Data generation program, data generation apparatus, and data generation method

Abstract

To improve convergence of processing for generating input data for a machine learning model, in inferring physical quantities from a stiffness matrix using the machine learning model.SOLUTION: A computer transforms a stiffness matrix to be analyzed, into a matrix to be processed, having a smaller condition number than those of the stiffness matrix. The computer performs dimensionality reduction using the matrix to be processed, and generates input data for a machine learning model that infers physical quantities for an analysis target based on a result of the dimensionality reduction.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to data generation technology. [Background technology]

[0002] A structural analysis simulation is a simulation that calculates the temporal and spatial changes of physical quantities related to an object to which an external force is applied. A simulation program for structural analysis simulation calculates physical quantities such as displacement and stress by solving partial differential equations using, for example, the finite element method (FEM).

[0003] Regarding structural analysis, a program for speeding up structural analysis simulation is known (see, for example, Patent Document 1). Subsurface simulation using a filtered grid connectivity graph is also known (see, for example, Patent Document 2). Simulation of phenomena characterized by partial differential equations is also known (see, for example, Patent Document 3). Data processing methods using multigrid methods are also known (see, for example, Patent Document 4). [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2023-9904 [Patent Document 2] U.S. Patent Application Publication No. 2023 / 0119861 [Patent Document 3] U.S. Patent Application Publication No. 2014 / 0207426 [Patent Document 4] Japanese Patent Application Laid-Open No. 2008-186361 Summary of the Invention [Problem to be solved by the invention]

[0005] In the structural analysis simulation of Patent Document 1, a solution to a system of simultaneous linear equations in which the stiffness matrix of the analysis target is used as a coefficient matrix is ​​obtained using a graph convolutional network (GCN). In this case, the process of generating input data for the GCN may have difficulty converging.

[0006] This problem does not only occur when solving simultaneous linear equations using GCNs, but also when using various machine learning models to find physical quantities related to an object of analysis.

[0007] In one aspect, the present invention aims to improve the convergence of a process for generating input data for a machine learning model when a physical quantity is inferred from a stiffness matrix using the machine learning model. [Means for solving the problem]

[0008] In one proposal, the data generation program causes a computer to execute the following processes.

[0009] The computer converts the stiffness matrix of the analysis object into a process object matrix having a condition number smaller than the condition number of the stiffness matrix. The computer performs dimension reduction processing using the process object matrix, and generates input data for a machine learning model that infers physical quantities related to the analysis object based on the result of the dimension reduction processing. [Effects of the Invention]

[0010] According to one aspect, when a physical quantity is inferred from a stiffness matrix using a machine learning model, the convergence of the process of generating input data for the machine learning model can be improved. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 2 is a functional configuration diagram of a data generating device according to an embodiment. [Figure 2] 10 is a flowchart of a data generation process. [Figure 3]FIG. 2 is a functional configuration diagram of a simulation device. [Figure 4] FIG. 10 is a diagram illustrating a conversion process for a processing target matrix B. [Figure 5] FIG. 10 is a diagram illustrating a stiffness matrix A and a first processing target matrix B. [Figure 6] FIG. 10 is a diagram showing a feature matrix of a stiffness matrix A and a first feature matrix F1. [Figure 7] FIG. 10 is a diagram showing a second processing target matrix B. [Figure 8] FIG. 10 is a diagram showing a second feature matrix F1. [Figure 9] 10 is a flowchart of a simulation process. [Figure 10] FIG. 2 is a hardware configuration diagram of an information processing device. DETAILED DESCRIPTION OF THE INVENTION

[0012] Hereinafter, embodiments will be described in detail with reference to the drawings.

[0013] In structural analysis simulations, the solution to the unknown displacement vector x can be calculated by solving the following simultaneous linear equations using the stiffness matrix A of the object and the force vector b representing the external force applied to the object.

[0014] Ax=b (1)

[0015] A linear solver is used to solve the system of linear equations. The linear solver calculates x using an iterative method such as the conjugate gradient method.

[0016] In the structural analysis simulation of Patent Document 1, a solution for x is inferred using a GCN, which is a trained machine learning model, instead of a linear solver. By inferring a solution using a GCN instead of a linear solver, which requires a large amount of calculation, the amount of calculation in the structural analysis simulation is reduced, and the calculation time is shortened. Such a GCN is sometimes called a surrogate model.

[0017] The information processing device in Patent Document 1 generates a stiffness matrix A and a force vector b from mesh data and boundary condition data of an object. The mesh data represents the shape of the object divided into multiple elements, and includes multiple nodes and multiple edges connecting these nodes. The boundary condition data represents the external forces applied to each node of the object.

[0018] Next, the information processing device generates feature data from the stiffness matrix A and the force vector b. The feature data is, for example, a feature matrix. Each row of the feature matrix corresponds to a node of the mesh data, and multiple elements in one row represent multiple feature amounts of one node. The multiple feature amounts of each node represent a feature vector.

[0019] Next, the information processing device performs principal component analysis (PCA) on the feature data to reduce the number of dimensions of the feature vector, generating feature data with reduced dimensions.The information processing device then inputs the mesh data and the feature data with reduced dimensions to a GCN, which infers a displacement vector x from the input mesh data and feature data.

[0020] By performing PCA on feature data, the features of each node are reflected to some extent in the features of nodes farther from it, realizing overall information transfer between nodes. This improves the inference accuracy of GCN for large-scale graphs.

[0021] However, depending on the target of structural analysis, the stiffness matrix A may be an ill-conditioned matrix. Ill-conditioned matrices are very sensitive to small changes and are therefore not well suited to numerical analysis. When PCA is performed on a feature matrix generated from an ill-conditioned stiffness matrix A, the singular value decomposition calculation becomes unstable and difficult to converge, which can result in the PCA taking a long time or not completing. If PCA does not complete, inference using GCN will not be performed.

[0022] 1 shows an example of the functional configuration of a data generating device according to an embodiment. The data generating device 101 in FIG. 1 includes a transforming unit 111, a dimension reducing unit 112, and a generating unit 113.

[0023] Fig. 2 is a flowchart showing an example of data generation processing performed by the data generating device 101 in Fig. 1. First, the conversion unit 111 converts the stiffness matrix of the analysis target into a processing target matrix having a condition number smaller than the condition number of the stiffness matrix (step 201).

[0024] Next, the dimension reduction unit 112 performs dimension reduction processing using the processing target matrix (step 202), and the generation unit 113 generates input data for a machine learning model that infers physical quantities related to the analysis target based on the results of the dimension reduction processing (step 203).

[0025] According to the data generating device 101 in FIG. 1, when a physical quantity is inferred from a stiffness matrix using a machine learning model, it is possible to improve the convergence of the process of generating input data for the machine learning model.

[0026] Fig. 3 shows an example of the functional configuration of a simulation device including the data generation device 101 of Fig. 1. The simulation device 301 of Fig. 3 includes a first generation unit 311, a conversion unit 312, a dimension reduction unit 313, a second generation unit 314, an inference unit 315, an output unit 316, and a storage unit 317.

[0027] The transform unit 312, the dimension reduction unit 313, and the second generation unit 314 correspond to the transform unit 111, the dimension reduction unit 112, and the generation unit 113 in FIG. 1, respectively.

[0028] The simulation device 301 performs a structural analysis simulation of an object in CAE (Computer-Aided Engineering), structural design, engineering design, etc. The object that is the target of the structural analysis simulation may be a structure such as a road, bridge, or building, the earth's crust, a fluid, etc., or an industrial product.

[0029] In a structural analysis simulation, the displacement of the object being analyzed is calculated by finding a solution to equation (1) at each time step. Displacement is an example of a physical quantity related to the object being analyzed.

[0030] The memory unit 317 stores mesh data 321, boundary condition data 322, and an inference model 323. The mesh data 321 represents the shape of an object divided into multiple elements, and includes multiple nodes and multiple edges connecting these nodes. The boundary condition data 322 represents external forces applied to each node of the object.

[0031] The inference model 323 is a trained machine learning model, and is sometimes called a surrogate model. For example, a neural network combining a graph neural network (GNN) and an MLP (Multilayer Perceptron) is used as the inference model 323. The GNN may be a GCN. A neural network combining a GCN and an MLP corresponds to the GCN in Patent Document 1.

[0032] The first generating unit 311 generates the stiffness matrix A and the force vector b of the formula (1) from the mesh data 321 and the boundary condition data 322, and stores them in the storage unit 317. Each element of the stiffness matrix A represents a feature amount related to the stiffness of the object.

[0033] The conversion unit 312 performs preprocessing on the stiffness matrix A to convert the stiffness matrix A into a target matrix B having a condition number smaller than that of the stiffness matrix A, and stores the target matrix B in the storage unit 317. The target matrix B is a matrix generated as a result of the preprocessing, and is a matrix to be processed in the dimension reduction process. The number of rows and columns of the target matrix B is the same as the number of rows and columns of the stiffness matrix A.

[0034] The condition number of the stiffness matrix A is a measure of the degree of change in the displacement vector x relative to the change in the force vector b in equation (1). The larger the condition number of the stiffness matrix A, the more sensitive the displacement vector x is to the change in the force vector b. The condition number c(M) of the matrix M is the inverse matrix M of the matrix M.-1 Using this, it is expressed by the following equation:

[0035] c(M)=nr(M)*nr(M -1 ) (2)

[0036] nr(M) represents the norm of matrix M, and nr(M -1 ) is the inverse matrix M -1 represents the norm of nr(M) and nr(M -1 ) is the L2 norm, then c(M) is expressed by the following equation:

[0037] c(M)=smax(M) / smin(M) (3)

[0038] smax(M) denotes the maximum singular value of matrix M, and smin(M) denotes the minimum singular value of matrix M.

[0039] Preconditioning is a process that improves the convergence of a linear system and can transform the original matrix into a well-conditioned matrix. Examples of preconditioning include diagonal scaling, incomplete decomposition, algebraic multigrid, domain decomposition, and block diagonal preconditioning. For example, the matrix B to be processed is the inverse matrix P of the preconditioning matrix P. -1 Using this, it is described by the following equation:

[0040] B=P -1 A (4)

[0041] In this case, equation (1) is transformed into the following equation:

[0042] P -1 Ax=P -1 b (5)

[0043] Therefore, the conversion unit 312 performs preprocessing on the force vector b to convert the force vector b into a preprocessed force vector v, and stores the force vector v in the storage unit 317. The force vector v is described by the following equation.

[0044] v=P -1 b (6)

[0045] The preconditioning matrix P is P -1 The condition number of A is selected to be smaller than the condition number of stiffness matrix A. This converts stiffness matrix A into a well-conditioned target matrix B suitable for numerical analysis, making the calculation of singular value decomposition in PCA more stable and facilitating convergence.

[0046] The dimension reduction unit 313 converts the processing target matrix B into a feature matrix F1 by arranging the feature amounts of the same node in the same row using a method similar to that used to convert stiffness matrices in Patent Document 1, and stores the result in the storage unit 317. Each row of the feature matrix F1 corresponds to each node of the mesh data 321, and multiple elements in one row represent multiple feature amounts related to the stiffness of one node.

[0047] The feature matrix F1 has the same number of elements as the target matrix B, and the feature values ​​of each element are unchanged. The number of rows in the feature matrix F1 is fewer than the number of rows in the target matrix B, and the number of columns in the feature matrix F1 is greater than the number of columns in the target matrix B.

[0048] FIG. 4 shows an example of a conversion process for a matrix B to be processed. FIG. 4(a) shows an example of the matrix B to be processed. The matrix B to be processed in FIG. 4(a) includes n×n submatrices M1(i,j) (i=1 to n, j=1 to n). n represents the number of nodes included in the mesh data 321, and each submatrix M1(i,j) is a matrix with 3 rows and 3 columns. Therefore, the matrix B to be processed is a matrix with 3n rows and 3n columns. The submatrix M1(i,j) represents the degree to which the jth node moves when an external force is applied to the ith node.

[0049] FIG. 4(b) shows an example of a feature matrix F1 generated by a conversion process from the processing target matrix B in FIG. 4(a). The feature matrix F1 in FIG. 4(b) includes n×n submatrices M2(i,j) (i=1 to n, j=1 to n). Each submatrix M2(i,j) is a matrix with 1 row and 9 columns. Therefore, the feature matrix F1 is a matrix with n rows and 9n columns. The n rows of the feature matrix F1 correspond to the n nodes, respectively.

[0050] The dimension reduction unit 313 rearranges the nine elements contained in the submatrix M1(i,j) in Figure 4(a) into one row, thereby extending the submatrix M1(i,j) horizontally and generating the submatrix M2(i,j).

[0051] Next, the dimension reduction unit 313 performs dimension reduction processing on the feature matrix F1 to generate a feature matrix F2 with a reduced number of dimensions, and stores the generated matrix in the storage unit 317. The feature matrix F2 has fewer elements than the processing target matrix B. The feature matrix F2 is an example of a processing result matrix. For example, PCA is used as the dimension reduction processing.

[0052] The second generation unit 314 generates feature data 324 using the feature matrix F2 and the force vector v and stores the generated feature data 324 in the storage unit 317. The second generation unit 314, for example, converts the force vector v into a feature matrix F3 having the same number of rows as the feature matrix F2, and generates a feature matrix F4 by concatenating the feature matrix F2 and the feature matrix F3. The second generation unit 314 then stores the generated feature matrix F4 in the storage unit 317 as the feature data 324.

[0053] The force vector v is an example of a vector related to the boundary conditions of the analysis target. The feature data 324 is an example of input data for the machine learning model.

[0054] By concatenating the feature matrix F2 and the feature matrix F3, the information of the force vector v that is not included in the feature matrix F2 can be included in the feature data 324.

[0055] The inference unit 315 inputs the mesh data 321 as a graph to the inference model 323, and also inputs the feature data 324 to the inference model 323, and infers a solution to the displacement vector x in equation (5) using the inference model 323. The inference model 323 finds a solution to the displacement vector x from the input mesh data 321 and feature data 324.

[0056] The inference model 323 is generated by training a pre-trained machine learning model using supervised machine learning. For example, mesh data and feature data of a known analysis target can be used as input training data. Furthermore, the solution to the displacement vector x obtained by solving the simultaneous linear equations of Equation (5) for the known analysis target using a linear solver is used as the ground truth label.

[0057] The output unit 316 outputs the solution inferred by the inference unit 315 as the solution to equation (1).

[0058] 3, PCA converges more easily by converting stiffness matrix A into processing target matrix B through preprocessing. This improves the convergence of the process for generating input data for the inference model 323, thereby shortening the calculation time. This speeds up the structural analysis simulation using the inference model 323.

[0059] The feature data included in the training data of the inference model 323 is also generated using preprocessing in the same manner as the feature data 324. This improves the convergence of the process for generating training data and reduces the calculation time.

[0060] The simulation device 301 may use other dimension reduction methods, such as a k-nearest neighbor method or a subspace method, instead of PCA as the dimension reduction method for the feature matrix F1. Even when other dimension reduction methods are used, the convergence of the dimension reduction method is improved and the calculation time is shortened, as in the case of PCA.

[0061] Instead of performing the dimension reduction process on the feature matrix F1, the simulation device 301 may convert the force vector v into a feature matrix F3 having the same number of rows as the feature matrix F2, and perform the dimension reduction process on the feature matrix obtained by concatenating the feature matrix F1 and the feature matrix F3. In this case, the feature matrix F2 with the reduced number of dimensions contains information about the force vector v, and therefore the feature matrix F2 is used as the feature data 324 as is.

[0062] Fig. 5 shows examples of the stiffness matrix A and the first processing target matrix B. Fig. 5(a) shows an example of the stiffness matrix A. The stiffness matrix A in Fig. 5(a) is a stiffness matrix for a structural analysis simulation that determines the deformation and stress when joining two mechanical parts by snap-fitting.

[0063] In this example, the mesh data 321 contains 2142 nodes, and the stiffness matrix A is a symmetric matrix with 6426 rows and 6426 columns. Black areas represent non-zero elements, and white areas represent zero elements. The condition number is 3039423.73, and the element values ​​are distributed in the range of -20000 to 60000.

[0064] FIG. 5(b) shows an example of a first processing target matrix B. The processing target matrix B in FIG. 5(b) is generated from the stiffness matrix A in FIG. 5(a) by a first pre-processing. The first pre-processing is diagonal scaling. A diagonal matrix D is used as a pre-processing matrix P for diagonal scaling, and the diagonal elements D(i,i) (i = 1 to n) of the diagonal matrix D match the diagonal elements A(i,i) of the stiffness matrix A.

[0065] The condition number of the processing target matrix B in FIG. 5(b) is 1405294.82, which is smaller than the condition number of the stiffness matrix A in FIG. 5(a). Therefore, the processing target matrix B is a matrix with better conditions than the stiffness matrix A. The element values ​​are distributed in the range of -1.0 to 1.0.

[0066] Fig. 6 shows examples of the feature matrix of stiffness matrix A and the first feature matrix F1. Fig. 6(a) shows an example of a feature matrix generated by the conversion process shown in Fig. 4 without applying preprocessing to the stiffness matrix A of Fig. 5(a). The feature matrix of Fig. 6(a) is a matrix with 2142 rows and 19278 columns, and the condition number is 70214.55. PCA on this feature matrix is ​​difficult to converge, and the result of the PCA processing is a feature matrix with 2142 rows and 1233 columns.

[0067] FIG. 6(b) shows an example of a first feature matrix F1 generated from the target matrix B in FIG. 5(b) by the conversion process shown in FIG. 4. The feature matrix F1 in FIG. 6(b) is a matrix with 2142 rows and 19278 columns. The condition number is 11.78, which is smaller than the condition number of the feature matrix in FIG. 6(a). Therefore, the feature matrix F1 is a matrix with better conditions than the feature matrix in FIG. 6(a).

[0068] The PCA for this feature matrix F1 is easy to converge, and the result of the PCA is a feature matrix F2 with 2142 rows and 1808 columns. Therefore, the feature matrix F2 contains more information than the feature matrix generated by PCA from the feature matrix in Figure 6(a).

[0069] FIG. 7 shows an example of the second processing target matrix B. The processing target matrix B in FIG. 7 is generated from the stiffness matrix A in FIG. 5(a) by the second preprocessing. The second preprocessing is block diagonal preprocessing. The procedure for block diagonal preprocessing is as follows.

[0070] (P1) The conversion unit 312 divides the stiffness matrix A into multiple blocks along the diagonal lines.

[0071] (P2) The conversion unit 312 decomposes the matrix K of each block into the product of a lower triangular matrix L and an upper triangular matrix U by incomplete LU decomposition, and calculates the inverse matrix L of the lower triangular matrix L. -1 and the inverse matrix U of the upper triangular matrix U -1 Using the above, the inverse matrix (LU) of the matrix LU -1 The transform unit 312 may use the complete LU decomposition instead of the incomplete LU decomposition.

[0072] (P3) The transform unit 312 calculates the inverse matrix (LU) of each block. -1 and matrix K (LU) -1 The matrix to be processed, B, is generated by concatenating K along the diagonal.

[0073] The matrix B to be processed in Figure 7 is generated by block diagonal preprocessing using blocks with 1071 rows and 1071 columns. Therefore, the number of blocks connected along the diagonal of the matrix B to be processed is 6. The condition number of the matrix B to be processed in Figure 7 is 75821.31, which is smaller than the condition number of the stiffness matrix A in Figure 5(a).

[0074] FIG. 8 shows an example of a second feature matrix F1. The feature matrix F1 in FIG. 8 is generated from the processing target matrix B in FIG. 7 by the conversion process shown in FIG. 4. The feature matrix F1 has 2142 rows and 19278 columns. The condition number is 38674.31, which is smaller than the condition number of the feature matrix in FIG. 6(a). Therefore, the feature matrix F1 is a matrix with better conditions than the feature matrix in FIG. 6(a).

[0075] Fig. 9 is a flowchart showing an example of simulation processing performed by the simulation device 301 of Fig. 3. The simulation processing of Fig. 9 is repeated for each time step.

[0076] First, the first generating unit 311 generates a stiffness matrix A and a force vector b from the mesh data 321 and the boundary condition data 322 (step 901). Then, the converting unit 312 converts the stiffness matrix A into a processing target matrix B by performing preprocessing on the stiffness matrix A (step 902).

[0077] Next, the dimension reduction unit 313 converts the target matrix B into a feature matrix F1 (step 903), and generates a feature matrix F2 by performing dimension reduction processing on the feature matrix F1 (step 904).Then, the second generation unit 314 generates feature data 324 using the feature matrix F2 and the force vector v (step 905).

[0078] Next, the inference unit 315 inputs the mesh data 321 and the feature data 324 into the inference model 323 and infers a solution for the displacement vector x using the inference model 323 (step 906). Then, the output unit 316 outputs the solution inferred by the inference unit 315 (step 907).

[0079] The simulation device 301 can perform not only structural analysis simulation of an object but also simulation of other analysis targets such as electric fields and magnetic fields. As the inference model 323 in Fig. 3, other machine learning models such as random forests may be used instead of the neural network.

[0080] 1 is merely an example, and some of the components may be omitted or changed depending on the application or conditions of the data generating device 101. The configuration of the simulation device 301 in FIG. 3 is merely an example, and some of the components may be omitted or changed depending on the application or conditions of the simulation device 301.

[0081] The flowcharts of FIGS. 2 and 9 are merely examples, and some of the processes may be omitted or changed depending on the configuration or conditions of the data generating device 101 or the simulation device 301.

[0082] 4 is merely an example, and the dimension reduction unit 313 may convert the processing target matrix B into the feature matrix F1 by using another rearrangement method. The stiffness matrix A, processing target matrix B, and feature matrix F1 shown in FIGS. 5 to 8 are merely examples, and the stiffness matrix A, processing target matrix B, and feature matrix F1 change depending on the analysis target.

[0083] Equations (1) to (6) are merely examples, and the simulation device 301 may perform the structural analysis simulation based on other calculation formulas.

[0084] FIG. 10 shows an example of the hardware configuration of an information processing device (computer) used as the data generating device 101 in FIG. 1 and the simulation device 301 in FIG.

[0085] 10 includes a CPU (Central Processing Unit) 1001, a memory 1002, an input device 1003, an output device 1004, an auxiliary storage device 1005, a media drive device 1006, and a network connection device 1007. These components are hardware and are connected to each other via a bus 1008.

[0086] The memory 1002 is, for example, a semiconductor memory such as a read-only memory (ROM) or a random access memory (RAM), and stores programs and data used in processing. The memory 1002 may operate as the storage unit 317 in FIG.

[0087] 1 by executing a program using the memory 1002. The CPU 1001 (processor) also operates as the first generation unit 311, the conversion unit 312, the dimension reduction unit 313, the second generation unit 314, and the inference unit 315 in FIG. 3 by executing a program using the memory 1002.

[0088] The input device 1003 is, for example, a keyboard, a pointing device, etc., and is used to input instructions or information from a user or operator. The output device 1004 is, for example, a display device, a printer, etc., and is used to output inquiries or instructions to a user or operator and processing results. The output device 1004 may operate as the output unit 316 in Figure 3, and the processing results may be an inferred solution.

[0089] The auxiliary storage device 1005 is, for example, a magnetic disk device, an optical disk device, a magneto-optical disk device, a tape device, or the like. The auxiliary storage device 1005 may be a hard disk drive or a solid state drive (SSD). The information processing device stores programs and data in the auxiliary storage device 1005 and can use them by loading them into the memory 1002. The auxiliary storage device 1005 may operate as the storage unit 317 in FIG. 3.

[0090] The medium drive device 1006 drives the portable recording medium 1009 and accesses the recorded contents thereof. The portable recording medium 1009 is a memory device, a flexible disk, an optical disk, a magneto-optical disk, etc. The portable recording medium 1009 may be a CD-ROM (Compact Disk Read Only Memory), a DVD (Digital Versatile Disk), a USB (Universal Serial Bus) memory, etc. A user or operator can store programs and data in the portable recording medium 1009 and load them into the memory 1002 for use.

[0091] In this way, the computer-readable recording medium that stores the program and data used in the processing is a physical (non-transitory) recording medium such as memory 1002, auxiliary storage device 1005, or portable recording medium 1009.

[0092] The network connection device 1007 is a communication circuit connected to a communication network such as a WAN (Wide Area Network) or a LAN (Local Area Network) and performs data conversion associated with communication. The information processing device receives programs and data from an external device via the network connection device 1007 and loads them into the memory 1002 for use. The network connection device 1007 may operate as the output unit 316 in FIG. 3.

[0093] It should be noted that the information processing device does not need to include all of the components shown in Figure 10, and some of the components may be omitted or modified depending on the application or conditions of the information processing device. For example, if an interface with a user or operator is not required, the input device 1003 and the output device 1004 may be omitted. If the portable recording medium 1009 or a communication network is not used, the medium drive device 1006 or the network connection device 1007 may be omitted.

[0094] Although the disclosed embodiments and their advantages have been described in detail, those skilled in the art may make various modifications, additions, and omissions without departing from the scope of the invention as clearly set forth in the claims.

[0095] The following notes are further provided regarding the embodiment described with reference to FIGS. (Appendix 1) converting a stiffness matrix of an analysis object into a matrix of an object to be processed having a condition number smaller than the condition number of the stiffness matrix; performing a dimension reduction process using the target matrix; generating input data for a machine learning model that infers physical quantities related to the analysis target based on the result of the dimension reduction process; A data generation program that causes a computer to execute processing. (Appendix 2) a result of the dimension reduction process includes a processed result matrix having fewer elements than the elements of the target matrix; The data generation program according to claim 1, characterized in that the process of generating input data for the machine learning model includes a process of generating input data for the machine learning model using the processing result matrix and a vector related to the boundary conditions of the analysis target. (Appendix 3) 3. The data generation program according to claim 1, wherein the dimension reduction process is principal component analysis. (Appendix 4) a conversion unit that converts a stiffness matrix of an analysis object into a processing object matrix having a condition number smaller than the condition number of the stiffness matrix; a dimension reduction unit that performs dimension reduction processing using the processing target matrix; a generation unit that generates input data for a machine learning model that infers physical quantities related to the analysis target based on a result of the dimension reduction process; A data generating device comprising: (Appendix 5) a result of the dimension reduction process includes a processed result matrix having fewer elements than the elements of the target matrix; The data generation device described in Appendix 4, characterized in that the generation unit generates input data for the machine learning model using the processing result matrix and a vector related to the boundary conditions of the analysis target. (Appendix 6) The data generating device according to claim 4 or 5, wherein the dimension reduction process is principal component analysis. (Appendix 7) converting a stiffness matrix of an analysis object into a matrix of an object to be processed having a condition number smaller than the condition number of the stiffness matrix; performing a dimension reduction process using the target matrix; generating input data for a machine learning model that infers physical quantities related to the analysis target based on the result of the dimension reduction process; A data generation method characterized in that processing is executed by a computer. (Appendix 8) a result of the dimension reduction process includes a processed result matrix having fewer elements than the elements of the target matrix; The data generation method described in Appendix 7, characterized in that the process of generating input data for the machine learning model includes a process of generating input data for the machine learning model using the processing result matrix and a vector related to the boundary conditions of the analysis target. (Appendix 9) 9. The data generation method according to claim 7, wherein the dimension reduction process is principal component analysis. [Explanation of symbols]

[0096] 101 Data generation device 111, 312 conversion unit 112, 313 Dimension reduction part 113 Generation part 301 Simulation Device 311 1st generation part 314 Second generation part 315 Reasoning Department 316 Output section 317 Storage section 321 mesh data 322 Boundary Condition Data 323 Inference Model 324 feature data 1001 CPU 1002 memory 1003 Input Device 1004 Output Device 1005 Auxiliary storage device 1006 Media drive unit 1007 Network connection device 1008 Bus 1009 Portable recording media

Claims

1. converting a stiffness matrix of an analysis object into a matrix of an object to be processed having a condition number smaller than the condition number of the stiffness matrix; performing a dimension reduction process using the target matrix; generating input data for a machine learning model that infers physical quantities related to the analysis target based on the result of the dimension reduction process; A data generation program that causes a computer to execute processing.

2. a result of the dimension reduction process includes a processed result matrix having fewer elements than the elements of the target matrix; The data generation program according to claim 1, characterized in that the process of generating input data for the machine learning model includes a process of generating input data for the machine learning model using the processing result matrix and a vector related to the boundary conditions of the analysis target.

3. 3. The data generation program according to claim 1, wherein the dimension reduction process is principal component analysis.

4. a conversion unit that converts a stiffness matrix of an analysis object into a processing object matrix having a condition number smaller than the condition number of the stiffness matrix; a dimension reduction unit that performs dimension reduction processing using the processing target matrix; a generation unit that generates input data for a machine learning model that infers physical quantities related to the analysis target based on a result of the dimension reduction process; A data generating device comprising:

5. converting a stiffness matrix of an analysis object into a matrix of an object to be processed having a condition number smaller than the condition number of the stiffness matrix; performing a dimension reduction process using the target matrix; generating input data for a machine learning model that infers physical quantities related to the analysis target based on the result of the dimension reduction process; A data generation method characterized in that processing is executed by a computer.

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