State estimation device, state estimation method, and state estimation program

Abstract

This state estimation device estimates a state of each point of a partial point group, which is a finite part of a point group structure in which one or more types of points spread infinitely through a space, by using, as input, a type and position of each point of the partial point group. The state estimation device includes: an acquisition unit that acquires a type and position of an input point as input information; and a state estimation unit that estimates a feature vector corresponding to the input information by a state estimation model that is a trained model obtained by machine learning a correspondence relationship between the type and position of a point in the partial point group and a feature vector representing a state of each point of the partial point group.

Description

State estimation device, state estimation method, and state estimation program

[0001] The present disclosure relates to a state estimation device, a state estimation method, and a state estimation program.

[0002] The materials that make up various materials, such as permanent magnets, superconductors, and batteries, are represented by a three-dimensional atomic arrangement pattern called a crystal structure. The physical properties of such materials, such as their formation energy and band gap, can be calculated by simulation based on the crystal structure. However, because simulations based on crystal structure require a significant amount of computational time, research is being conducted into methods for quickly predicting physical properties using machine learning models.

[0003] For example, Non-Patent Document 1 describes a method in which a machine learning model using a graph neural network (GNN) is used to repeatedly calculate interactions between atoms that are close to each other in a crystal structure in real space, calculate the atomic state as a feature vector, and predict physical property values, etc. based on the calculated feature vector.

[0004] Tian Xie and Jeffrey C. Grossman, "Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties", Phys. Rev. Lett. 120, 145301 Published 6 April 2018. Keqiang Yan, Yi Liu, Yuchao Lin, and Shuiwang Ji. Periodic graph transformers for crystal material property prediction. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh (eds.), Advances in Neural Information Processing Systems, volume 35, pp. 15066-15080. Curran Associates, Inc., 2022. Arthur Kosmala, Johannes Gasteiger, Nicholas Gao, Stephan Gunnemann (u with diaeresis), “Ewald-based Long-Range Message Passing for Molecular Graphs”, arXiv:2303.04791, 2023. Chengxuan Ying, Tianle Cai, Shengjie Luo, Shuxin Zheng, Guolin Ke, Di He, Yanming Shen, and Tie-Yan Liu. Do transformers really perform badly for graph representation? In Advances in Neural Information Processing Systems, volume 34, pp. 28877-28888. Curran Associates, Inc., 2021.

[0005] Interactions between atoms, such as Coulomb forces, exist that affect each other over relatively long distances within the unit lattice arrangement that constitutes a crystal. The methods described in Non-Patent Documents 1 and 2 have difficulty appropriately incorporating such long-distance interactions. Non-Patent Document 3 describes a method for incorporating long-range interactions by incorporating a Fourier transform into a GNN, but because it is composed of a GNN based on a finite graph structure, it does not directly formulate an infinitely expanding structure. Furthermore, Non-Patent Document 4 incorporates interactions between atoms in a molecular structure, but because a crystal structure is a structure that expands infinitely in space, this method cannot be applied to a crystal structure.

[0006] The present disclosure has been made in consideration of the above, and aims to provide a state estimation device, a state estimation method, and a state estimation program that are capable of appropriately reflecting interactions between each point that constitutes an infinitely expanding point cloud structure, both at short distances and long distances.

[0007] A state estimation device according to the present disclosure is a state estimation device that receives as input the type and position of each point in a point cloud portion, which is a finite portion of a point cloud structure in which one or more types of points extend infinitely in space, and estimates a state of each of the points in the point cloud portion. The state estimation device includes: an acquisition unit that acquires the input type and position of the point as input information; and a state estimation unit that estimates the feature vector corresponding to the input information using a state estimation model that is a learning model that has been machine-learned to determine a correspondence between the type and position of the point in the point cloud portion and a feature vector that represents a state of each of the points in the point cloud portion. The state estimation model has been machine-learned to estimate the feature vector based on a calculation result obtained by calculating an interaction between each of the points in the point cloud portion and other points in the point cloud structure, in real space, in an inverse space obtained by Fourier transforming the real space, or in both the real space and the inverse space, using a function that is defined to include an infinite series sum of an interaction function that attenuates the state of each of the points in the point cloud portion in accordance with the distance from the other points in the point cloud structure.

[0008] A state estimation method according to the present disclosure is a state estimation method for estimating a state of each of one or more points in a point cloud portion, which is a finite portion of a point cloud structure in which one or more types of points extend infinitely in space, by using as input the type and position of each of the points in the point cloud portion, the state estimation method including: an acquisition step of acquiring the input type and position of the point as input information; and a state estimation step of estimating the feature vector corresponding to the input information using a state estimation model, which is a learning model that has been machine-learned to determine a correspondence between the type and position of the point in the point cloud portion and a feature vector that represents a state of each of the points in the point cloud portion, wherein the state estimation model has been machine-learned to estimate the feature vector based on a calculation result obtained by calculating an interaction between each of the points in the point cloud portion and other points in the point cloud structure, in real space, in an inverse space obtained by Fourier transforming the real space, or in both the real space and the inverse space, using a function that is defined to include an infinite series sum of an interaction function that attenuates the state of each of the points in the point cloud portion in accordance with the distance from the other points in the point cloud structure.

[0009] A state estimation program according to the present disclosure is a state estimation program that receives as input the type and position of each point in a point cloud portion, which is a finite portion of a point cloud structure in which one or more types of points extend infinitely in space, and estimates a state of each of the points in the point cloud portion. The state estimation program causes a computer to execute an acquisition process that acquires the input type and position of the point as input information, and a state estimation process that estimates the feature vector corresponding to the input information using a state estimation model that is a learning model that has learned by machine learning a correspondence between the type and position of the point in the point cloud portion and a feature vector that represents the state of each of the points in the point cloud portion. The state estimation model has been machine-learned to estimate the feature vector based on a calculation result obtained by calculating, for each of the points in the point cloud portion, an interaction between each of the points in the point cloud portion and other points in the point cloud structure, in real space, in an inverse space obtained by Fourier transforming the real space, or in both the real space and the inverse space, using a function that is defined to include an infinite series sum of an interaction function that attenuates the state of each of the points in the point cloud portion in accordance with the distance from the other points in the point cloud structure.

[0010] According to the present disclosure, it is possible to provide a state estimation device, a state estimation method, and a state estimation program that can appropriately reflect interactions between each point that constitutes a point cloud structure at both short and long distances.

[0011] FIG. 1 is a diagram schematically illustrating an example of a state estimation device according to the present embodiment. FIG. 2 is a functional block diagram illustrating an example of a state estimation device according to the present embodiment. FIG. 3 is a diagram schematically illustrating an example of a state estimation model. FIG. 4 is a diagram schematically illustrating an example of processing in a self-attention layer. FIG. 5 is a diagram schematically illustrating an example of processing in a self-attention layer. FIG. 6 is a diagram illustrating an example of the arrangement of multiple self-attention blocks provided in a state estimation model. FIG. 7 is a diagram illustrating an example of the arrangement of multiple self-attention blocks provided in a state estimation model. FIG. 8 is a diagram illustrating an example of the arrangement of multiple self-attention blocks provided in a state estimation model. FIG. 9 is a diagram illustrating an example of the arrangement of multiple self-attention blocks provided in a state estimation model. FIG. 10 is a graph schematically illustrating an example of the magnitude of interaction between atoms calculated using multiple self-attention blocks. FIG. 11 is a flowchart illustrating an example of a state estimation method according to the present embodiment.

[0012] Hereinafter, embodiments of a state estimation device, a state estimation method, and a state estimation program according to the present disclosure will be described with reference to the accompanying drawings. Note that the present invention is not limited to these embodiments. Furthermore, the components in the following embodiments include those that are easily replaceable by a person skilled in the art, or those that are substantially identical.

[0013] FIG. 1 is a diagram schematically illustrating an example of a state estimation device 100 according to the present embodiment. FIG. 2 is a functional block diagram illustrating an example of the state estimation device 100 according to the present embodiment. The state estimation device 100 illustrated in FIGS. 1 and 2 estimates the state of each point in a point cloud portion, which is a finite portion of a point cloud structure in which one or more types of points extend infinitely in space. In this embodiment, an example of such a point cloud structure will be described, taking a substance having a three-dimensional crystalline structure as an example. In this case, each point represents an atom constituting the substance. Furthermore, the point cloud portion represents a unit lattice of the crystalline structure. As illustrated in FIG. 2, the state estimation device 100 includes a processing unit 10, a storage unit 20, and a communication unit 30.

[0014] The processing unit 10 performs various types of information processing. The processing unit 10 includes a processor such as a CPU (Central Processing Unit) and memories such as a ROM (Read Only Memory) and a RAM (Random Access Memory). The processing unit 10 includes an acquisition unit 11, a state estimation unit 12, and a physical property estimation unit 13.

[0015] The acquisition unit 11 acquires the type and position of the input point as input information. In this embodiment, for a substance whose state is to be estimated, configuration information indicating the arrangement in real space of atoms included in a unit lattice and a lattice vector in real space of the unit lattice are acquired as input information. The configuration information and the lattice vector can be input using, for example, an input device (not shown). The configuration information includes information on the type of atom and the position of the atom. The position information of the atom can be, for example, coordinates in a Cartesian coordinate system where the starting point of the lattice vector is the origin.

[0016] The state estimation unit 12 estimates a feature vector based on the input information (arrangement information, lattice vector) acquired by the acquisition unit 11. The feature vector is a vector that indicates, as a feature, the state of an atom included in a unit lattice of a substance based on interactions between the atom and other atoms of the substance in real space and interactions in reciprocal space. The reciprocal space is a space obtained by Fourier transforming the real space. The state estimation unit 12 estimates the feature vector using a state estimation model 40 described below. The state estimation unit 12 outputs the estimated feature vector.

[0017] The state estimation model 40 is machine-learned to estimate a feature vector based on the calculation results obtained by calculating the interactions between each atom of the unit cell and other atoms in the crystal structure in real space, in reciprocal space obtained by Fourier transforming the real space, or in both real space and reciprocal space, using a function defined to include an infinite series sum of interaction functions that attenuate the state of each atom of the unit cell depending on the distance from the other atoms in the crystal structure.

[0018] In the present embodiment, the principle of estimating the state of each atom in a finite structure (target structure) in an infinitely expanding structure will be described below. Let S be the atomic number of the infinite structure, S = {1, 2, 3, ...}, and let X be the type of atom in the structure S. ０ = {x １ ０ , x ２ ０ , x ３ ０ , ...}, and the position of an atom in the structure S is P = {p １ , p ２ , p ３ , ...}, and the type of atom X ０ and input information based on the atom position P is X = {x １ , x ２ , x ３ , ...}, and a part of S consisting of N finite atoms is defined as T⊂S. In the structure S, for atom i which is a target atom of the target structure T, the interaction function that decays depending on the distance from another atom j of the structure S is defined as f ｉｊ Let y be the feature vector indicating the state of atom i. ｉ Then, the feature vector y ｉ is the total interaction coefficient Zｉ and the total interaction vector a ｉ A function g that receives and returns a vector ｉ Using The input information X is expressed as, for example, X=NeuralNet(X ０ , P), and the type of atom X ０ and the atomic position P are vectorized by a neural network or a transformation function. ｉ , total interaction vector a ｉ teeth, The interaction function f ｉｊ If is always positive, then f ｉｊ The absolute value outside of can be omitted. Also, the interaction vector v from atom j to atom i ｉｊ teeth, where the interaction function f ｉｊ teeth, That is, the interaction function f ｉｊ is a decay function whose absolute value approaches 0 as the input value increases. ｉｊ is a vector (x ｉ , x ｊ ) and position (p ｉ , p ｊ ) may be additionally used. By setting a function including an infinite series sum of the interaction function as described above, the feature vector can be calculated appropriately.

[0019] When the infinite structure S is a periodic crystal structure, the type of atoms X ０ and the atomic position P is a finite basic repeating element S ｃｅｌｌ and D translation direction vectors L = {l １ , ..., l Ｄ}, a D-dimensional integer vector n, and i(n) which is an atom at a position moved by a D-dimensional translation Ln, The position P is obtained by infinitely repeating the unit lattice, which is the basic element arrangement, through translation operations based on D column vectors in the matrix L. The type and state of each atom are the same as those of the corresponding unit lattice. ｃｅｌｌ Then, the feature vector y of the target atom i is ｉ In this case, Z ｉ and a ｉ teeth, As described above, the target structure T is expressed as a unit cell S ｃｅｌｌ By setting the state of each target atom as the estimation target, y ｉ（ｎ） = y ｉ The periodicity of the lattice allows us to express the states of all atoms in the crystal structure.

[0020] Total interaction coefficient Z in real space ｉ and the total interaction vector a ｉ is the coordinate variable r = (x １ , …, x ｄ ), using where f' is ｉｊ , f´´ ｉｊ is an interaction function that takes into account periodicity and receives a D-dimensional vector, and f ｉｊ In a manner distinct from It is expressed as:

[0021] Total interaction coefficient Z in reciprocal space ｉ and the total interaction vector a ｉ is the spatial angular frequency vector ω ｍ Using the Fourier series expansion by where i (in bold) represents the imaginary unit. Also, the spatial angular frequency vector ω ｍ is an extension of the concept of angular frequency in a normal one-dimensional time axis to a D-dimensional space, In addition, the interaction function f', which takes periodicity into account, is expressed as follows: ｉｊ , f´´ ｉｊ F' is the Fourier coefficient of ｉｊ , F´´ｉｊ teeth, By calculating the interactions in the real space and the reciprocal space as described above, short-range interactions can be calculated efficiently in the real space, and long-range interactions can be calculated efficiently in the reciprocal space.

[0022] Here, the principle of state estimation according to this embodiment will be described when applied to a Transformer encoder. When the principle of state estimation according to this embodiment is applied to a Transformer encoder, in real space, a feature vector y ｉ teeth, Also, the interaction function f ｉｊ (r) is the query vector q ｉ , key vector k ｉ and the value vector v ｉ , and the radius σ that determines the attenuation range ｉ Using It is expressed as σ ｉ is defined as a constant. Alternatively, σ ｉ is the radius r that determines the scale of the attenuation range ０ Using the function ρ that returns a positive value and the learning parameters w (scalar) and w (bold, vector), or, The distance variable r is defined as follows: Also, the query vector q ｉ , key vector k ｉ and the value vector v ｉ is the learning parameter W of the state estimation model Ｑ , W Ｋ , W Ｖ Using Also, the interaction vector v ｉｊ is the constant W Ｇ and a K-dimensional one-hot vector b indicating the distance between the two atoms, The k-th element of the one-hot vector b is expressed as the maximum distance r that the one-hot vector b can express. ｍａｘ Using Also, the constant μｋ teeth, It is expressed as:

[0023] Furthermore, when the principle of state estimation according to this embodiment is applied to the encoder of the Transformer, in the inverse space, the feature vector y ｉ teeth, The interaction function f' is expressed as follows: ｉｊ F' is the Fourier coefficient of (r) ｉｊ (r) is the query vector q ｉ , key vector k ｉ and the value vector v ｉ The learning parameter w of the state estimation model (with a "-" sign above w) and the radius σ that determines the attenuation range ｉ bar ("σ ｉ " and "-" above it, It is expressed as σ ｉ The bar is defined by a constant, or σ ｉ The bar has a radius r that determines the scale of the attenuation range. ０ Bar ("r ０ "), a function ρ that returns a positive value, and learning parameters w (a "-" over "w", a scalar) and w (a "-" over a bold "w", a vector). or, etc. Also, the interaction function f' ｉｊ F', the Fourier coefficient of (r) ｉｊ (r) is Also, the query vector q ｉ , key vector k ｉ and the value vector v ｉ is the learning parameter W of the state estimation model Ｑ , W Ｋ , W Ｖ Using As described above, by applying the Transformer to the encoder, the feature vector can be calculated efficiently and accurately.

[0024] When the principle of state estimation according to this embodiment is applied to the Transformer encoder, the state estimation model 40 uses the learning parameter W Ｑ , W Ｋ , W Ｖ There are H different query vectors q ｉ , key vector k ｉ and the value vector v ｉ The interactions are calculated in parallel, and the calculation results are combined to obtain the feature vector y ｉ = (y ｉ １ , y ｉ ２ , ..., y ｉ Ｈ In this case, the state estimation unit 12 may input the feature vector estimated by the state estimation model to another neural network NN and calculate the output value X' as follows: X'=NN(y １ , y ２ , ..., y Ｎ In this case, the state estimation unit 12 uses X', which is the output value of the neural network NN, as input information, and calculates the function g ｉ The feature vector y ｉ As described above, the H kinds of query vectors q ｉ , key vector k ｉ and the value vector v ｉ Since the interaction can be calculated using these in parallel, the feature vector can be estimated with high accuracy while reducing the amount of calculation.

[0025] A specific example applying the above principle will be described below. The state estimation model 40 according to this embodiment estimates a feature vector using a QKV calculation configuration in an encoder of a deep learning model called a Transformer, which is used in, for example, language translation. In the state estimation model 40, the lattice vector, which is input information, is used as a token in the Transformer, and the configuration information (position) of each atom is used as information indicating the position of the token. The state estimation model 40 estimates a feature vector that takes into account interactions occurring between atoms using the QKV calculation configuration in the Transformer. The state estimation model 40 estimates a feature vector based on one or both of a function indicating interactions in real space and a function indicating interactions in reciprocal space. This allows for efficient estimation of a feature vector that takes into account both strong interactions occurring between atoms in close proximity and interactions that cannot be ignored even when the atoms are far apart. The state estimation model 40 is generated by connecting a feature vector output when certain input information is input to a neural network that estimates physical properties using the feature vector, and by performing learning using various well-known learning methods such as backpropagation so as to reduce the error between the predicted physical property value and the correct value.

[0026] FIG. 3 is a schematic diagram illustrating an example of a state estimation model 40 according to this embodiment. As shown in FIG. 3, the state estimation model 40 includes multiple self-attention blocks 41 that incrementally estimate feature vectors. The multiple self-attention blocks 41 may include, for example, a self-attention block or a multi-head attention block applied to the encoder of a deep learning model called a Transformer used in language translation. The self-attention block 41 includes a self-attention layer 41a and a transformation layer 41b. The self-attention block 41 may further include a multilayer perceptron (MLP). In this embodiment, by repurposing the configuration of the self-attention block 41 arranged in the Transformer encoder, it is possible to effectively incorporate both short-range and long-range interactions between atoms.

[0027] Next, an example of the processing in the self-attention layer 41a will be described. FIG. 4 is a diagram schematically illustrating an example of the processing in the self-attention layer 41a. As shown in FIG. 4, in the self-attention layer 41a, an input vector x (x １ , x ２ , ..., x ｉ , x ｎ ) is input, query q(q １ , q ２ , …, q ｉ , q ｎ ), key k(k １ , k ２ , ..., k ｊ , k ｎ ), value v(v １ , v ２ , …, v ｊ , v ｎ ) to generate the

[0028] The self-attention layer 41a calculates the input vector x ｉ Query q corresponding to ｉ Regarding the key k, the relevance q ｉ Ｔ k ｊCalculate the probability distribution p ｉ The self-attention layer 41a calculates the calculated probability distribution p ｉ Based on the value v ｊ The expected value y between ｉ Output y ｉ Let's say.

[0029] By providing multiple self-attention layers 41a, feature vectors can be estimated in stages.

[0030] A substance with a three-dimensional crystal structure has a structure in which unit cells are repeated multiple times in three dimensions. Therefore, the self-attention layer 41a determines a repeating pattern in which unit cells are repeated multiple times, and estimates a feature vector for each atom included in a reference unit cell of the repeating pattern based on the interaction between the atom and other atoms included in the repeating pattern. When determining a repeating pattern, the self-attention layer 41a can calculate the position information of atoms included in the repeating pattern based on the input position information.

[0031] 5 is a diagram showing an example of processing in the self-attention layer 41a. As shown in FIG. 5, for example, for atoms a, b, and c, an input vector x (x ａ , x ｂ , x ｃ ) is input, the self-attention layer 41a ａ , q ｂ , q ｃ ), key k(k ｉ ａ , k ｉ ｂ , k ｉ ｃ ), value v(v ｉ ａ , v ｉ ｂ , v ｉ ｃ The self-attention layer 41a generates position information P ｉ Ｋ , Pｉ Ｖ is calculated as preprocessing. ｉ Ｋ is the key k (k ｉ ａ , k ｉ ｂ , k ｉ ｃ ) is a vector to be added to the position information P ｉ Ｖ is the value v(v ｉ ａ , v ｉ ｂ , v ｉ ｃ ) is a vector to be added to the calculated position information P ｉ Ｋ , P ｉ Ｖ is added to the key k and the value v, respectively, and then a feature vector y is estimated. This makes it possible to appropriately reflect the interactions between atoms in a repeating pattern in which unit lattices are repeated multiple times. Note that a three-dimensional crystal structure is composed of unit lattices repeated multiple times, and the state of atoms in each unit lattice is the same for each unit lattice that is repeated. Therefore, the self-attention layer 41a calculates the feature vector y by using the states of atoms a, b, and c in the unit lattice (y ａ , y ｂ , y ｃ ) can be estimated. By using the states of atoms a, b, and c in the unit lattice as basic variables, the self-attention layer 41a can appropriately reflect the influence of the atoms (atoms located close and far away) that constitute the countless other unit lattices around the unit lattice of interest, by utilizing the positional information of the atoms and the property of the periodic arrangement of the unit lattice.

[0032] 6 to 9 are diagrams showing examples of arrangements of multiple self-attention blocks provided in a state estimation model.

[0033] 6 and 7 have multiple self-attention blocks 41, including a real-space attention block 42 and a reciprocal-space attention block 43. The real-space attention block 42 is a self-attention block that estimates feature vectors for atoms included in a unit lattice to be estimated based on interactions between other atoms in real space. When calculating interactions by finding repetitive patterns, the real-space attention block 42 performs processing in order from atoms with small interatomic distances to atoms with large interatomic distances.

[0034] The reciprocal space attention block 43 is a self-attention block that estimates feature vectors for atoms included in the unit lattice to be estimated based on interactions in reciprocal space with other atoms. The reciprocal space attention block 43 calculates reciprocal lattice vectors by Fourier transforming lattice vectors, and estimates feature vectors using the reciprocal lattice vectors. In the reciprocal space attention block 43, the variable corresponding to the interatomic distance becomes frequency. That is, the reciprocal space attention block 43 processes atoms in order from those with small interatomic frequencies to those with large interatomic frequencies. Therefore, the reciprocal space attention block 43 processes atoms in order from those with large interatomic distances in real space to those with small interatomic distances.

[0035] By providing the real space attention block 42 and the reciprocal space attention block 43 separately, it is possible to effectively reflect in the feature vector both the influence of the interaction between atoms with short interatomic distances and the influence of the interaction between atoms with long interatomic distances. Note that the learning parameters of the real space attention block 42 and the reciprocal space attention block 43 can be configured to be independently learned when training the state estimation model 40.

[0036] The state estimation models 40A and 40B are configured to alternately perform processing by the real space attention block 42 and processing by the inverse space attention block 43. The state estimation model 40A shown in Fig. 6 is configured to first perform processing by the real space attention block 42. The state estimation model 40B shown in Fig. 7 is configured to first perform processing by the inverse space attention block 43.

[0037] 8 is configured such that all of the multiple self-attention blocks 41 are real-space attention blocks 42, and no inverse-space attention block 42 is provided. The state estimation model 40C is configured to continuously perform processing using the real-space attention blocks 42. Note that the learning parameters of the real-space attention blocks 42 can be configured to be independently learned when the state estimation model 40 is trained.

[0038] The state estimation model 40D shown in FIG. 9 has a multi-head attention block 44 as the self-attention block 41. The multi-head attention block 44 estimates feature vectors in parallel for atoms included in the atomic unit lattice to be estimated based on their interactions with other atoms in real space and reciprocal space. A plurality of multi-head attention blocks 44 are provided. The plurality of multi-head attention blocks 44 estimate the feature vectors in stages. The learning parameters of the multi-head attention blocks 44 can be configured to be independently learned when the state estimation model 40 is trained.

[0039] The various self-attention blocks 41 (the real-space attention block 42, the reciprocal-space attention block 43, and the multi-head attention block 44) described above can be configured in various ways, for example, depending on the type of atoms constituting the substance to be estimated or the type of interaction occurring between atoms. Furthermore, when estimating a feature vector using a state estimation model and when training the state estimation model, any settings can be made depending on the allowable computational resources, required accuracy, and so on.

[0040] FIG. 10 is a graph showing an example of the magnitude of interaction between atoms calculated by multiple self-attention blocks 41. FIG. 10 shows the magnitude of interaction between one atom and other atoms as a function of the interatomic distance, using one atom as an example. In the upper and lower sections of FIG. 10, the horizontal axis represents the interatomic distance, and the vertical axis represents the magnitude of interaction. In the upper section of FIG. 10, the solid curve L1 represents the magnitude of interaction calculated for real space. In the lower section of FIG. 10, the dashed curve L2 represents the magnitude of interaction calculated for reciprocal space. As shown in FIG. 10, calculating the interaction in reciprocal space makes it possible to appropriately reflect long-range interactions that cannot be sufficiently ignored by simply calculating the interaction in real space.

[0041] The real-space attention block 42 and the reciprocal-space attention block 43 can individually set the distance range from the atom in the reference unit cell to the atom for which the interaction with the atom is to be calculated. In other words, the real-space attention block 42 and the reciprocal-space attention block 43 can individually set the calculation range for the distance from the atom included in the reference unit cell up to which interactions with other atoms are calculated. Figure 10 shows a case where the range of interatomic distances calculated by the real-space attention block 42 is R1 (e.g., a range from a short distance to a fixed distance D1 from the reference atom), and the range of interatomic distances calculated by the reciprocal-space attention block 43 is R2 (e.g., a range from infinity to a fixed distance D2). For example, the calculation ranges of the real-space attention block 42 and the reciprocal-space attention block 43 can be set differently depending on whether the estimation target is a semiconductor or metal or an insulator. For example, when the estimation target is a semiconductor or metal, the calculation range of the real-space attention block 42 can be narrowed and the calculation range of the reciprocal-space attention block 43 can be widened. Also, for example, when the estimation target is an insulator, the calculation range of the real space attention block 42 can be widened and the calculation range of the inverse space attention block 43 can be narrowed.

[0042] The physical property estimation unit 13 can estimate the physical properties of a material based on the estimated feature vector. The physical property estimation unit 13 can estimate the physical properties using a physical property estimation model 50. The physical property estimation model 50 is a learning model that uses the feature vector output from the state estimation unit 12 as an explanatory variable and the physical properties of the material as an objective variable, and performs machine learning to determine the correspondence between the explanatory variables and the objective variable. Note that the physical property estimation unit 13 does not need to use the physical property estimation model 50 when estimating the physical properties. The physical properties of a material may be, for example, physical property values ​​such as band gap and formation energy, a category distribution indicating material category (e.g., "metal, nonmetal" or "superconducting, metal, nonmetal"), or a feature vector of a crystal structure. Alternatively, they may be a vector sequence indicating the physical properties of each atom of the material. Note that the feature vector output from the state estimation unit 12 may be used as input for another machine learning model. The state estimation unit 12 may estimate other states of atoms.

[0043] The storage unit 20 stores information such as various programs and data. The storage unit 20 includes storage such as a hard disk drive (HDD) and a solid state drive (SSD). The storage unit 20 stores, for example, the state estimation model 40 and the physical property estimation model 50 described above.

[0044] The storage unit 20 stores a state estimation program that, for example, receives input of the type and position of each point in a point cloud portion, which is a finite portion of a point cloud structure in which one or more types of points extend infinitely in space, and estimates the state of each point in the point cloud portion. The state estimation program causes a computer to execute the following steps: an acquisition process that acquires the input type and position of each point as input information; and a state estimation process that estimates a feature vector corresponding to the input information using a state estimation model 40, which is a learning model that has been machine-learned to learn correspondences between the type and position of each point in the point cloud portion and a feature vector representing the state of each point in the point cloud portion. In this state estimation program, the state estimation model 40 is machine-learned to estimate a feature vector based on calculation results obtained by calculating interactions between each point in the point cloud portion and other points in the point cloud structure in real space, in an inverse space obtained by Fourier transforming the real space, or in both real space and the inverse space, using a function defined to include an infinite series sum of interaction functions that attenuate the states of each point in the point cloud portion depending on the distance from other points in the point cloud structure.

[0045] The communication unit 30 performs wired or wireless communication with external devices and includes an interface such as a network interface card.

[0046] When generating the state estimation model 40 and the physical property estimation model 50, for example, a composite model may be constructed in which the feature vector output from the state estimation model 40 is input to the physical property estimation model 50, and machine learning may be performed on this composite model. That is, the substance location information and lattice vectors input to the state estimation model 40 are used as explanatory variables, and the physical properties of the substance output from the physical property estimation model 50 are used as objective variables, and a composite model is generated by machine learning to determine the correspondence between the explanatory variables and the objective variables. In this case, in the composite model, the state estimation model 40 in which the substance location information and lattice vectors are used as explanatory variables and the substance feature vectors are used as objective variables, and the physical properties of the substance are used as objective variables are individually generated.

[0047] Next, a state estimation method according to this embodiment will be described. Fig. 11 is a flowchart showing an example of the state estimation method according to this embodiment. As shown in Fig. 11, the state estimation method according to this embodiment includes an acquisition step S10, a state estimation step S20, and a state estimation step S30.

[0048] In the acquisition step S10, for a substance to be estimated, configuration information indicating the configuration in real space of atoms included in a unit lattice and a lattice vector in real space of the unit lattice are acquired as input information. For example, when an operator inputs the configuration information and the lattice vector to the state estimation apparatus 100 using an input device or the like (not shown), the acquisition unit 11 of the processing unit 10 acquires the input configuration information and the lattice vector as input information.

[0049] The state estimation step S20 estimates a feature vector for the estimation target based on the above-described state estimation model 40 and the input information acquired in the acquisition step S10. The state estimation unit 12 inputs the layout information and lattice vector, which are input information, to the state estimation model 40, and acquires the feature vector, which is the estimation result by the state estimation model 40. The state estimation unit 12 outputs the acquired feature vector.

[0050] The physical property estimation step S30 estimates the physical properties of the substance based on the feature vector estimated in the state estimation step S20. The physical property estimation unit 13 inputs the feature vector output from the state estimation unit 12 to the physical property estimation model 50, and acquires the physical properties that are the estimation results of the physical property estimation model 50.

[0051] Table 1 below shows an example of the mean absolute error (MEA) when estimating each physical property of a crystal structure using machine learning on the "Materials Project" dataset. Examples of physical properties include formation energy, band gap, bulk modulus, and shear modulus. Table 2 also shows an example of the MEA when estimating each physical property of a crystal structure using machine learning on the "JARVIS-DFT 3D 2021" dataset. Examples of physical properties include formation energy, total energy, band gap (OPT) calculated using the "OptB88vdW functional," band gap (MBJ) calculated using the "Tran-Blaha modified Becke-Johnson potential," and energy above hull (E hull). In Tables 1 and 2, the three numbers below each property name indicate the size of the dataset subsets for training, validation, and testing, respectively.

[0052] In Tables 1 and 2, Comparative Examples 1 and 7 are the mean absolute errors of the estimation results using the method described in "Tian Xie and Jeffrey C. Grossman. Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Phys. Rev. Lett., 120:145301, Apr 2018." Comparative Examples 2 and 8 are the mean absolute errors of the estimation results using the method described in "K. T. Schutt (u with umlaut), H. E. Sauceda, P.-J. Kindermans, A. Tkatchenko, and K.-R. Muller (u with umlaut). SchNet - A deep learning architecture for molecules and materials. The Journal of Chemical Physics, 148(24):241722, 03 2018." Comparative Examples 3 and 9 are the mean absolute errors of the estimation results using the method described in "Chi Chen, Weike Ye, Yunxing Zuo, Chen Zheng, and Shyue Ping Ong. Graph networks as a universal machine learning framework for molecules and crystals. Chemistry of Materials, 31(9):3564-3572, May 2019."Comparative Examples 4 and 10 are the mean absolute errors of the estimation results using the method described in "Steph-Yves Louis, Yong Zhao, Alireza Nasiri, Xiran Wang, Yuqi Song, Fei Liu, and Jianjun Hu. Graph convolutional neural networks with global attention for improved materials property prediction. Phys. Chem. Chem. Phys., 22:18141-18148, 2020." Comparative Examples 5 and 11 are the mean absolute errors of the estimation results using the method described in "Kamal Choudhary and Brian DeCost. Atomistic line graph neural network for improved materials property predictions. npj Computational Materials, 7(1):185, Nov 2021." Comparative Examples 6 and 12 are the mean absolute errors of the estimation results using the method described in "Keqiang Yan, Yi Liu, Yuchao Lin, and Shuiwang Ji. Periodic graph transformers for crystal material property prediction. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh (eds.), Advances in Neural Information Processing Systems, volume 35, pp. 15066-15080. Curran Associates, Inc., 2022."

[0053] Furthermore, in Tables 1 and 2, Examples 1 and 3 are mean absolute errors of the estimation results obtained by calculating the interactions between atoms in real space based on the above-described principle of state estimation according to this embodiment. Examples 2 and 4 are mean absolute errors of the estimation results when stochastic weighted averaging is not used in Examples 1 and 3. Example 5 is the mean absolute error of the estimation results obtained by calculating the interactions between atoms in real space and reciprocal space based on the above-described principle of state estimation according to this embodiment.

[0054] As shown in Table 1, the mean absolute errors of the estimation results according to Examples 1 and 2 are lower than the mean absolute errors of the estimation results according to Comparative Examples 1 to 6 for all physical property values.

[0055] As shown in Table 2, the mean absolute errors of the estimation results according to Examples 3 to 5 are lower for all physical property values ​​than the mean absolute errors of the estimation results according to Comparative Examples 1 to 6. Furthermore, when Example 3 and Example 5 are compared, the mean absolute errors for the band gap (OPT) and E hull are smaller in Example 5 than in Example 3. In this way, by calculating the interactions in both real space and reciprocal space, it is possible to obtain estimation results with even higher accuracy.

[0056] As described above, the state estimation device 100 according to the present embodiment is a state estimation device that estimates the state of each atom in a unit lattice, which is a finite part of a crystal structure in which one or more types of atoms extend infinitely in space, by inputting the type and position of each atom in the unit lattice. The state estimation device 100 includes an acquisition unit 11 that acquires the input type and position of the atoms as input information, and a state estimation unit 12 that estimates a feature vector corresponding to the input information using the state estimation model 40, which is a learning model that has learned by machine learning the correspondence between the type and position of the atoms in the unit lattice and the feature vector representing the state of each atom in the unit lattice. The state estimation model 40 is machine-learned to estimate a feature vector based on the calculation results obtained by calculating, for each atom in the unit lattice, interactions between each atom in the unit lattice and other atoms in the crystal structure in real space, in a reciprocal space obtained by Fourier transforming the real space, or in both real space and the reciprocal space, using a function that is defined to include an infinite series sum of interaction functions that attenuate the state of each atom in the unit lattice depending on the distance from other atoms in the crystal structure.

[0057] Furthermore, the state estimation method according to this embodiment is a state estimation method for estimating the state of each atom in a unit lattice, which is a finite part of a crystal structure in which one or more types of atoms extend infinitely in space, using as input the type and position of each atom in the unit lattice. The state estimation method includes an acquisition step S10 for acquiring the input type and position of the atoms as input information, and a state estimation step S20 for estimating a feature vector corresponding to the input information using a state estimation model 40, which is a learning model that has learned by machine learning the correspondence between the type and position of the atoms in the unit lattice and a feature vector representing the state of each atom in the unit lattice. The state estimation model 40 has been learned by machine learning to estimate a feature vector based on calculation results obtained by calculating, for each atom in the unit lattice, interactions between each atom and other atoms in the crystal structure in real space, in a reciprocal space obtained by Fourier transforming the real space, or in both real space and reciprocal space, using a function defined to include an infinite series sum of interaction functions that attenuate the state of each atom in the unit lattice depending on the distance from other atoms in the crystal structure.

[0058] Furthermore, the state estimation program according to this embodiment is a state estimation program that estimates the state of each atom in a unit lattice, which is a finite part of a crystal structure in which one or more types of atoms extend infinitely in space, by inputting the type and position of each atom in the unit lattice. The state estimation program causes a computer to execute an acquisition process that acquires the input type and position of the atom as input information, and a state estimation process that estimates a feature vector corresponding to the input information using a state estimation model 40, which is a learning model that has learned by machine learning the correspondence between the type and position of the atom in the unit lattice and a feature vector that represents the state of each atom in the unit lattice. The state estimation model 40 is machine-learned to estimate a feature vector based on the calculation results obtained by calculating, for each atom in the unit lattice, the interaction between each atom and other atoms in the crystal structure in real space, in a reciprocal space obtained by Fourier transforming the real space, or in both real space and reciprocal space, using a function defined to include an infinite series sum of interaction functions that attenuate the state of each atom in the unit lattice depending on the distance from other atoms in the crystal structure.

[0059] According to this configuration, a state estimation model 40 is used that has been machine-learned to estimate a feature vector based on the calculation results obtained by calculating interactions between each atom of the unit lattice and other atoms in the crystal structure in real space, reciprocal space, or both real space and reciprocal space using a function that is defined to include an infinite series sum of interaction functions that attenuate the state of each atom of the unit lattice depending on the distance from the other atoms in the crystal structure. This makes it possible to estimate a feature vector that reflects the calculation results of interactions between atoms in an infinitely expanding crystal structure. Therefore, the influence of both interactions between atoms with short interatomic distances and interactions between atoms with long interatomic distances can be appropriately reflected in the feature vector.

[0060] In the state estimation device 100 according to this embodiment, the state estimation model 40 has a plurality of self-attention blocks 41 that estimate feature vectors in a stepwise manner.

[0061] According to this configuration, feature vectors can be estimated with high accuracy and speed because feature vectors are estimated stepwise using multiple self-attention blocks 41. In this embodiment, by repurposing the configuration of the self-attention block 41 arranged in the encoder of a deep learning model called a Transformer used in language translation, etc., it becomes possible to effectively incorporate both short-distance and long-distance interactions.

[0062] In the state estimation device 100 according to this embodiment, the self-attention block 41 determines a repeating pattern in which unit lattices are repeated multiple times, and estimates a feature vector for each atom included in a reference unit lattice in the repeating pattern based on interactions between the atoms and other atoms included in the repeating pattern.

[0063] According to this configuration, it is possible to perform processing that corresponds to the structure of a substance in which unit lattices containing atoms are repeatedly arranged in multiple layers, and therefore it is possible to estimate a feature vector with high accuracy.

[0064] In the state estimation device 100 according to this embodiment, the self-attention block 41 calculates position information of atoms included in the repetitive pattern based on the placement information.

[0065] According to this configuration, it is possible to appropriately calculate the position information of atoms included in the repeating pattern.

[0066] In the state estimation device 100 of this embodiment, the multiple self-attention blocks 41 include a real-space attention block 42, which is a self-attention block that estimates feature vectors for atoms included in the unit lattice to be estimated based on interactions between other atoms in real space, and a reciprocal-space attention block 43, which is a self-attention block that estimates feature vectors for atoms included in the unit lattice to be estimated based on interactions between other atoms in reciprocal space.

[0067] According to this configuration, the real space attention block 42 and the inverse space attention block 43 process the influence of the interaction between real space and inverse space separately, thereby enabling efficient processing.

[0068] In the state estimation device 100 according to this embodiment, the state estimation model 40 is configured to alternately perform estimation using a real space attention block 42 and estimation using an inverse space attention block 43 .

[0069] According to this configuration, by alternately performing estimation by the real space attention block 42 and estimation by the inverse space attention block 43, it is possible to appropriately determine interactions in real space and inverse space.

[0070] In the state estimation device 100 according to this embodiment, the state estimation model 40 is configured to first perform estimation by the real space attention block 42 .

[0071] According to this configuration, by first performing estimation by the real space attention block 42, it is possible to appropriately reflect the influence of interactions in the real space, which are more dominant in the value of the feature vector.

[0072] In the state estimation device 100 according to this embodiment, the state estimation model 40 allows the real-space attention block 42 and the reciprocal-space attention block 43 to individually set the range of distances from the atom in the reference unit cell to the atom for which the interaction with the atom is to be calculated.

[0073] According to this configuration, the real space attention block 42 and the reciprocal space attention block 43 individually set the range of distance from the atom in the reference unit cell to the atom for which the interaction with the atom is calculated, thereby making it possible to appropriately reflect the effects of both interactions between atoms with short interatomic distances and interactions between atoms with long interatomic distances in the feature vector.

[0074] In the state estimation device 100 according to this embodiment, the multiple self-attention blocks 41 have a multi-head attention block 44 that estimates feature vectors in parallel for atoms included in the unit cell to be estimated based on their interactions with other atoms in real space and reciprocal space.

[0075] According to this configuration, the calculation of the interactions in the real space and the reciprocal space can be performed in parallel, so that the feature vector can be estimated with high accuracy while suppressing the amount of calculation.

[0076] The state estimation device 100 according to this embodiment further includes a property estimation unit 13 that estimates the property of a substance based on the feature vector estimated by the state estimation unit 12 .

[0077] According to this configuration, the physical properties of a substance are estimated based on a feature vector that appropriately reflects the provision of both interactions between atoms with short interatomic distances and interactions between atoms with long interatomic distances, thereby enabling the physical properties to be estimated with high accuracy.

[0078] The technical scope of the present disclosure is not limited to the above-described embodiments, and appropriate modifications can be made without departing from the spirit of the present disclosure. For example, in the above-described embodiments, the substance of the state estimation device 100 has been described as a substance having a three-dimensional crystal structure. The substance of the state estimation device 100 is not limited to a substance having a three-dimensional crystal structure, and may be a one-dimensional object, a two-dimensional object, or an object having four or more dimensions, as long as a unit pattern including unit constituents is repeatedly arranged. Furthermore, the positions of atoms input as input information may indicate relative positions.

[0079] L1, L2...curves, 10...processing unit, 11...acquisition unit, 12...state estimation unit, 13...state estimation unit, 20...storage unit, 30...communication unit, 40, 40A, 40B, 40C, 40D...state estimation model, 41...self-attention block, 42...real space attention block, 43...reverse space attention block, 44...multi-head attention block, 50...state estimation model, 100...state estimation device

Claims

1. A state estimation device that estimates a state of each of a point cloud part, which is a finite part of a point cloud structure in which one or more types of points extend infinitely in space, by inputting the type and position of each of the points in the point cloud part, the state estimation device comprising: an acquisition unit that acquires the input type and position of the point as input information; and a state estimation unit that estimates the feature vector corresponding to the input information using a state estimation model that is a learning model that has been machine-learned to acquire a correspondence between the type and position of the point in the point cloud part and a feature vector that represents the state of each of the points in the point cloud part, wherein the state estimation model has been machine-learned to estimate the feature vector based on a calculation result obtained by calculating an interaction between each of the points in the point cloud part and other points in the point cloud structure, in real space, in an inverse space obtained by performing a Fourier transform on the real space, or in both the real space and the inverse space, using a function defined to include an infinite series sum of an interaction function that attenuates the state of each of the points in the point cloud part according to the distance from the other points in the point cloud structure.

2. Change the type of the point to X ０ = {x １ ０ , x ２ ０ , x ３ ０ , ...}, and the position of the point is P = {p １ , p ２ , p ３ , ...}, and the type of the point X ０ and the input information based on the position P of the point is expressed as X={x １ , x ２ , x ３ , ...}, and the interaction function that attenuates with respect to the point i that is a target point of the point cloud portion in the point cloud structure according to the distance between the point i and another point j in the point cloud structure is f ｉｊ The feature vector indicating the state of the point i is y ｉ Then, the feature vector y ｉ is the total interaction coefficient Z ｉ and the total interaction vector a ｉ A function g that receives and returns a vector ｉ Using and the total interaction coefficient Z ｉ teeth, The total interaction vector a ｉ teeth, and an interaction vector v from the point j to the point i. ｉｊ teeth, The interaction function f ｉｊ teeth, The state estimation device according to claim 1 , wherein 3. When the point group structure has periodicity, the point type X ０ and the position P of the point is a set of N finite basic repeating elements S ｃｅｌｌ and D translation direction vectors L = {l １ , …, l Ｄ }, a D-dimensional integer vector n, and a point i(n) moved by a D-dimensional translation Ln, The point cloud portion is represented by the basic repeating element S ｃｅｌｌ Then, the feature vector y of the point i which is the target atom ｉ In the above, Z ｉ and a ｉ teeth, The state estimation device according to claim 2 , wherein the state estimation device is represented by the following expression:

4. The total interaction coefficient Z in the real space ｉ and the total interaction vector a ｉ is the coordinate variable r=(x １ , …, x ｄ ), using f' is an interaction function taking into account the periodicity. ｉｊ , f' ｉｊ teeth, The total interaction coefficient Z in the reciprocal space is represented by ｉ and the total interaction vector a ｉ is the spatial angular frequency ω ｍ Using the Fourier series expansion by The spatial angular frequency ω ｍ teeth, The interaction function f' taking into account the periodicity is expressed as follows: ｉｊ , f' ｉｊ F' is the Fourier coefficient of ｉｊ , F' ｉｊ teeth, The state estimation device according to claim 3 , wherein the state estimation device is represented by the following formula:

5. In the real space, the feature vector y ｉ teeth, The interaction function f ｉｊ (r) is the query vector q ｉ , key vector k ｉ and the value vector v ｉ , and the radius σ that determines the attenuation range ｉ Using and σ ｉ is a constant or a radius r that determines the scale of the attenuation range ０ Using the function ρ that returns a positive value and the learning parameters w (scalar) and w (bold, vector), or, The distance variable r is defined as The query vector q ｉ , key vector k ｉ and the value vector v ｉ is the learning parameter W of the state estimation model Ｑ , W Ｋ , W Ｖ Using The interaction vector v ｉｊ is a constant W Ｇ and a K-dimensional one-hot vector b indicating the distance between the two points, The one-hot vector b is expressed by the maximum distance r that the one-hot vector b can express. ｍａｘ Using and the constant μ ｋ teeth, The state estimation device according to claim 3 , wherein the state estimation device is represented by the following formula:

6. In the inverse space, the feature vector y ｉ teeth, The interaction function f' taking into account the periodicity is expressed as follows: ｉｊ F' is the Fourier coefficient of (r) ｉｊ (ω ｍ ) is the query vector q ｉ , key vector k ｉ and the value vector v ｉ and the radius σ that determines the attenuation range ｉ bar ("σ ｉ " with "-" on top, and σ ｉ The bars are either a constant or a radius r that determines the scale of the attenuation range. ０ Bar ("r ０ "), a function ρ that returns a positive value, and learning parameters w (a "-" over "w", a scalar) and w (a "-" over a bold "w", a vector), or, The interaction function f'' taking the periodicity into account is defined as follows: ｉｊ F' is the Fourier coefficient of (r) ｉｊ (ω ｍ )teeth, The query vector q ｉ , the key vector k ｉ and the value vector v ｉ is the learning parameter W of the state estimation model Ｑ , W Ｋ , W Ｖ Using The state estimation device according to claim 5 , wherein the state estimation device is represented by the following formula:

7. The state estimation model is Ｑ , W Ｋ , W Ｖ There are H different query vectors q ｉ , key vector k ｉ and the value vector v ｉ The interactions are calculated in parallel, and the calculation results are combined to obtain the feature vector y ｉ = (y ｉ １ , y ｉ ２ , …, y ｉ Ｈ The state estimation device according to claim 6, further comprising:

8. The state estimation unit inputs the feature vector estimated by the state estimation model to another neural network NN, and outputs the result as an output value X', as follows: X'=NN(y １ , y ２ , …, y Ｎ The state estimation device according to claim 7 , further comprising:

9. The state estimation unit uses X', which is the output value of the neural network NN, as the input information and calculates the function g ｉ The feature vector y ｉ The state estimation device according to claim 8 , further comprising:

10. A state estimation method for estimating a state of each of a point cloud part, which is a finite part of a point cloud structure in which one or more types of points extend infinitely in space, by inputting the type and position of each of the points in the point cloud part, the state estimation method comprising: an acquisition step of acquiring the input type and position of the point as input information; and a state estimation step of estimating the feature vector corresponding to the input information using a state estimation model that is a learning model that has been machine-learned to learn a correspondence between the type and position of the point in the point cloud part and a feature vector representing the state of each of the points in the point cloud part, the state estimation model being machine-learned to learn a correspondence between the type and position of the point in the point cloud part and a feature vector representing the state of each of the points in the point cloud part, the state estimation model being machine-learned to estimate the feature vector based on a calculation result obtained by calculating an interaction between each of the points in the point cloud part and other points in the point cloud structure in real space, in an inverse space obtained by Fourier transforming the real space, or in both the real space and the inverse space, using a function defined to include an infinite series sum of an interaction function that attenuates the state of each of the points in the point cloud part according to the distance from the other points in the point cloud structure.

11. A state estimation program for estimating a state of each of a point cloud part, which is a finite part of a point cloud structure in which one or more types of points extend infinitely in space, by inputting the type and position of each of the points in the point cloud part, the state estimation program causes a computer to execute an acquisition process for acquiring the input type and position of the point as input information, and a state estimation process for estimating the feature vector corresponding to the input information using a state estimation model that is a learning model that has been machine-learned to learn a correspondence between the type and position of the point in the point cloud part and a feature vector representing the state of each of the points in the point cloud part, the state estimation model being machine-learned to estimate the feature vector based on a calculation result obtained by calculating an interaction between each of the points in the point cloud part and other points in the point cloud structure in real space, in an inverse space obtained by Fourier transforming the real space, or in both the real space and the inverse space, using a function defined to include an infinite series sum of an interaction function that attenuates the state of each of the points in the point cloud part according to the distance from the other points in the point cloud structure.

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