Information processing program, information processing device, and information processing method

Abstract

To improve the analytical accuracy of principal component analysis. [Solution] An information processing device flattens a matrix of linear equations into row vectors, creates a combined matrix that combines multiple row vectors in the vertical direction, and then performs principal component analysis on the combined matrix to reduce the dimensions of the combined matrix.

Description

[Technical Field]

[0001] The present invention relates to an information processing program, an information processing device, and an information processing method. [Background technology]

[0002] A conventional method is to discretize the governing equations that represent physical phenomena and obtain approximate numerical solutions using a computer. This method is used in structural simulations, fluid simulations, electromagnetic field simulations, and so on.

[0003] In recent years, unlike conventional simulations that find solutions to linear equations calculated in the above simulations based on physics, there has been a method that speeds up calculations by having an AI (Artificial Intelligence) surrogate model learn how to find solutions and then make predictions. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2023-009904 Summary of the Invention [Problem to be solved by the invention]

[0005] Incidentally, when an AI surrogate model predicts the solution to a linear equation, principal component analysis (PCA) is performed as a preprocessing step. However, because the analytical accuracy of general PCA is not high, the linear equation is solved using the results of such analysis, and the solution accuracy is also not high.

[0006] In one aspect, an object of the present invention is to provide an information processing program, an information processing device, and an information processing method that can improve the analytical accuracy of principal component analysis. [Means for solving the problem]

[0007] In order to solve the above-mentioned problems and achieve the object, an information processing program of the present invention is characterized by causing a computer to execute processing to flatten a matrix of linear equations into row vectors, create a connection matrix by connecting multiple row vectors in the vertical direction, and perform principal component analysis on the connection matrix to reduce the dimensions of the connection matrix. [Effects of the Invention]

[0008] According to one embodiment, the analysis accuracy of principal component analysis can be improved. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a diagram illustrating a reference technique. [Figure 2] FIG. 2 is a diagram illustrating an example of the overall configuration of the information processing system according to the first embodiment. [Figure 3] FIG. 3 is a diagram illustrating the processing contents of the information processing device according to the first embodiment. [Figure 4] FIG. 4 is a functional block diagram illustrating a functional configuration of the information processing apparatus according to the first embodiment. [Figure 5] FIG. 5 is a diagram illustrating a specific example of the process performed by the matching processor according to the first embodiment. [Figure 6] FIG. 6 is a diagram illustrating a specific example of processing performed by the flattening processing unit according to the first embodiment. [Figure 7] FIG. 7 is a diagram illustrating a specific example of a process performed by the combining unit according to the first embodiment. [Figure 8] FIG. 8 is a diagram illustrating a specific example of a process performed by the removal unit according to the first embodiment. [Figure 9] FIG. 9 is a diagram illustrating a specific example of processing performed by the dimension reduction unit according to the first embodiment. [Figure 10] FIG. 10 is a diagram illustrating a processing flow of the information processing device according to the first embodiment. [Figure 11] FIG. 11 is a diagram illustrating a method for solving a linear equation according to the first embodiment. [Figure 12] FIG. 12 is a flowchart illustrating an example of a processing flow according to the first embodiment. [Figure 13] FIG. 13 is a diagram illustrating an example of the overall configuration of an information processing system according to the second embodiment. [Figure 14] FIG. 14 is a functional block diagram illustrating a functional configuration of the information processing device according to the second embodiment. [Figure 15] FIG. 15 is a flowchart illustrating an example of the overall processing flow of the information processing device according to the second embodiment. [Figure 16] FIG. 16 is a diagram illustrating an example of a hardware configuration. DETAILED DESCRIPTION OF THE INVENTION

[0010] Hereinafter, an information processing program, an information processing device, and an information processing method according to the present application will be described in detail with reference to the accompanying drawings. Note that the information processing program, the information processing device, and the information processing method according to the present application are not limited to these embodiments.

[0011] Example 1 An information processing device 100 according to a first embodiment described below is an example of a computer that performs processing to reduce the dimensions of data by principal component analysis or the like in preprocessing for predicting a solution to a linear equation.

[0012] (Reference technology) First, we will explain an overview of a reference technology related to calculating solutions to linear equations using an AI surrogate model. Figure 1 is a diagram explaining the reference technology. As shown in Figure 1, after initial condition data and boundary condition data are input, the reference technology calculates a linear equation Ax = b through pre-calculation, solves x that satisfies Ax = b, and outputs x through post-calculation.

[0013] Here, solving Ax = b is often a bottleneck in the overall calculation process, and the reference technology enables high-speed calculations by replacing this process with an AI surrogate model.

[0014] For example, when performing processing related to a structural analysis simulation that analyzes the deformation of an object in response to an applied force, the AI ​​surrogate model calculates a matrix A indicating a stiffness matrix and a vector b indicating a force vector from initial conditions indicating mesh data representing the shape of the object and boundary condition data indicating the forces acting on the object indicated by the mesh data. Then, the AI ​​surrogate model organizes matrix A and vector b, respectively, and generates feature data linking the features associated with each node. This data is then input to a graph neural network (GNN). The displacement vector x output by the GNN is then obtained as the solution to Ax = b.

[0015] Here, since matrix A is a large matrix, the reference technology performs principal component analysis to create a dimension-reduced feature matrix that contains information about the entire graph. For example, the reference technology reshapes elements (three rows) corresponding to the x, y, and z directions of matrix A to create a matrix representing discretized nodes, and then performs principal component analysis to create a dimension-reduced feature matrix.

[0016] In this reference technology, the analytical accuracy of principal component analysis is not high, and the accuracy of solving linear equations using machine learning models such as AI surrogate models is also not high. For example, when reformatting a matrix, the reference technology treats every third row as a node feature, making it unable to handle the increased dimensions that occur in contact problems, etc. Also, since the reference technology performs principal component analysis individually on each piece of matrix data, the meaning of the principal components may differ between data. Furthermore, the reference technology creates a transformation matrix every time it performs principal component analysis, which takes time to create the feature matrix. Furthermore, the reference technology uses a dense transformation matrix in principal component analysis, which increases memory usage during principal component analysis.

[0017] (Overall composition) Next, an overall configuration of an information processing system according to the present embodiment 1 will be described. Fig. 2 is a diagram illustrating an example of the overall configuration of the information processing system according to the present embodiment 1. As shown in Fig. 2, the information processing system according to the present embodiment 1 includes an information processing device 100 that trains an AI model made up of a neural network (NN) that predicts a displacement vector x, which is a solution, from a matrix A and a constant vector b in a linear equation Ax=b.

[0018] The information processing device 100 is an information processing device that performs preprocessing on the matrix A and the constant vector b in the linear equation Ax=b to create a feature matrix and a feature vector, respectively, and trains an AI model consisting of a neural network using training data generated from the feature matrix and the feature vector, and is realized by an AI surrogate model or the like.

[0019] The information processing device 100 is particularly characterized by preprocessing for creating a feature matrix related to matrix A. Therefore, the following describes the details of the preprocessing performed by the information processing device 100 on matrix A. For example, the information processing device 100 performs flattening processing, combining processing, and the like (to be described later) on matrix A, and then performs principal component analysis to create a feature matrix indicating the feature quantities of matrix A.

[0020] The preprocessing of the matrix A by the information processing device 100 can be applied to any linear equation other than the structural analysis simulation.

[0021] (Processing of information processing device 100) Next, a description will be given of the processing content of the information processing device 100 according to the present embodiment 1. In consideration of the above-mentioned reference technology, the information processing device 100 flattens the matrix of the linear equation into row vectors, creates a connection matrix by connecting a plurality of row vectors in the vertical direction, and then performs principal component analysis on the connection matrix to reduce the dimensions of the connection matrix.

[0022] 3 is a diagram illustrating the processing details of the information processing device according to the first embodiment. As described above, in the reference technology, the principal component analysis is performed separately for each of the matrices A1 and A2, so that the principal components of the dimension-reduced A1~ and A2~ have different meanings, resulting in a decrease in the analytical accuracy of the principal component analysis. Note that "A1~" is assumed to have "~" written directly above "A1".

[0023] In response to this, the information processing device 100, for example, flattens each of the matrices A1 and A2 into a row vector. Then, the information processing device 100 vertically combines the flattened row vectors of A1 and A2 to create a combined matrix with two rows. Then, the information processing device 100 performs principal component analysis on the combined matrix with two rows to create feature matrices (A1~, A2~) with reduced dimensions.

[0024] That is, the information processing device 100 performs principal component analysis only once on the combined matrix created by flattening and combining each piece of matrix data. n The principal components of 1 to 3 have the same meaning, and the analytical accuracy of the principal component analysis can be improved. As a result, the information processing device 100 can also improve the accuracy of solving linear equations.

[0025] (Functional configuration of information processing device 100) Next, a functional configuration of the information processing device 100 will be described. Fig. 4 is a functional block diagram showing the functional configuration of the information processing device according to the first embodiment. As shown in Fig. 4, the information processing device 100 includes a communication unit 110, a control unit 120, and a storage unit 130. The communication unit 110 is a processing unit that controls communication with other devices, and is realized by, for example, a communication interface.

[0026] The storage unit 130 is a processing unit that stores various data and programs executed by the control unit 120, and is realized by, for example, a memory, a hard disk, etc. For example, the storage unit 130 stores data such as logic and calculation methods in each process by the control unit 120, which will be described later.

[0027] The control unit 120 is a processing unit that controls the entire information processing device 100, and is realized by, for example, a processor. The control unit 120 has a matching processing unit 121, a flattening processing unit 122, a combination unit 123, a removal unit 124, a dimension reduction unit 125, and a training unit 126. The matching processing unit 121, the flattening processing unit 122, the combination unit 123, the removal unit 124, the dimension reduction unit 125, and the training unit 126 are realized by electronic circuits included in the processor, processes executed by the processor, etc.

[0028] The matching processor 121 matches the number of rows and columns of matrices of multiple linear equations with other matrices. For example, the matching processor 121 performs zero padding on smaller matrices to unify the matrix sizes of multiple matrices in the linear equations.

[0029] Here, a specific example of the processing performed by the matching processor 121 will be described. Fig. 5 is a diagram illustrating a specific example of the processing performed by the matching processor according to the first embodiment. The example in Fig. 5 shows a process of converting a matrix A1, which is a matrix of a linear equation, to a matrix A2. n This shows the case where the matrix sizes are matched by padding with zeros.

[0030] 5, the matching processor 121 first identifies the largest matrix A2 among the matrices to be matched. Then, the matching processor 121 performs the matching on matrices other than the identified A2 (for example, A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A21, A22, A23, A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A48, A49, A50, A51, A52, A53, A54, A55, A56, A57, A58, A59, A60, A61, A62, A63, A64, A65, A66, A67, A68, A69, A70, A71, A72, A73, A74, A75, A76, A77, A78, A79, A79, A81, A82, A83, A84, A85, A86, A87, A88, A89, A89, A90, A91, A92, A93, A94, A95, A96, A97, A98, A99, A99, A109, A110, A111, A120, A130, A140, A150, A161, A171, A182, A19, A19, A n ), we perform zero padding by adding rows and columns with zero elements to make the matrix size match A2.

[0031] The smoothing unit 122 smoothes the matrix of the linear equation into a row vector. For example, the smoothing unit 122 smooths each element of the matrix of the linear equation to create a row vector formed into one row.

[0032] Here, a specific example of the processing of the flattening processor 122 will be described. Fig. 6 is a diagram illustrating a specific example of the processing performed by the flattening processor according to the first embodiment. The example in Fig. 6 illustrates a case where a 4x4 matrix of a matrix A of a linear equation is flattened into a 1x16 row vector.

[0033] First, in matrix No. 1, which is the target of the flattening process, numerical values ​​are arranged as follows: (1,1)=1, (2,2)=2, etc. Elements without numerical values ​​are assigned 0. In this state, flattening processor 122 flattens each of the elements (1,1) to (4,4) and creates a 1×16 row vector formed by arranging them in the order (1,1), (1,2), etc.

[0034] The combining unit 123 creates a combined matrix by combining multiple row vectors in the vertical direction. For example, the combining unit 123 creates a combined matrix by combining multiple row vectors created by the flattening processing unit 122 in the vertical direction (lengthwise direction) so that each element corresponds to another.

[0035] Here, a specific example of the processing of the combining unit 123 will be described. Fig. 7 is a diagram illustrating a specific example of the processing performed by the combining unit according to the first embodiment. The example in Fig. 7 illustrates a case where 1x16 row vectors are combined for matrices No. 1 and No. 2 of linear equations.

[0036] 7, the combining unit 123 vertically combines the row vectors of matrix No. 1 and matrix No. 2 so that the (X, Y) element of matrix No. 1 and the (X, Y) element of matrix No. 2 are located in the same column, thereby creating a 2 × 16 combined matrix. For example, the combining unit 123 creates a combined matrix in which element 1 of (1, 1) of matrix No. 1 and element 11 of (1, 1) of matrix No. 2 are located in the same column.

[0037] The elimination unit 124 eliminates, from the connection matrix, column vectors whose elements are all 0. For example, the elimination unit 124 eliminates column vectors whose elements are all 0 from the connection matrix created by the combination unit 123 to create a connection matrix with fewer columns.

[0038] Here, a specific example of the processing of the removal unit 124 will be described. Fig. 8 is a diagram illustrating a specific example of the processing performed by the removal unit according to the first embodiment. The example in Fig. 8 describes a case where a column vector in which all elements are 0 is removed from the 2 × 16 connection matrix described in Fig. 7 to create a connection matrix in which the columns are narrowed.

[0039] 8, the elimination unit 124 identifies elements of each column vector in the 2×16 connection matrix, and identifies column vectors (1,2), (1,3), ..., whose elements are all 0. Then, the elimination unit 124 removes the identified column vectors to create a 2×8 connection matrix with the columns narrowed. Here, the elimination unit 124 can obtain and store the positions of the removed column vectors.

[0040] The dimension reduction unit 125 performs principal component analysis on the connection matrix to reduce the dimensions of the connection matrix. For example, the dimension reduction unit 125 performs principal component analysis on the connection matrix from which column vectors whose elements are all 0 have been removed, and creates a feature matrix of matrix A whose dimensions have been reduced by using the top principal components of the transformed data.

[0041] The transformation matrix used in the principal component analysis is created, for example, by performing singular value decomposition on the target matrix, and the created transformation matrix is ​​stored in the storage unit 130. The total number of elements in the created transformation matrix is ​​determined according to the number of feature quantities of the target matrix; for example, the more feature quantities the target matrix has, the greater the total number of elements in the dense matrix will be.

[0042] Here, a specific example of the processing of the dimension reduction unit 125 will be described. Fig. 9 is a diagram showing a specific example of the processing performed by the dimension reduction unit according to the first embodiment. The example in Fig. 9 describes a case where a principal component analysis is performed on a 2x8 connection matrix to create a matrix indicating feature amounts with reduced dimensions.

[0043] As shown in FIG. 9, the dimension reduction unit 125 multiplies a 2×8 connection matrix, from which column vectors with all elements equal to 0 have been removed, by a transformation matrix created by singular value decomposition, and creates a 2×2 matrix indicating feature quantities consisting of A1~ and A2~ using the higher-order principal components of the transformed data.

[0044] The training unit 126 generates training data by combining each of the constant vectors of the multiple linear equations with a dimension-reduced combined matrix generated for the matrices of the multiple linear equations, and uses the training data to train a machine learning model that predicts the solution to the linear equation to be solved.

[0045] For example, the training unit 126 generates training data by concatenating a feature matrix created for a constant vector b with a dimension reduced for multiple matrices A in a linear equation Ax=b, and performs training of an AI model consisting of a neural network using the training data as an explanatory variable and the solution x of the linear equation as a target variable.

[0046] (Example) Next, a flow of preprocessing for matrix A performed by the information processing device 100 will be described. Fig. 10 is a diagram illustrating a flow of processing performed by the information processing device according to the first embodiment. In the example of Fig. 10, matrices A1 to A2 of a plurality of linear equations are n 1 shows a case where the series of processes described above are executed to create a feature matrix.

[0047] First, the information processing device 100 calculates the matrices A1 to A2 of a plurality of linear equations. n, and all matrix sizes are unified to A2 (FIG. 10(1)). Next, the information processing device 100 performs a flattening process on each matrix whose matrix size has been unified, and creates a plurality of row vectors (FIG. 10(2)). Subsequently, the information processing device 100 creates a combined matrix by vertically combining each row vector so that each element corresponds to another (FIG. 10(3)).

[0048] Then, the information processing device 100 removes column vectors whose elements are all 0 from the connection matrix to create a compact connection matrix (FIG. 10(4)). After that, the information processing device 100 performs principal component analysis on the connection matrix to obtain A1 to A n Create a dimension-reduced feature matrix consisting of

[0049] Through the above-described series of processes, the information processing device 100 performs principal component analysis only once on the combined matrix created by flattening and combining each piece of matrix data. n The principal components of ~ have the same meaning, which can improve the analytical accuracy of principal component analysis.

[0050] Next, a method for training an AI model consisting of a NN implemented by the information processing device 100 will be described. Fig. 11 is a diagram for explaining a method for solving a linear equation according to Example 1. The example in Fig. 11 shows a case where, for a linear equation Ax=b that is a training target, training data created from a feature matrix indicating the feature amounts of a matrix A and a feature vector indicating the feature amounts of a constant vector b is input to the NN to train prediction of a displacement vector x that is a solution to the linear equation.

[0051] As shown in FIG. 11, the information processing device 100 performs a series of pre-processing processes from the matching process to the dimension reduction process described above on the matrix A of the linear equation that is the training target, and generates A1 to A n The information processing device 100 also performs preprocessing on the constant vector b to create a feature matrix with reduced dimensions, which is composed of b1 to b n A feature vector consisting of

[0052] The information processing device 100 then creates training data by concatenating the created feature matrices and feature vectors, such as A1~ and b1, A2~ and b2, etc. The information processing device 100 then inputs the created training data into a neural network and outputs a displacement vector x that is a solution to the linear equation, such as x1 corresponding to A1~-b1 and x2 corresponding to A2~-b2. The information processing device 100 then updates parameters that are highly relevant to calculating the solution so that the output result approaches the correct answer information.

[0053] In addition, when training an AI model consisting of a NN, the information processing device 100 can identify and store the positions of column vectors whose all elements are 0 in the processing by the above-mentioned removal unit 124 and the transformation matrix in the processing by the above-mentioned dimension reduction unit 125.

[0054] (Processing procedure of information processing device 100) Next, an example of a processing procedure of the information processing device 100 according to the first embodiment will be described with reference to Fig. 12. Fig. 12 is a flowchart showing an example of a processing flow according to the first embodiment. Note that the steps in the flowchart shown in Fig. 12 may be executed in a different order, and some processing may be added or omitted.

[0055] First, the information processing device 100 determines whether matching processing is necessary for the matrices of the linear equations (S101). If matching processing is necessary (S101; Yes), the information processing device 100 unifies the matrix sizes by padding with zeros (S102). Then, after the processing of S102, or if matching processing is not necessary (S101; No), the information processing device 100 flattens each unified matrix into a row vector (S103).

[0056] Next, the information processing device 100 vertically combines the flattened row vectors to create a connection matrix (S104). Then, the information processing device 100 removes column vectors whose elements are all 0 from the connection matrix (S105). After that, the information processing device 100 performs principal component analysis on the connection matrix after the removal, to create a feature matrix with reduced dimensions (S106), and the process ends.

[0057] (effect) As described above, the information processing device 100 flattens the matrices of linear equations into row vectors, creates a connection matrix by vertically connecting multiple row vectors, and then performs principal component analysis on the connection matrix to reduce the dimensions of the connection matrix. As a result, the information processing device 100 performs principal component analysis only once on the connection matrix created by flattening and connecting each matrix, so that the principal components of each piece of dimension-reduced data have the same meaning, thereby improving the analytical accuracy of the principal component analysis. Furthermore, because the information processing device 100 flattens each matrix, it can also appropriately process matrices whose dimensions have increased due to a contact problem or the like.

[0058] Furthermore, the information processing device 100 matches the number of rows and columns of a matrix of a plurality of linear equations with those of other matrices. As a result, the information processing device 100 can unify the matrix sizes of a plurality of matrices, and therefore can unify the number of elements of row vectors after flattening.

[0059] Furthermore, the information processing device 100 removes column vectors in which all elements of the connection matrix are 0. As a result, the information processing device 100 can reduce the number of feature quantities of the connection matrix that are the subject of principal component analysis, and can reduce the total number of elements of the transformation matrix and reduce the amount of memory used during principal component analysis.

[0060] Furthermore, the information processing device 100 generates training data by combining each of the constant vectors of the multiple linear equations with a dimension-reduced combined matrix generated for each of the matrices of the multiple linear equations, and uses the training data to train a machine learning model that predicts solutions to the linear equations to be solved. As a result, the information processing device 100 can train an AI model consisting of a neural network that predicts solutions to the linear equations to be solved, using the feature matrix of matrix A created by principal component analysis with high analytical accuracy.

[0061] Example 2 In the first embodiment, a series of processing steps in preprocessing the matrix A of a linear equation and an example of training an AI model made up of a neural network are described, but the present invention is not limited to this. For example, the information processing device 100 can predict a solution to a linear equation to be solved by using an AI model made up of a trained neural network.

[0062] Therefore, in the second embodiment, an information processing device 100A that executes a process of predicting a solution to a linear equation to be solved using an AI model made up of a trained NN will be described. Note that a description of the same configuration and process as in the first embodiment will be omitted.

[0063] (Overall composition) Fig. 13 is a diagram illustrating an example of the overall configuration of an information processing system according to Example 2. An information processing device 100A illustrated in Fig. 13 has a configuration similar to that of the information processing device 100 in the information processing system according to Example 1 illustrated in Fig. 2, and predicts a solution to a linear equation to be solved using a trained AI model made up of a neural network.

[0064] The information processing device 100A predicts x, which is a solution of the linear equation Ax=b, by performing the same processing as that of the linear equation training method shown in Fig. 11 on the linear equation to be solved. Note that, instead of the training data of the first embodiment, the information processing device 100A generates feature data by concatenating a feature matrix of the matrix A of the linear equation Ax=b to be solved and a feature vector of the constant vector b.

[0065] (Functional configuration of information processing device 100A) Fig. 14 is a functional block diagram illustrating a functional configuration of an information processing device according to Example 2. The information processing device 100A illustrated in Fig. 14 is different from the information processing device 100 according to Example 1 in that it includes a prediction unit 127. Below, functional configuration units that perform processing different from the processing according to Example 1 will be described in order.

[0066] The elimination unit 124 uses information indicating the positions of column vectors whose all elements are 0, which were identified when the training data was generated, to eliminate column vectors whose all elements are 0. For example, with respect to the coupling matrix of matrix A of the linear equation to be solved, the elimination unit 124 eliminates column vectors whose positions are the same as the positions of column vectors whose all elements are 0 in the coupling matrix, which were identified when the training data was created.

[0067] In performing principal component analysis, the dimension reduction unit 125 reduces the dimensions of the connection matrix for prediction using a transformation matrix identified when the training data was generated. For example, when performing principal component analysis on the connection matrix of matrix A of the linear equation to be solved, the dimension reduction unit 125 performs principal component analysis using the transformation matrix created when the training data was generated to create a feature matrix of matrix A.

[0068] The prediction unit 127 inputs the dimension-reduced prediction connection matrix and the constant vector to a machine learning model, and predicts a solution to the linear equation based on information output from the machine learning model. For example, the prediction unit 127 inputs feature data obtained by connecting the feature matrix preprocessed according to the first embodiment and the preprocessed feature vector for the linear equation to be solved to a trained machine learning model consisting of a neural network, and obtains the output displacement vector x as the solution to the linear equation.

[0069] (Processing procedure of information processing device 100A) Next, an example of a processing procedure of the information processing device 100A according to the second embodiment will be described with reference to Fig. 15. Fig. 15 is a flowchart showing an example of the overall processing flow of the information processing device according to the second embodiment. Note that the steps in the flowchart shown in Fig. 15 may be executed in a different order, and some processes may be added or omitted.

[0070] First, the information processing device 100A calculates a matrix A and a constant vector b in a linear equation Ax=b by discretization from the initial condition and the boundary condition (S201). Then, the information processing device 100A creates a feature matrix indicating the feature amount of the matrix A by preprocessing (S202). Next, the information processing device 100A creates a feature vector indicating the feature amount of the constant vector b by preprocessing (S203).

[0071] The information processing device 100A then generates feature data by concatenating the created feature matrix and feature vector (S204). Next, the information processing device 100A inputs the generated feature data to an AI model consisting of a neural network (S205). Thereafter, the information processing device 100A acquires a displacement vector x, which is a solution to the linear equation Ax=b output by the AI ​​model (S206), and ends the process.

[0072] (effect) As described above, the information processing device 100A flattens the matrix of the linear equation to be solved into row vectors, creates a prediction connection matrix by vertically connecting multiple row vectors, performs principal component analysis on the prediction connection matrix to reduce the dimensions of the prediction connection matrix, inputs the dimension-reduced prediction connection matrix and the constant vectors into an AI model, and predicts a solution to the linear equation based on the information output from the AI ​​model.

[0073] As a result, the information processing device 100A generates feature data using a feature matrix created by principal component analysis with high analytical accuracy, and therefore can predict the solution of a linear equation with higher accuracy.

[0074] Furthermore, the information processing device 100A uses information indicating the positions of column vectors whose all elements are 0, which were identified during the generation of the training data, to remove column vectors whose all elements are 0. As a result, the information processing device 100A removes positions similar to the positions of column vectors whose all elements are 0, which were identified during training, from the connection matrix of matrix A related to preprocessing, so that it is not necessary to identify the positions of column vectors to be removed during preprocessing of matrix A, thereby reducing the processing load.

[0075] Furthermore, when performing principal component analysis, the information processing device 100A reduces the dimensions of the connection matrix for prediction using a transformation matrix identified when generating training data. As a result, the information processing device 100A performs principal component analysis on the connection matrix of matrix A related to preprocessing using the transformation matrix identified during training, so that it is not necessary to create a transformation matrix every time matrix A is preprocessed, thereby reducing the processing load and reducing the time required for principal component analysis.

[0076] Example 3 Although the embodiments of the present invention have been described above, the present invention may be embodied in various different forms other than the above-described embodiments.

[0077] (Numbers, etc.) The numbers of rows and columns of the matrices and element values ​​used in the above embodiments are merely examples and can be changed as desired. The processing flow described in each flowchart can also be changed as appropriate within a consistent range.

[0078] (system) The information including the processing procedures, control procedures, specific names, various data and parameters shown in the above documents and drawings can be changed arbitrarily unless otherwise specified.

[0079] Furthermore, the components of each device shown in the figure are functional concepts and do not necessarily have to be physically configured as shown. In other words, the specific form of distribution and integration of each device is not limited to that shown. In other words, all or part of them can be functionally or physically distributed and integrated in any unit depending on various loads, usage conditions, etc.

[0080] Furthermore, all or any part of the processing functions performed by each device may be realized by a CPU and a program analyzed and executed by the CPU, or may be realized as hardware using wired logic.

[0081] (Hardware) Fig. 16 is a diagram showing an example of a hardware configuration. Since the information processing device 100 and the information processing device 100A have the same configuration, only the information processing device 100 will be described here. As shown in Fig. 16, the information processing device 100 includes a communication device 100a, an HDD (Hard Disk Drive) 100b, a memory 100c, and a processor 100d. The components shown in Fig. 16 are connected to each other via a bus or the like.

[0082] The communication device 100a is a network interface card or the like, and communicates with other devices. The HDD 100b stores programs and DBs that operate the functions shown in FIG.

[0083] The processor 100d reads out from the HDD 100b or the like a program that executes the same processes as the respective processing units shown in FIG. 4 and loads it into the memory 100c, thereby operating a process that executes each function described in FIG. 4 or the like. For example, this process executes the same functions as the respective processing units of the information processing device 100. Specifically, the processor 100d reads out from the HDD 100b or the like a program having the same functions as the matching processing unit 121, the flattening processing unit 122, the combining unit 123, the removing unit 124, the dimension reduction unit 125, the training unit 126, and the like. Then, the processor 100d executes a process that executes the same processes as the matching processing unit 121, the flattening processing unit 122, the combining unit 123, the removing unit 124, the dimension reduction unit 125, the training unit 126, and the like.

[0084] In this way, the information processing device 100 operates as an information processing device that executes an information processing method by reading and executing a program. The information processing device 100 can also realize functions similar to those of the above-described embodiment by reading the program from a recording medium using a medium reading device and executing the read program. Note that the program in these other embodiments is not limited to being executed by the information processing device 100. For example, the above-described embodiment may also be applied in the same way to cases where another computer or server executes the program, or where these execute the program in cooperation with each other.

[0085] This program may be distributed via a network such as the Internet. Alternatively, this program may be recorded on a computer-readable recording medium such as a hard disk, a flexible disk (FD), a CD-ROM, a magneto-optical disk (MO), or a digital versatile disk (DVD), and may be read out from the recording medium and executed by a computer. [Explanation of symbols]

[0086] 100,100A Information Processing Equipment 110 Communications Department 120 control section 121 Matching processing unit 122 Flattening processing section 123 Joint 124 Removal section 125 Dimensionality reduction part 126 Training Department 127 Prediction Department 130 Storage section

Claims

1. On the computer, Flatten the matrix of linear equations into a row vector, A combination matrix is ​​created by combining the plurality of row vectors in the vertical direction; performing principal component analysis on the connection matrix to reduce the dimension of the connection matrix; An information processing program characterized by causing a process to be executed.

2. The computer, performing a process of matching the number of rows and columns of a matrix of a plurality of said linear equations with that of another matrix; The planarization process includes: flattening each of the plurality of matrices, each of which has the same number of rows and columns as the other matrices, into a matrix with one row; 2. The information processing program according to claim 1, wherein:

3. The computer, performing a process of removing column vectors whose all elements are 0 from the coupling matrix; The process of reducing the dimension is Reducing the dimension of the coupling matrix by removing the column vectors whose all elements are 0; 3. The information processing program according to claim 1, wherein the information processing program is a program for processing a plurality of data.

4. 3. The information processing program according to claim 2, wherein the matching process performs zero padding on a matrix of a small size of the matrix of the plurality of linear equations.

5. The computer, generating training data by combining each of the constant vectors of the plurality of linear equations with the dimension-reduced combination matrix generated for each of the matrices of the plurality of linear equations; using the training data to train a machine learning model that predicts solutions to the linear equation to be solved; 4. The information processing program according to claim 3, wherein the information processing program executes processing.

6. The computer, flattening the matrix of linear equations to be solved into the row vector; A combined matrix for prediction is created by combining the plurality of row vectors in the vertical direction; performing principal component analysis on the prediction connection matrix to reduce the dimension of the prediction connection matrix; inputting the dimension-reduced prediction connection matrix and constant vector into the machine learning model, and predicting a solution to the linear equation based on information output from the machine learning model; 6. The information processing program according to claim 5, further comprising: a program for causing a process to be executed.

7. The removing process includes: using information indicating the positions of column vectors whose all elements are 0, which were identified when the training data was generated, to remove the column vectors whose all elements are 0; The process of reducing the dimension is Reducing the dimension of the prediction connection matrix from which the column vectors whose all elements are 0 have been removed; 7. The information processing program according to claim 6,

8. The process of reducing the dimension is In performing the principal component analysis, a transformation matrix specified when generating the training data is used to reduce the dimension of the connection matrix for prediction.

7. The information processing program according to claim 6,

9. a flattening unit that flattens a matrix of linear equations into a row vector; a combining unit that creates a combining matrix by combining a plurality of the row vectors in the vertical direction; a dimension reduction unit that performs principal component analysis on the connection matrix to reduce the dimension of the connection matrix; An information processing device comprising:

10. An information processing method executed by an information processing device, a flattening step for flattening the matrix of linear equations into a row vector; a combining step of creating a combined matrix by combining a plurality of the row vectors in the vertical direction; a dimension reduction step of performing principal component analysis on the connection matrix to reduce the dimension of the connection matrix; An information processing method comprising:

Images