unit 14 acquires the atomic features by inputting the atomic information into a trained neural network provided within itself.

[0089] Next, the input information constructing unit 16 constructs information for generating graph information of molecules, etc., from the input boundary conditions, coordinates, and atomic characteristics (S104). For example, as shown in the example of FIG. 3, the input information constructing unit 16 generates information describing the structure of molecules, etc.

[0090] Next, the structural feature extraction unit 18 extracts structural features (S106). The extraction of structural features is performed by two processes: a process of generating node features and edge features for each atom of a molecule, etc., and a process of updating the node features and edge features. The edge feature includes information on the angle between two adjacent atoms with the atom of interest as the vertex. The generated node features and edge features are extracted as updated node features and updated edge features, respectively, via a trained neural network.

[0091] Next, the physical property prediction unit 20 predicts the physical property from the updated node features and the updated edge features (S108). The physical property prediction unit 20 outputs information from the updated node features and the updated edge features via the trained neural network, and predicts the physical property based on this output information.

[0092] Next, the estimation device 1 outputs the estimated physical property values ​​to the outside or inside of the estimation device 1 via the output unit 22 (S110). As a result, it becomes possible to estimate and output physical property values ​​based on information including information on the characteristics of atoms in the latent space and angle information between adjacent atoms in a molecule or the like taking into account boundary conditions.

[0093] As described above, according to this embodiment, graph data including node features including atomic features and edge features including angle information between two adjacent atoms are used based on boundary conditions, atomic arrangement in molecules, etc., and extracted atomic features, and updated node features and edge features including the features of adjacent atoms are extracted, and the physical property values ​​are estimated using the extraction results, making it possible to estimate physical property values ​​with high accuracy. Since atomic features are extracted in this way, the same estimation device 1 can be easily applied even when the number of types of atoms is increased.

[0094] In this embodiment, the output is obtained by combining differentiable operations. That is, the output estimation result can be traced back to the information of each atom. For example, when the total energy P in the input structure is estimated, the force acting on each atom can be calculated by calculating the differential of the input coordinates in the estimated total energy P. This differentiation can be performed without any problems because a neural network is used and, as will be described later, other operations are also performed by differentiable operations. By acquiring the force acting on each atom in this way, it is possible to perform structural relaxation using this force at high speed. In addition, for example, it is possible to calculate energy using coordinates as input and replace DFT calculation by N-th order automatic differentiation. Similarly, differential operations expressed in Hamiltonian etc. can also be easily acquired from the output of the estimation device 1, and various physical property analyses can be performed at high speed.

[0095] By using this estimation device 1, for example, it becomes possible to search for materials having desired physical properties, for various molecules, more specifically, for molecules having various structures, molecules including various atoms, etc. For example, it is also possible to search for catalysts having high reactivity with a certain compound.

[0096] [Training device] The training device according to this embodiment trains the above-mentioned estimation device 1. In particular, training is performed for neural networks provided in the atomic feature acquisition unit 14, the structural feature extraction unit 18, and the physical property prediction unit 20 of the estimation device 1. In this specification, training refers to generating a model that has a structure such as a neural network and is capable of producing an appropriate output for an input.

[0097] 7 is an example of a block diagram of the training device 2 according to this embodiment. The training device 2 includes an error calculation unit 24 and a parameter update unit 26 in addition to the atomic feature acquisition unit 14, input information configuration unit 16, structural feature extraction unit 18, and physical property prediction unit 20 included in the estimation device 1. The input unit 10, storage unit 12, and output unit 22 may be common to the estimation device 1, or may be unique to the training device 2. Detailed explanations of components that are the same as those in the estimation device 1 will be omitted.

[0098] The flow indicated by the solid lines is processing for forward propagation, and the flow indicated by the dashed lines is processing for backward propagation.

[0099] Training data is input to the training device 2 via the input unit 10. The training data includes input data and output data that serves as teacher data.

[0100] The error calculation unit 24 calculates the error between the teacher data and the output from each neural network in the atomic feature acquisition unit 14, the structural feature extraction unit 18, and the physical property prediction unit 20. The method of calculating the error for each neural network is not limited to the same calculation, and may be appropriately selected based on the parameters to be updated or the network configuration.

[0101] The parameter update unit 26 back-propagates the error in each neural network and updates the parameters of the neural network based on the error calculated by the error calculation unit 24. The parameter update unit 26 may compare the training data through all neural networks, or may update the parameters for each neural network using the training data.

[0102] Each module of the above-mentioned estimation device 1 can be formed by differentiable calculations. Therefore, it is possible to calculate the gradient in the order of the physical property value prediction unit 20, the structural feature extraction unit 18, the input information configuration unit 16, and the atomic feature acquisition unit 14, and it is possible to appropriately back-propagate errors in places other than the neural network.

[0103] For example, if you want to estimate the total energy as a physical property, (x i , y i , z i ) is the coordinate (relative coordinate) of the i-th atom, A is the atomic characteristic, and the total energy P = Σ i F i (x i , y i , z i , A i ) In this case, dP / dx i Since differential values ​​such as can be defined for all atoms, it becomes possible to back-propagate errors from the output to the calculation of the atomic characteristics in the input.

[0104] As another example, each module may be individually optimized. For example, the first network provided in the atomic feature acquisition unit 14 may be generated by optimizing a neural network that can extract physical property values ​​from one-hot vectors using atomic identifiers and physical property values. The optimization of each network will be described below.

[0105] (Atom Feature Acquisition Unit 14) The first network of the atom feature acquisition unit 14 can be trained to output a feature value when, for example, an atom identifier or a one-hot vector is input. As described above, this neural network may be one that uses, for example, a Variational Encoder Decoder based on a VAE.

[0106] 8 is an example of a network formation used for training the first network 146. For example, the first network 146 may use the encoder 142 portion of a variational encoder / decoder including an encoder 142 and a decoder 144.

[0107] The encoder 142 is a neural network that outputs features in the latent space for each type of atom, and is the first network used in the estimation device 1.

[0108] The decoder 144 is a neural network that outputs physical property values ​​when it receives the vector in the latent space output by the encoder 142. In this way, it is possible to train the encoder 142 by connecting the decoder 144 after the encoder 142 and performing supervised learning.

[0109] As described above, one-hot vectors representing the properties of atoms are input to the first network 146. This may include a one-hot vector generation unit 140 that generates a one-hot vector when an atomic number, an atomic name, or a value indicating the properties of each atom is input, as described above.

[0110] The data used as the teacher data may be, for example, various physical property values. These physical property values ​​may be obtained, for example, from a scientific chronology.

[0111] 9 is a table showing an example of physical property values. For example, the atomic properties listed in this table are used as training data for the output of the decoder 144.

[0112] In the table, the values ​​in parentheses are those calculated by the method described in the parentheses. The ionic radii are calculated from the first to fourth coordinates. As a specific example, for oxygen, the ionic radii are calculated for coordinates 2, 3, 4, and 6, in that order.

[0113] When a one-hot vector indicating an atom is input to a neural network having the encoder 142 and the decoder 144 shown in Fig. 8, optimization is performed so that the property shown in Fig. 9 is output, for example. In this optimization, the error calculation unit 24 calculates the loss between the output value and the teacher data, and the parameter update unit 26 executes backpropagation based on this loss, obtains a gradient, and updates the parameters. By performing optimization, the encoder 142 functions as a network that outputs a vector in a latent space from the one-hot vector, and the decoder 144 functions as a network that outputs a physical property value from the vector in the latent space.

[0114] The parameters are updated using, for example, a variational encoder / decoder. As described above, the reparameterization trick may be used.

[0115] After the optimization is completed, the neural network forming the encoder 142 is designated as the first network 146, and the parameters for the encoder 142 are obtained. The output value is, for example, z μ or a vector of variance σ 2 In addition, as another example, z μ and σ 2 and the structural feature extraction unit 18 of the estimation device 1 outputs both z μ and σ 2 In the case where random numbers are used, for example, a fixed random number table may be used so that the process can be back-propagated.

[0116] It should be noted that the physical property values ​​of the atoms shown in the table of FIG. 9 are merely an example, and it is not necessary to use all of these physical property values. Furthermore, physical property values ​​other than those shown in this table may be used.

[0117] When using various physical property values, a certain physical property value may not exist depending on the type of atom. For example, in the case of a hydrogen atom, the second ionization energy does not exist. In such a case, for example, optimization of the network may be performed assuming that this value does not exist. In this way, even if there is a non-existent value, it is possible to generate a neural network that outputs a physical property value. In this way, even if it is not possible to input all physical property values, the atomic feature acquisition unit 14 according to this embodiment can generate the features of the atom.

[0118] Furthermore, by generating the first network 146 in this way, the one-hot vector is mapped in a continuous space, so that atoms with similar properties are transferred to nearby atoms in the latent space, and atoms with significantly different properties are transferred to distant atoms in the latent space. Therefore, for atoms in between, even if the properties do not exist in the training data, the results can be output by interpolation. Also, even if there is insufficient training data for some atoms, it becomes possible to estimate the features.

[0119] The atomic feature vectors extracted in this manner can also be input to the estimation device 1. Even if the amount of learning data for some atoms is insufficient or missing during training of the estimation device 1, estimation can be performed by interpolating the interatomic features. In addition, the amount of data required for training can be reduced.

[0120] Fig. 10 shows some examples of features extracted by this encoder 142 decoded by the decoder 144. The solid line indicates the value of the teacher data, and what is shown with a variance for the atomic number is the output value of the decoder 144. The variance indicates the output value input to the decoder 144 with a variance for the feature vector based on the features and variance output by the encoder 142.

[0121] From top to bottom, the examples show the covalent radius using Pyykko's method, the van der Waals radius using UFF, and the second ionization energy. The horizontal axis is the atomic number, and the vertical axis is in the appropriate units for each.

[0122] The graph of sharing radius shows that good values ​​are output for the training data.

[0123] It can be seen that good values ​​are output for the training data for the van der Waals radius and second ionization energy as well. The values ​​deviate from the expected values ​​when the atomic number exceeds 100, but this is because the values ​​are not currently available as training data, and training is being carried out without the training data. This results in a large variance in the data, but a certain degree of value is output. Also, as mentioned above, it can be seen that the second ionization energy of the hydrogen atom does not exist, but is output as an interpolated value.

[0124] In this way, it can be seen that by using training data for the output of the decoder 144, the encoder 142 can accurately acquire features in the latent space.

[0125] (Structural feature extraction unit 18) Next, the training of the second and third networks in the structural feature extraction unit 18 will be described.

[0126] 11 is a diagram extracting a portion related to the neural network of the structural feature extraction unit 18. The structural feature extraction unit 18 of the present embodiment includes a graph data extraction unit 180, a second network 182, and a third network 184.

[0127] The graph data extraction unit 180 extracts graph data such as node features and edge features from input data on the structure of molecules, etc. This extraction does not require training if it is performed by a rule-based method that allows inversion.

[0128] However, a neural network may also be used to extract graph data. In this case, it is also possible to train a network including the second network 182, the third network 184, and the fourth network of the physical property prediction unit 20 together.

[0129] When the second network 182 receives the feature (node ​​feature) of the atom of interest and the feature of the adjacent atom output by the graph data extraction unit 180, it updates and outputs the node feature. This updating may be formed by a neural network that converts from a (n_site, site_dim, n_nbr_comb, 2) dimension to a (n_site, site_dim, n_nbr_comb, 1) dimensional tensor by sequentially applying a convolution layer, batch normalization, gates and other data, activation function, pooling, and batch normalization, then converts from a (n_site, site_dim, n_nbr_comb, 1) dimension to a (n_site, site_dim, 1, 1) dimension by sequentially applying a convolution layer, batch normalization, gates and other data, activation function, pooling, and batch normalization, and finally calculates the sum of the input node feature and this output to update the node feature via the activation function.

[0130] When the third network 184 receives the features of adjacent atoms and edge features output by the graph data extraction unit 180, it updates and outputs the edge features. For this update, for example, a convolution layer, batch normalization, gates and other data are divided and an activation function, pooling, and batch normalization are applied in order to convert, then a convolution layer, batch normalization, gates and other data are divided and an activation function, pooling, and batch normalization are applied in order to convert, and finally the edge feature input and this output are summed to update the edge feature via the activation function. For the edge feature, for example, a tensor of the same dimensions (n_site, site_dim, n_nbr_comb, 2) as the input is output.

[0131] The neural network thus formed can perform backpropagation of errors from the output to the input, since the processing in each layer is differentiable. Note that the above-mentioned network configuration is shown as an example, and is not limited to this, and any configuration may be used as long as the node features can be updated to appropriately reflect the features of adjacent atoms, and the calculations in each layer are substantially differentiable. "Substantially differentiable" refers to cases where the calculations are approximately differentiable, in addition to cases where the calculations are differentiable.

[0132] The error calculation unit 24 calculates an error based on the update node feature back-propagated by the parameter update unit 26 from the physical property prediction unit 20 and the update node feature output by the second network 182. The parameter update unit 26 updates the parameters of the second network 182 using this error.

[0133] Similarly, the error calculation unit 24 calculates an error based on the updated edge feature back-propagated by the parameter update unit 26 from the physical property prediction unit 20 and the updated edge feature output by the third network 184. The parameter update unit 26 updates the parameters of the third network 184 using this error.

[0134] In this way, the neural network provided in the structural feature extraction unit 18 is trained together with the training of the parameters of the neural network provided in the physical property value prediction unit 20 .

[0135] (Physical property prediction unit 20) The fourth network included in the physical property prediction unit 20 outputs a physical property value when the updated node feature and the updated edge feature output by the structural feature extraction unit 18 are input. The fourth network has a structure such as an MLP.

[0136] The fourth network can be trained in the same manner as in the training of a normal MLP, etc. The loss used may be, for example, Mean Absolute Error (MAE), Mean Square Error (MSE), etc. As described above, this error is backpropagated to the input of the structural feature extraction unit 18, thereby training the second network, the third network, and the fourth network.

[0137] The fourth network may have different forms depending on the physical property values ​​to be obtained (output). That is, the output values ​​of the second network, the third network, and the fourth network may be different based on the physical property values ​​to be obtained. Therefore, the fourth network may be in a form that can be appropriately obtained based on the physical property values ​​to be obtained, or may be trained.

[0138] In this case, the parameters of the second and third networks may be set to initial values ​​that have already been trained or optimized to obtain other physical property values. Also, a plurality of physical property values ​​to be output as the fourth network may be set, and in this case, training may be performed using the plurality of physical property values ​​simultaneously as teacher data.

[0139] As another example, the first network may also be trained by backpropagating to the atomic feature acquisition unit 14. Furthermore, instead of training the first network in combination with other networks from the beginning of training to the fourth network, transfer learning may be performed by training the first network in advance using the above-mentioned training method for the atomic feature acquisition unit 14 (for example, a variational encoder / decoder using the reparametrization trick), and then backpropagating from the fourth network through the third network and the second network to the first network. This makes it possible to easily obtain an estimation device that can obtain a desired estimation result.

[0140] Incidentally, the estimation device 1 equipped with the neural network thus obtained is capable of backpropagation from output to input. In other words, it is possible to differentiate the output data with respect to the input variable. From this, for example, it is also possible to know how the physical property value output by the fourth network changes by changing the coordinates of the input atoms. For example, if the physical property value of the output is potential, the positional differentiation is the force acting on each atom. Using this, it is also possible to perform optimization to minimize the energy of the input structure to be estimated.

[0141] The details of each neural network described above are trained as described above, but any commonly known training method may be used for the overall training. For example, any appropriate learning method such as loss function, batch normalization, training termination condition, activation function, optimization method, batch learning, mini-batch learning, online learning, etc. may be used.

[0142] FIG. 12 is a flow chart illustrating the overall training process.

[0143] The training device 2 first trains the first network (S200).

[0144] Next, the training device 2 trains the second network, the third network, and the fourth network (S210). At this timing, as described above, the training device 2 may also train up to the first network.

[0145] When the training is completed, the training device 2 outputs the parameters of each trained network via the output unit 22. Here, the output of parameters is a concept that includes outputting the parameters to the inside of the training device 2, such as storing the parameters in the storage unit 12 in the training device 2, in addition to outputting the parameters to the outside of the training device 2.

[0146] FIG. 13 is a flowchart showing the process of training the first network (S200 in FIG. 12).

[0147] First, the training device 2 accepts input of data to be used for training via the input unit 10 (S2000). The input data is stored, for example, in the storage unit 12 as necessary. Data required for training the first network are vectors corresponding to atoms, information required for generating one-hot vectors in this embodiment, and quantities indicating atomic properties corresponding to the atoms (for example, the amount of substance of the atom). The quantities indicating atomic properties are, for example, those shown in FIG. 9. Also, the one-hot vector itself corresponding to the atom may be input.

[0148] Next, the training device 2 generates a one-hot vector (S2002). If a one-hot vector is input in S2000, this process is not essential. In other cases, a one-hot vector corresponding to an atom is generated based on information that is converted into a one-hot vector, such as the number of protons.

[0149] Next, the training device 2 forward propagates the generated or input one-hot vector to the neural network shown in Fig. 8 (S2004). The one-hot vector corresponding to an atom is converted into a physical property value via the encoder 142 and the decoder 144.

[0150] Next, the error calculation unit 24 calculates the error between the physical property value output from the decoder 144 and the physical property value acquired from the scientific chronology or the like (S2006).

[0151] Next, the parameter update unit 26 back-propagates the calculated error and updates the parameters (S2008). The error back-propagation is performed up to the one-hot vector, i.e., the input of the encoder.

[0152] Next, the parameter update unit 26 judges whether the training is completed (S2010). This judgment is made based on a predetermined training end condition, for example, completion of a predetermined number of epochs, securing of a predetermined accuracy, etc. The training may be batch learning or mini-batch learning, but is not limited to these.

[0153] If the training is not completed (S2010: NO), the process from S2004 to S2008 is repeated. In the case of mini-batch learning, the process may be repeated by changing the data to be used.

[0154] If the training is completed (S2010: YES), the training device 2 outputs the parameters via the output unit 22 (S2012) and ends the process. Note that the output may be only the parameters related to the encoder 142, i.e., the parameters related to the first network 146, or the parameters of the decoder 144 may be output together. 2 It is converted from a one-hot vector with a dimension of order 1 to a vector representing features in a latent space with, for example, 16 dimensions.

[0155] FIG. 14 is a diagram showing the estimation result of the energy of a molecule, etc. by the structural feature extraction unit 18 and the physical property prediction unit 20 trained using the output of the first network of this embodiment as an input, and the estimation result of the energy of the same molecule, etc. by the structural feature extraction unit 18 and the physical property prediction unit 20 of this embodiment trained using the output related to atomic features of a comparative example (CGCNN: Crystal Graph Convolutional Networks, https: / / arxiv.org / abs / 1710.10324v2) as an input.

[0156] The figure on the left is based on a comparative example, and the figure on the right is based on the first network of this embodiment. In these graphs, the horizontal axis shows the values ​​obtained by DFT, and the vertical axis shows the values ​​estimated by each method. In other words, it is ideal for all values ​​to exist on the diagonal line from the bottom left to the top right, and the greater the variation, the lower the accuracy.

[0157] From these figures, it can be seen that the deviation from the diagonal is smaller than that of the comparative example, and more accurate physical property values ​​are output, that is, more accurate atomic features (vectors in the latent space) can be obtained. The MAE of each is 0.031 for the present embodiment and 0.045 for the comparative example.

[0158] Next, an example of the process for training the second network to the fourth network will be described. Fig. 15 is a flow chart showing an example of the process for training the second network, the third network, and the fourth network (S210 in Fig. 12).

[0159] First, the training device 2 acquires the characteristics of the atoms (S2100). This acquisition may be performed by the first network each time, or the characteristics of each atom estimated by the first network may be stored in advance in the storage unit 12 and this data may be read out.

[0160] Next, the training device 2 converts the atomic features into graph data via the graph data extraction unit 180 of the structural feature extraction unit 18, and inputs this graph data to the second network and the third network. The updated node features and updated edge features acquired by the forward propagation are processed if necessary and input to the fourth network, thereby forward propagating through the fourth network (S2102).

[0161] Next, the error calculation unit 24 calculates the error between the output of the fourth network and the teacher data (S2104).

[0162] Next, the parameter update unit 26 back-propagates the error calculated by the error calculation unit 24 to update the parameters (S2106).

[0163] Next, the parameter update unit 26 determines whether the training has been completed (S2108), and if it has not been completed (S2108: NO), it repeats the processes from S2102 to S2106, and if it has been completed, it outputs the optimized parameters (S2110) and ends the process.

[0164] When the first network is trained using transfer learning, the process of FIG. 15 is performed after the process of FIG. 13. When the process of FIG. 15 is performed, the data acquired in S2100 is one-hot vector data. Then, in S2102, the data is forward propagated through the first network, the second network, the third network, and the fourth network. Necessary processes, for example, processes executed by the input information configuration unit 16, are also appropriately executed. Then, the processes of S2104 and S2106 are executed to optimize the parameters. For updating on the input side, the one-hot vector and the back-propagated error are used. In this way, by re-learning the first network, it is also possible to optimize the vector of the latent space acquired in the first network based on the physical property value that is ultimately desired to be acquired.

[0165] 16 shows an example of values ​​estimated by this embodiment and the above-mentioned comparative example for some physical properties. The left side is the comparative example, and the right side is this embodiment. The horizontal and vertical axes are the same as in FIG. 14.

[0166] As can be seen from this figure, the variation in values ​​is smaller in this embodiment than in the comparative example, and it is clear that the physical property values ​​can be estimated close to the results of DFT.

[0167] As described above, according to the training device 2 of this embodiment, the characteristics of atomic properties (physical properties) can be acquired as low-dimensional vectors, and further, by converting these acquired atomic characteristics into graph data including angle information and inputting them into a neural network, it is possible to perform highly accurate estimation of the physical properties of molecules, etc. by machine learning.

[0168] In this training, the architecture for feature extraction and property prediction is common, so the amount of training data can be reduced when increasing the number of atomic types. In addition, since it is sufficient to include atomic coordinates and the coordinates of adjacent atoms for each atom in the input data, it is possible to apply the method to various forms such as molecules and crystals.

[0169] The estimation device 1 trained by such a training device 2 can quickly estimate physical property values ​​such as energy of a system that has an arbitrary atomic arrangement, such as a molecule, a crystal, a pair of molecules, a pair of molecules, a crystal, or a crystal interface, as an input. In addition, since the physical property values ​​can be position-differentiated, it becomes possible to easily calculate the force acting on each atom. For example, in the case of energy, a huge amount of calculation time has been required to calculate various physical property values ​​using first-principles calculations, but it is now possible to calculate this energy quickly by forward propagating the trained network.

[0170] As a result, for example, it is possible to optimize the structure so as to minimize the energy, and by linking with a simulation tool, it is possible to speed up the calculation of the properties of various substances based on this energy and the differentiated force. Also, for example, for molecules in which the atomic arrangement has been changed, it is possible to estimate the energy quickly by simply changing the input coordinates and inputting them into the estimation device 1, without having to perform complex energy calculations again. As a result, it is easy to search for materials over a wide range by simulation.

[0171] A part or all of each device (estimation device 1 or training device 2) in the above-mentioned embodiment may be configured with hardware, or may be configured with information processing of software (program) executed by a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit) or the like. In the case of being configured with information processing of software, software for realizing at least a part of the functions of each device in the above-mentioned embodiment may be stored in a non-transient storage medium (non-transient computer-readable medium) such as a flexible disk, a CD-ROM (Compact Disc-Read Only Memory) or a USB (Universal Serial Bus) memory, and the software information processing may be executed by reading the software into a computer. The software may also be downloaded via a communication network. Furthermore, the software may be implemented in a circuit such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array), so that the information processing is executed by hardware.

[0172] There is no limitation on the type of storage medium that stores the software. The storage medium is not limited to removable media such as magnetic disks or optical disks, but may be fixed storage media such as hard disks or memory. The storage medium may be provided inside the computer or outside the computer.

[0173] 17 is a block diagram showing an example of a hardware configuration of each device (the estimation device 1 or the training device 2) in the above-mentioned embodiment. Each device may be realized as a computer 7 including a processor 71, a main storage device 72, an auxiliary storage device 73, a network interface 74, and a device interface 75, which are connected via a bus 76.

[0174] Although the computer 7 in FIG. 17 includes one of each component, it may include a plurality of the same components. Although one computer 7 is shown in FIG. 17, the software may be installed in a plurality of computers, and each of the plurality of computers may execute the same or different parts of the software. In this case, it may be in the form of distributed computing in which each computer executes the process by communicating via a network interface 74 or the like. That is, each device (estimation device 1 or training device 2) in the above-mentioned embodiment may be configured as a system in which one or more computers execute instructions stored in one or more storage devices to realize the function. Also, it may be configured such that information transmitted from a terminal is processed by one or more computers provided on a cloud, and the processing results are transmitted to the terminal.

[0175] Various calculations of each device (estimation device 1 or training device 2) in the above-mentioned embodiment may be executed in parallel using one or more processors, or using multiple computers via a network. Moreover, various calculations may be distributed to multiple computing cores in a processor and executed in parallel. Moreover, a part or all of the processes, means, etc. of the present disclosure may be executed by at least one of a processor and a storage device provided on a cloud that can communicate with a computer 7 via a network. Thus, each device in the above-mentioned embodiment may be in the form of parallel computing using one or more computers.

[0176] The processor 71 may be an electronic circuit (processing circuit, processing circuitry, CPU, GPU, FPGA, ASIC, etc.) including a computer control device and an arithmetic device. The processor 71 may also be a semiconductor device including a dedicated processing circuit. The processor 71 is not limited to an electronic circuit using electronic logic elements, and may be realized by an optical circuit using optical logic elements. The processor 71 may also include an arithmetic function based on quantum computing.

[0177] The processor 71 performs arithmetic processing based on data and software (programs) input from each device, etc., configured internally of the computer 7, and can output arithmetic results and control signals to each device, etc. The processor 71 may control each component constituting the computer 7 by executing the OS (Operating System) of the computer 7, applications, etc.

[0178] Each device (estimation device 1 and / or training device 2) in the above-described embodiment may be realized by one or more processors 71. Here, the processor 71 may refer to one or more electronic circuits arranged on one chip, or may refer to one or more electronic circuits arranged on two or more chips or devices. When multiple electronic circuits are used, the electronic circuits may communicate with each other by wire or wirelessly.

[0179] The main memory 72 is a memory device that stores instructions executed by the processor 71 and various data, and information stored in the main memory 72 is read by the processor 71. The auxiliary memory 73 is a memory device other than the main memory 72. These memory devices refer to any electronic components capable of storing electronic information, and may be semiconductor memories. The semiconductor memories may be either volatile memories or nonvolatile memories. The memory devices for saving various data in each device (estimation device 1 or training device 2) in the above-mentioned embodiments may be realized by the main memory 72 or the auxiliary memory 73, or may be realized by an internal memory built into the processor 71. For example, the memory unit 12 in the above-mentioned embodiments may be implemented in the main memory 72 or the auxiliary memory 73.

[0180] A plurality of processors may be connected (coupled) to one storage device (memory), or a single processor may be connected. A plurality of storage devices (memories) may be connected (coupled) to one processor. When each device (estimation device 1 or training device 2) in the above-mentioned embodiment is composed of at least one storage device (memory) and a plurality of processors connected (coupled) to this at least one storage device (memory), a configuration may be included in which at least one processor among the plurality of processors is connected (coupled) to at least one storage device (memory). This configuration may also be realized by storage devices (memories) and processors included in a plurality of computers. Furthermore, a configuration in which a storage device (memory) is integrated with a processor (for example, a cache memory including an L1 cache and an L2 cache) may be included.

[0181] The network interface 74 is an interface for connecting to the communication network 8 wirelessly or by wire. The network interface 74 may be one that complies with existing communication standards. The network interface 74 may exchange information with an external device 9A connected via the communication network 8.

[0182] The external device 9A includes, for example, a camera, a motion capture device, an output destination device, an external sensor, or an input source device. The external device 9A may include an external storage device (memory), for example, a network storage. The external device 9A may also be a device having some of the functions of the components of each device (the estimation device 1 or the training device 2) in the above-mentioned embodiments. The computer 7 may receive some or all of the processing results via the communication network 8 like a cloud service, or may transmit them to the outside of the computer 7.

[0183] The device interface 75 is an interface such as a USB that directly connects to the external device 9B. The external device 9B may be an external storage medium or a storage device (memory). The storage unit 12 in the above-described embodiment may be realized by the external device 9B.

[0184] The external device 9B may be an output device. The output device may be, for example, a display device for displaying an image, or a device for outputting sound or the like. Examples of the output device include, but are not limited to, an output destination device such as an LCD (Liquid Crystal Display), a CRT (Cathode Ray Tube), a PDP (Plasma Display Panel), an organic EL (Electro Luminescence) panel, a speaker, a personal computer, a tablet terminal, or a smartphone. The external device 9B may also be an input device. The input device includes a device such as a keyboard, a mouse, a touch panel, or a microphone, and provides information input by these devices to the computer 7.

[0185] In this specification (including the claims), the expression "at least one of a, b, and c" or "at least one of a, b, or c" (including similar expressions) includes any of a, b, c, ab, ac, bc, or abc. Also, it may include multiple instances of any element, such as aa, abb, aabbcc, etc. Furthermore, it also includes the addition of other elements other than the enumerated elements (a, b, and c), such as having d, as in abcd.

[0186] In this specification (including claims), expressions such as "using data as input / based on / according to / in response to data" (including similar expressions) include cases where various data itself is used as input, and cases where various data that have been processed in some way (e.g., noise-added, normalized, intermediate representation of various data, etc.) are used as input, unless otherwise specified. In addition, when it is stated that a result is obtained "based on / according to / in response to data," it includes cases where the result is obtained based only on the data, and may also include cases where the result is obtained by being influenced by other data, factors, conditions, and / or states other than the data. In addition, when it is stated that "data is output," it includes cases where various data itself is used as output, and cases where various data that have been processed in some way (e.g., noise-added, normalized, intermediate representation of various data, etc.) are output, unless otherwise specified.

[0187] In this specification (including the claims), the terms "connected" and "coupled" are intended as open-ended terms including any of direct connection / coupling, indirect connection / coupling, electrically connection / coupling, communicatively connection / coupling, functionally connection / coupling, physically connection / coupling, etc. The terms should be interpreted appropriately depending on the context in which the terms are used, but any connection / coupling form that is not intentionally or naturally excluded should be interpreted as being included in the terms without any restriction.

[0188] In this specification (including the claims), the expression "A configured to B" may include that the physical structure of element A has a configuration capable of performing operation B, and that the permanent or temporary setting / configuration of element A is configured / set to actually perform operation B. For example, when element A is a general-purpose processor, it is sufficient that the processor has a hardware configuration capable of performing operation B, and is configured to actually perform operation B by setting a permanent or temporary program (instruction). Also, when element A is a dedicated processor or dedicated arithmetic circuit, it is sufficient that the circuit structure of the processor is implemented to actually perform operation B, regardless of whether control instructions and data are actually attached.

[0189] Furthermore, in this specification (including claims), when multiple pieces of hardware of the same type perform a predetermined process, each of the multiple pieces of hardware may perform only a part of the predetermined process, may perform all of the predetermined process, or may not perform the predetermined process in some cases. In other words, when it is described that "one or multiple pieces of predetermined hardware perform a first process, and the hardware performs a second process," the hardware performing the first process and the hardware performing the second process may be the same or different.

[0190] For example, in this specification (including the claims), when multiple processors perform multiple processes, each of the multiple processors may perform only a part of the multiple processes, may perform all of the multiple processes, or in some cases may not perform any of the multiple processes.

[0191] Also, for example, in this specification (including the claims), when multiple memories store data, each of the multiple memories may store only a portion of the data, may store the entire data, or in some cases may not store any of the data.

[0192] In this specification (including the claims), terms implying containing or possessing (e.g., "comprising / including" and "having") are intended to be open-ended terms that include cases in which the term contains or possesses things other than the object indicated by the object of the term. When the object of such terms implies no quantity or a singular number (such as an article "a" or "an"), the expression should be construed as not being limited to a specific number.

[0193] In this specification (including the claims), even if expressions such as "one or more" or "at least one" are used in some places and expressions that do not specify a quantity or suggest a singular number (expressions using the articles a or an) are used in other places, the latter expressions are not intended to mean "one." In general, expressions that do not specify a quantity or suggest a singular number (expressions using the articles a or an) should be interpreted as not necessarily being limited to a specific number.

[0194] In this specification, when a particular advantage / result is described as being obtained from a particular configuration of an embodiment, it should be understood that the same effect can also be obtained from one or more other embodiments having the same configuration, unless there is a reason to the contrary. However, it should be understood that the presence or absence of the effect generally depends on various factors, conditions, and / or states, and that the effect is not necessarily obtained by the configuration. The effect is merely obtained by the configuration described in the embodiment when various factors, conditions, and / or states are satisfied, and the effect is not necessarily obtained in the invention according to the claim that specifies the configuration or a similar configuration.

[0195] In this specification (including the claims), the term "maximize" and the like include finding a global maximum, finding an approximation of a global maximum, finding a local maximum, and finding an approximation of a local maximum, and should be interpreted appropriately according to the context in which the term is used. It also includes finding approximations of these maxima probabilistically or heuristically. Similarly, the term "minimize" and the like include finding a global minimum, finding an approximation of a global minimum, finding a local minimum, and finding an approximation of a local minimum, and should be interpreted appropriately according to the context in which the term is used. It also includes finding approximations of these minima probabilistically or heuristically. Similarly, the term "optimize" and the like include finding a global optimum, finding an approximation of a global optimum, finding a local optimum, and finding an approximation of a local optimum, and should be interpreted appropriately according to the context in which the term is used. It also includes finding approximations of these optimums probabilistically or heuristically.

[0196] Although the embodiments of the present disclosure have been described in detail above, the present disclosure is not limited to the above-mentioned individual embodiments. Various additions, modifications, replacements, partial deletions, etc. are possible within the scope of the conceptual idea and intent of the present invention derived from the contents defined in the claims and their equivalents. For example, the numerical values ​​used in the explanations in all the above-mentioned embodiments are shown as examples and are not limited to these. In addition, the order of each operation in the embodiments is shown as an example and is not limited to these.

[0197] For example, in the above-described embodiment, the characteristic values ​​are estimated using the characteristics of the atoms, but information such as the temperature of the system, pressure, the charge of the entire system, and the spin of the entire system may also be taken into consideration. Such information may be input, for example, as a supernode connected to each node. In this case, by forming a neural network to which the supernodes can be input, it becomes possible to output an energy value or the like that further takes into consideration information such as temperature.

[0198] (Additional Note) Each of the above-described embodiments can be realized, for example, by using a program as follows. (1) When executed by one or more processors, inputting the vectors to a first network that extracts features of the atoms in a latent space from the vectors; Estimating features of atoms in a latent space via the first network; program. (2) When executed by one or more processors, Constructing a structure of the target atom based on the input atomic coordinates, atomic characteristics, and boundary conditions; Based on the structure, the distances between the atoms and the angles between the three atoms are obtained; updating the node features and the edge features using the features of the atoms as node features and the distance and the angle as edge features, and estimating the node features and the edge features; program. (3) When executed by the one or more processors, A vector indicating the properties of atoms included in a target is input to the first network according to any one of claims 1 to 7, and features of the atoms in a latent space are extracted; constructing a structure of the target atoms based on the coordinates of the atoms, the extracted atomic features in the latent space, and boundary conditions; inputting the atomic features and the node features based on the structure into the second network according to any one of claims 10 to 12 to obtain the updated node features; inputting the features of the atoms and the edge features based on the structure into the third network according to any one of claims 13 to 16 to obtain the updated edge features; The acquired updated node features and the updated edge features are input to a fourth network that estimates physical properties from node features and edge features, and a physical property value of the object is estimated. program. (4) When executed by one or more processors, inputting the vectors relating to atoms to a first network that extracts features of the atoms in a latent space from the vectors relating to the atoms; inputting the characteristics of the atoms in the latent space to a decoder that outputs physical property values ​​of the atoms when the characteristics of the atoms in the latent space are input, and estimating the property values ​​of the atoms; The one or more processors calculate an error between the estimated atomic property value and training data; Backpropagating the calculated error to update the first network and the decoder; outputting the parameters of the first network; program. (5) When executed by one or more processors, the method constructs a structure of the target atoms based on the input atomic coordinates, atomic characteristics, and boundary conditions; Based on the structure, the distances between the atoms and the angles between the three atoms are obtained; inputting information based on the atomic features, the distance, and the angle into a second network, which uses the atomic features as node features to obtain updated node features, and a third network, which uses the distance and the angle as edge features to obtain updated edge features; Calculating an error based on the updated node features and the updated edge features; Backpropagating the calculated error to update the second network and the third network. program. (6) When executed by one or more processors, the method includes: inputting vectors indicating properties of atoms included in a target to a first network that extracts atomic features in a latent space from vectors related to atoms; and extracting atomic features in a latent space. constructing a structure of the target atoms based on the coordinates of the atoms, the extracted atomic features in the latent space, and boundary conditions; Based on the structure, the distances between the atoms and the angles between the three atoms are obtained; The atomic features are used as node features to obtain updated node features; the atomic features and the node features based on the structure are input to a second network to obtain the updated node features; The distance and the angle are used as edge features to obtain updated edge features; the atomic features and the edge features based on the structure are input to a third network to obtain the updated edge features; The acquired updated node features and the updated edge features are input to a fourth network that estimates physical properties from node features and edge features, and a physical property value of the object is estimated; Calculating an error from the estimated physical property value of the object and teacher data; back-propagating the calculated error to the fourth network, the third network, the second network, and the first network, and updating the fourth network, the third network, the second network, and the first network; program. (7) The programs described in (1) to (6) may each be stored in a non-transitory computer-readable medium, and one or more processors may be configured to execute the methods described in (1) to (6) by reading one or more programs described in (1) to (6) stored in the non-transitory computer-readable medium. [Explanation of symbols]

[0199] 1: Estimation device, 10: Input section, 12: Storage part, 14: Atomic feature acquisition unit, 140: One-hot vector generation unit, 142: Encoder, 144: Decoder, 146: First Network, 16: Input information configuration unit, 18: Structural feature extraction unit; 180: Graph data extraction unit; 182: Second Network, 184: Third Network, 20: Physical property prediction unit, 22: Output section, 2: Training equipment, 24: Error calculation section, 26: Parameter update section

Claims

1. At least one storage device; At least one processor; The at least one processor Obtaining the characteristics of atoms contained in multiple atoms, generating a graph based on the information of the plurality of atoms; inputting the graph into a neural network to estimate physical property values ​​of the plurality of atoms; the at least one processor estimates the physical property by inputting the features into the neural network as node features of the graph. Estimation device.

2. the features are generated using a first neural network; The estimation device according to claim 1 .

3. The first neural network is a model trained using physical property values ​​of atoms as teacher data. The estimation device according to claim 2 .

4. the first neural network is the encoder in a trained neural network forming an encoder and a decoder; The estimation device according to claim 2 or 3.

5. The at least one processor generates a feature of the atom by inputting information of the atom included in the plurality of atoms into the first neural network. The estimation device according to any one of claims 2 to 4.

6. The atomic information included in the plurality of atoms includes at least one of nuclear information, the number of protons, the number of neutrons, the number of electrons, the atomic number, a group in the periodic table, a period, a block, a half-life between isotopes, an atomic name, an atomic number, and an atomic identifier. The estimation device according to claim 5 .

7. the at least one storage device storing a characteristic of the atom; the at least one processor obtains the atomic signature from the at least one storage device. The estimation device according to any one of claims 1 to 4.

8. The features are vectors in a latent space. An estimation device according to any one of claims 1 to 7.

9. The neural network comprises: a second neural network that receives at least the node feature and outputs an updated node feature; a third neural network that receives at least the edge features of the graph and outputs updated edge features; The estimation device according to any one of claims 1 to 8.

10. The configurations of the second neural network and the third neural network are determined based on the physical property values ​​to be estimated. The estimation device according to claim 9.

11. a fourth neural network that outputs the physical property value when at least the updated node feature and the updated edge feature are input. The estimation device according to claim 9 or 10.

12. The configuration of the fourth neural network is determined based on the physical property value to be estimated. The estimation device according to claim 11.

13. The fourth neural network outputs a plurality of the physical property values. The estimation device according to claim 11 or 12.

14. The edge features include information about distances and angles between atoms. An estimation device according to any one of claims 9 to 13.

15. The at least one processor generating the edge feature based on information about a target atom included in the plurality of atoms and information about a plurality of atoms present within a predetermined range from the target atom; An estimation device according to any one of claims 9 to 14.

16. The information on the plurality of atoms includes information on three-dimensional positional relationships of the plurality of atoms. An estimation device according to any one of the preceding claims.

17. The information on the three-dimensional positional relationship includes information on distances and angles between atoms. The estimation device according to claim 16.

18. The physical property value includes at least energy. An estimation device according to any one of the preceding claims.

19. The at least one processor calculates the force acting on each atom by position-differentiating the energy.

20. The estimation device according to claim 18.

20. the at least one processor uses backpropagation of the neural network to calculate the forces acting on each of the atoms; 20. The estimation device according to claim 19.

21. The at least one processor performs optimization to minimize the energy of the structure using the calculated forces acting on each atom. The estimation device according to claim 20.

22. the at least one processor generates the graph based on the types of the plurality of atoms, coordinate information of the plurality of atoms, and boundary conditions. An estimation device according to any one of the preceding claims.

23. The neural network is constructed to generate an output that is invariant to translations and rotations of the input structure. An estimation device according to any one of the preceding claims.

24. The neural network includes a graph-based configuration. An estimation device according to any one of the preceding claims.

25. The physical property value is estimated using an estimation device according to any one of claims 1 to 24. Estimation method.

26. 26. The method of claim 25, wherein the at least one processor is configured to perform the estimation method of claim 25. program.

27. At least one storage device; At least one processor; The at least one processor Obtaining the characteristics of atoms contained in multiple atoms, generating a graph based on the information of the plurality of atoms; inputting the graph into a neural network to estimate physical property values ​​of the plurality of atoms; Calculating an error between the estimated physical property value and teacher data; updating parameters of the neural network based on the error; the at least one processor estimates the physical property by inputting the features into the neural network as node features of the graph. training equipment.

28. The neural network comprises: a second neural network that receives at least the node feature and outputs an updated node feature; a third neural network that receives at least the edge features of the graph and outputs updated edge features; Including, the at least one processor updates parameters of the second neural network and parameters of the third neural network based on the error.

28. A training device according to claim 27.

29. a fourth neural network that outputs the physical property value when at least the updated node feature and the updated edge feature are input; the at least one processor updates parameters of the fourth neural network based on the error.

29. A training device according to claim 28.

30. The edge features include information about distances and angles between atoms.

30. Training device according to claim 28 or 29.

31. the features are generated using a first neural network; 31. A training device according to any one of claims 27 to 30.

32. The at least one processor generates a feature of the atom by inputting information of the atom included in the plurality of atoms into the first neural network.

32. A training device according to claim 31.

33. the at least one processor updates parameters of the first neural network based on the error.

33. A training device according to claim 31 or 32.

34. The at least one processor transfer trains the first neural network based on the error.

34. A training device according to claim 33.

35. The first neural network is an encoder of a neural network forming an encoder and a decoder, The at least one processor Calculating an error between an output value obtained by inputting training atomic information into a neural network forming the encoder and decoder and teacher data; updating parameters of neural networks forming said encoder and decoder based on said errors; 33. A training device according to claim 31 or 32.

36. The training atomic information includes at least one of the following: atomic nucleus information, the number of protons, the number of neutrons, the number of electrons, the atomic number, the group, period, block, and half-life between isotopes in the periodic table, the atomic name, the atomic number, and the atomic identifier; 36. A training device according to claim 35.

37. The features are vectors in a latent space.

37. A training device according to any one of claims 27 to 36.

38. The information on the plurality of atoms includes information on three-dimensional positional relationships of the plurality of atoms.

38. A training device according to any one of claims 27 to 37.

39. The information on the three-dimensional positional relationship includes information on distances and angles between atoms.

39. A training device according to claim 38.

40. The neural network includes a graph-based configuration.

40. A training device according to any one of claims 27 to 39.

41. Training the neural network using a training device according to any one of claims 27 to 40. Training method.

42. 42. causing the at least one processor to perform the training method of claim 41. program.

43. Generating the neural network using a training device according to any one of claims 27 to 40. Model generation method.

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