Information processing method, program, and information processing device

Abstract

To provide information processing methods and other tools that make CFD simulations easier to use. [Solution] The information processing method generates multiple sets of input datasets 411, each defined within its respective input range, for input data to be input into a CFD (Computational Fluid Dynamics) simulation. The computer then inputs each of the generated input datasets 411 into the CFD simulation, obtains a CFD output dataset 415 output from the CFD simulation, and generates a CFD surrogate model 36 based on the combination of each input dataset 411 and the corresponding CFD output dataset 415.

Description

Technical Field

[0001] The present invention relates to an information processing method, a program, and an information processing apparatus.

Background Art

[0002] CFD (Computational Fluid Dynamics) simulations are used in the technological development of various fields (Patent Document 1). CFD simulation software is commercially available from multiple companies and is also provided as open source.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] General-purpose CFD simulation software can accept a large number of input parameters. For example, when using CFD simulation software for the design of the aerodynamic characteristics of a product, multiple simulations are performed while systematically changing the input parameters to obtain a combination of input parameters that can achieve the desired aerodynamic characteristics.

[0005] However, in order to appropriately set the input parameters, both expertise in fluid dynamics and expertise in numerical analysis are required. When simulating the aerodynamic characteristics of a product with a complex shape, the cost of calculation is high. Therefore, it is difficult to fully utilize CFD simulations in actual technological development.

[0006] In one aspect, an object is to provide an information processing method or the like that makes it easier to utilize CFD simulations.

Means for Solving the Problems

[0007] The information processing method generates multiple sets of input datasets, each defined within its respective input range, which are input to a CFD simulation. Each of these generated input datasets is then input to the CFD simulation to obtain a CFD output dataset, which is output from the CFD simulation. The surrogate model training data, which includes multiple combinations of the input dataset and the corresponding CFD output dataset, is divided into multiple groups. Multiple CFD surrogate models are generated using each group, and a specific CFD surrogate model is selected based on the performance of each of the multiple CFD surrogate models. The computer performs the process. [Effects of the Invention]

[0008] In one respect, it can provide information processing methods and other tools that make CFD simulations easier to use. [Brief explanation of the drawing]

[0009] [Figure 1] This is an explanatory diagram illustrating the general method for generating a CFD surrogate model. [Figure 2] This is an explanatory diagram illustrating the configuration of an information processing system. [Figure 3] This is a flowchart illustrating the processing flow of a program that generates CFD surrogate models. [Figure 4] This is a flowchart illustrating the processing flow of a CFD subroutine. [Figure 5] This is a flowchart illustrating the processing flow of the training data evaluation subroutine. [Figure 6] This is a flowchart illustrating the processing flow of the subroutine for generating surrogate models. [Figure 7] This is a flowchart illustrating the processing flow of an active learning subroutine. [Figure 8] This flowchart explains the processing flow of the program when using the CFD surrogate model. [Figure 9] This is an explanatory diagram illustrating the configuration of the information processing system in Embodiment 2. [Modes for carrying out the invention]

[0010] [Embodiment 1] Figure 1 is an explanatory diagram illustrating the overview of how to generate a CFD surrogate model. The CFD surrogate model 36 is a machine learning model generated using input and output data from multiple sets of CFD simulations as training data. Within the range covered by the training data, using the CFD surrogate model 36 allows you to obtain simulation results at a significantly lower cost compared to using CFD simulations.

[0011] The generation process for input dataset 411 is described below. Input dataset 411 is the input data for a CFD simulation. Input dataset 411 includes numerous parameters, such as three-dimensional geometry data representing the shape of the product under design, boundary conditions for the region where the CFD simulation is performed, fluid properties, and initial conditions. Each parameter has an input range defined by physical constraints and computational constraints.

[0012] Three-dimensional shape data can include, for example, data from a 3D CAD (Computer-Aided Design) system used for product shape design. Boundary conditions include, for example, the conditions of the fluid flowing into the computational domain, such as velocity, flow rate, pressure, and temperature, the conditions of the fluid flowing out of the computational domain, and the conditions of the walls excluding the inlet and outlet. Fluid physical properties include, for example, fluid density, viscosity, specific heat, thermal conductivity, and compressibility. Initial conditions include, for example, the velocity distribution, temperature distribution, and pressure distribution at the start of the calculation.

[0013] During the generation of the input dataset 411, the user specifies, for example, a set of input datasets 411 and the range of changes for representative parameters. In the following description, parameters with a specified range of changes are referred to as variable parameters. The user sets the explanatory variables of the CFD surrogate model 36 to be generated as variable parameters.

[0014] If there are two variable parameters, the parameter space that represents the range of values that the parameters can take is two-dimensional. In the following description, a case where there are two variable parameters, the Reynolds number and the aspect ratio of the cavity which is the calculation target space, and the parameter space is two-dimensional will be described as an example. The parameter space may be one-dimensional or three-dimensional or higher-dimensional.

[0015] The control unit 21 (see FIG. 2) automatically generates a predetermined number of sets of variable parameters that are evenly distributed in the parameter space, for example, using LHS (Latin Hypercube Sampling). The predetermined number is, for example, twenty sets. In the following description, the automatically generated sets of variable parameters will be referred to as sampling points. Details of the method for automatically generating sampling points using LHS will be omitted.

[0016] Based on the input data set 411 input by the user, the control unit 21 generates a predetermined number of input data sets 411 in which the variable parameter part is changed to sampling points. The control unit 21 creates a setting file 413 corresponding to each input data set 411. For example, the control unit 21 copies the setting file 413 prepared for each field in which the CFD simulation is executed and records it in association with the input data set 411. The setting file 413 may be prepared for each type of variable parameter or for each range of variable parameters. The control unit 21 may copy the previously used setting file 413 and record it in association with the input data set 411.

[0017] The setting file 413 includes various setting conditions used for the execution of the CFD simulation software 31, such as the kinematic viscosity of the fluid, the mesh resolution of the mesh that divides the calculation target space, the time range for calculating the behavior of the fluid, the calculation time interval, and the threshold value for evaluating the convergence of the iterative calculation.

[0018] The control unit 21 inputs each input data set 411 and the setting file 413 corresponding to the input data set 411 into the CFD simulation software 31 to obtain a CFD output data set 415. The control unit 21 may input each input data set 411 into the CFD simulation software 31, and the setting file 413 associated with the input data set 411 may be automatically read during the execution of the CFD simulation software 31.

[0019] The CFD output data set 415 includes, for example, time-series data such as the velocity, temperature, density, etc. of the fluid at each node distributed in the calculation target space. The user can use the CFD output data set 415 to create, for example, an animation visualizing the behavior of the fluid flowing around the product.

[0020] The control unit 21 may utilize the CFD simulation software 31 provided in the form of SaaS (Software as a Service) by a large computer or cloud service etc. connected to the information processing device 20 (see FIG. 2) via a network.

[0021] As described above, a set of the input data set 411 and the CFD output data set 415 having the same number as the sampling points is generated. In the following description, the set of the input data set 411 and the CFD output data set 415 is referred to as a CFD data set 41. The surrogate model training data 419 is constituted by the CFD data sets 41 having the same number as the sampling points.

[0022] The control unit 21 extracts a plurality of target variables from each CFD output data set 415 included in the surrogate model training data 419. For the target variables, for example, the center velocity and the center coordinates of the vortex etc. are used. The control unit 21 may receive an instruction from the user regarding the target variables to be extracted. The user can appropriately select the target variables according to the analysis purpose etc.

[0023] The control unit 21 evaluates the quality of the surrogate model training data 419 and provides feedback. A specific example will be given to illustrate this.

[0024] The control unit 21 performs principal component analysis on the target variable extracted from the CFD output dataset 415 to detect outliers. An overview of the method for detecting outliers using principal component analysis is provided below.

[0025] The control unit 21 performs principal component analysis on the target variable and extracts multiple principal components. The target variable can be plotted on a space with the extracted principal components as coordinate axes. The control unit 21 performs cluster analysis and extracts normal clusters where the target variable is clustered together.

[0026] The control unit 21 calculates the distance between the center coordinates of a normal cluster and the target variable not included in the normal cluster, for example, using the Mahalanobis distance. The control unit 21 determines that any target variable whose distance exceeds a predetermined threshold is an outlier.

[0027] In the CFD output dataset 415 where outliers have been detected, there is a possibility that anomalies such as divergence have occurred in the calculation results of the CFD simulation software 31. The control unit 21 outputs information about the CFD dataset 41, including the CFD output dataset 415 where outliers have been detected and the corresponding input dataset 411. The output is, for example, recorded in the data lake 18 (see Figure 2). The output may also be a notification to the user via the display unit 25 (see Figure 2).

[0028] The control unit 21 may output information regarding CFD datasets 41 in which no outliers are detected. Preferably, the control unit 21 excludes CFD datasets 41 containing outliers from the surrogate model training data 419 used to generate the CFD surrogate model 36. In other words, it is preferable that the surrogate model training data 419 is composed of CFD datasets 41 that do not contain outliers.

[0029] The control unit 21 evaluates the distribution of sampling points across the entire parameter space generated using LHS. Specifically, the control unit 21 calculates quantitative indicators such as the minimum distance between sampling points and the coverage rate of sampling points, and compares these with predetermined thresholds to determine whether the sampling points are appropriately distributed within the parameter space, that is, whether they are distributed evenly and with sufficient density throughout the entire parameter space.

[0030] If the control unit 21 determines that the arrangement of sampling points is inappropriate, it outputs information regarding which part of the parameter space is lacking sampling points. The output may be recorded in the data lake 18, for example. The output may also be a notification to the user via the display unit 25.

[0031] The control unit 21 may also determine whether the sampling points are evenly distributed in the parameter space after removing the sampling points corresponding to the CFD output dataset 415 that have been determined to be outliers by principal component analysis.

[0032] Furthermore, the control unit 21 uses kernel density estimation to determine whether there is a bias in the sampling points for a portion of the parameter space, such as a range of a specific Reynolds number. If a bias is detected in the sampling points, the control unit 21 outputs information such as the region where additional sampling points should be added to reduce the bias. The output is, for example, recorded in the data lake 18. The output may also be a notification to the user via the display unit 25.

[0033] The control unit 21 determines whether the CFD dataset 41 is consistent with known physical laws. For example, it is a known physical law that vortices do not form when the Reynolds number is low. Specifically, when a fluid flows around a cylinder, it is known that no vortices form when the Reynolds number is below 40, and a Karman vortex street forms when the Reynolds number is between 40 and 200.

[0034] Therefore, if the product shape is cylindrical and the Reynolds number is around 30, but the CFD output dataset 415 contains vortices, the control unit 21 will determine that the CFD dataset 41 is not consistent with the laws of physics. The control unit 21 may also determine whether or not the CFD dataset 41 is consistent with the laws of physics based, for example, on a comparison between the CFD output dataset 415 and existing wind tunnel experiment data.

[0035] If the control unit 21 determines that there are CFD datasets 41 that are inconsistent with the laws of physics, it outputs which CFD datasets 41 are inconsistent with the laws of physics and how. The output is, for example, recorded in the data lake 18. The output may also be a notification to the user via the display unit 25. The control unit 21 preferably excludes the CFD datasets 41 that are inconsistent with the laws of physics from the surrogate model training data 419 used to generate the CFD surrogate model 36. That is, it is preferable that the surrogate model training data 419 is composed of CFD datasets 41 that are inconsistent with the laws of physics.

[0036] A user who has reviewed the records in data lake 18, or a user who has received a notification, instructs the control unit 21, for example, on the coordinates of additional sampling points. The user may also instruct the control unit 21 on how to automatically generate the additional sampling points. The control unit 21 may automatically generate the additional sampling points according to a pre-specified method. Based on the added sampling points, the control unit 21 generates an input dataset 411, runs the CFD simulation software 31, and obtains a new CFD output dataset 415.

[0037] After sufficient quality surrogate model training data 419 has been created, the control unit 21 generates a CFD surrogate model 36 by active learning. The CFD surrogate model 36 is a machine learning model that accepts explanatory variables as input and outputs the target variable. This will be explained in detail using the example where the explanatory variables are variable parameters, namely the Reynolds number and the cavity aspect ratio, and the target variables are the central velocity and the vortex center coordinates.

[0038] The control unit 21 generates a CFD surrogate model 36 based on the surrogate model training data 419. In the initial stages of generating the CFD surrogate model 36, it is preferable for the control unit 21 to use a Gaussian process model to generate the CFD surrogate model 36. Details of the procedure for generating the CFD surrogate model 36 will be described later using a flowchart.

[0039] The control unit 21 identifies regions within the parameter space where the prediction uncertainty of the surrogate model is high, and regions where the gradient with respect to the target variable is large, in which case the number of sampling points should be increased. The control unit 21 generates additional sampling points within the identified regions. The control unit 21 may also expand the parameter space by generating additional sampling points outside the range of the parameter space.

[0040] The control unit 21 generates an additional input dataset 421 with the variable parameter portion set as additional sampling points. The control unit 21 creates a configuration file 413 corresponding to each input dataset 411. The control unit 21 inputs the additional input dataset 421 and the configuration file 413 into the CFD simulation software 31 to obtain an additional CFD dataset 42. It is preferable for the control unit 21 to add the additional CFD dataset 42 to the surrogate model training data 419 and record it.

[0041] The control unit 21 extracts the target variable from the additional CFD dataset 42. The control unit 21 updates the CFD surrogate model 36 using the explanatory variables corresponding to the additional sampling points and the target variable extracted from the additional CFD dataset 42.

[0042] The control unit 21 performs active learning of the CFD surrogate model 36 by repeating a loop from identifying regions where sampling points should be increased to updating the CFD surrogate model 36 using the additional CFD dataset 42. The control unit 21 stops updating the CFD surrogate model 36, for example, when it can no longer find regions where sampling points should be increased, or when the number of active learning loops exceeds a predetermined threshold. With this, the CFD surrogate model 36 is completed.

[0043] Users can obtain the target variable with minimal computational load by inputting explanatory variables within a range that does not deviate significantly from the training data into the completed CFD surrogate model 36. Since the CFD surrogate model 36 does not require the creation of the entire input dataset 411, it can be easily used even by users with little experience in fluid dynamics analysis.

[0044] For example, in applications where the explanatory variables are finely modified to extract the explanatory variables that yield the most desirable target variable, the computational cost can be significantly reduced by using the CFD surrogate model 36. The user can then obtain a CFD output dataset 415 under the desired conditions by performing a CFD simulation using the explanatory variables selected with the CFD surrogate model 36.

[0045] The results of computationally intensive CFD simulations are recorded in the surrogate model training data 419. The user may generate a new CFD surrogate model 36 by selecting a new target variable from the CFD output dataset 415 and new explanatory variables from the input dataset 411, depending on the purpose of the analysis.

[0046] Figure 2 is an explanatory diagram illustrating the configuration of the information processing system. The information processing system 10 includes an information processing device 20 and a data lake 18.

[0047] The information processing device 20 comprises a control unit 21, a main memory 22, an auxiliary memory 23, a communication unit 24, a display unit 25, an input unit 26, and a bus. The control unit 21 is an arithmetic control device that executes the program of this embodiment. One or more CPUs (Central Processing Units), GPUs (Graphics Processing Units), or multi-core CPUs are used in the control unit 21. The control unit 21 is connected to each hardware component of the information processing device 20 via the bus.

[0048] The main memory 22 is a storage device such as SRAM (Static Random Access Memory), DRAM (Dynamic Random Access Memory), or flash memory. The main memory 22 temporarily stores information necessary during processing performed by the control unit 21 and the program currently being executed by the control unit 21.

[0049] The auxiliary storage device 23 is a storage device such as SRAM, flash memory, hard disk, or magnetic tape. The auxiliary storage device 23 stores the CFD simulation software 31, the CFD surrogate model 36, the program to be executed by the control unit 21, and various data necessary for the execution of the program.

[0050] As mentioned above, the CFD simulation software 31 may be provided in the form of SaaS (Software as a Service) via a large computer or cloud service connected to the information processing device 20 via a network.

[0051] The communication unit 24 is an interface for communication between the information processing device 20 and a network or other devices. The display unit 25 is, for example, a liquid crystal display device or an organic EL (Electro-Luminescence) display device. The input unit 26 is, for example, a keyboard or a mouse. The display unit 25 and the input unit 26 may be stacked to form a touch panel.

[0052] The information processing device 20 is a general-purpose information device such as a personal computer, tablet, or smartphone used by the user. The information processing device 20 may also be a mainframe computer, a virtual machine running on a mainframe computer, multiple personal computers performing distributed processing, or a cloud computing system.

[0053] The data lake 18 is a storage area that can flexibly store both structured and unstructured data. The data lake 18 can be built, for example, on a network drive or on a cloud storage service.

[0054] Figure 3 is a flowchart illustrating the processing flow of a program that generates a CFD surrogate model. The control unit 21 obtains instructions from the user (step S501). User instructions include, for example, an example of the input dataset 411, an example of the configuration file 413, variable parameters to be used for explanatory variables, the range of changes for each variable parameter, the target variable, and the number of sampling points to generate initially.

[0055] The control unit 21 automatically generates sampling points that are evenly distributed in the parameter space, for example, using LHS (step S502). In step S502, the control unit 21 may adaptively select a quasi-Monte Carlo method such as the Sobel sequence or the Halton sequence in addition to LHS.

[0056] The control unit 21 generates an input dataset 411 based on the input dataset 411 acquired in step S501, by changing the variable parameter portion to a sampling point (step S503).

[0057] The control unit 21 creates a configuration file 413 corresponding to each input dataset 411. For example, the control unit 21 creates a new configuration file 413 by copying a configuration file 413 prepared for each field in which CFD simulations are performed. The control unit 21 may also copy the previously used configuration file 413 and record it in association with the input dataset 411. The control unit 21 associates the input dataset 411 with the configuration file 413 and stores them in the main memory 22, auxiliary memory 23, or data lake 18.

[0058] The control unit 21 starts the CFD subroutine (step S504). The CFD subroutine is a subroutine that executes a CFD simulation. The processing flow of the CFD subroutine will be described later.

[0059] The control unit 21 extracts the target variable based on the CFD output dataset 415 output from the CFD simulation (step S505). The control unit 21 then starts the training data evaluation subroutine (step S506). The training data evaluation subroutine evaluates the quality of the surrogate model training data 419. The processing flow of the training data evaluation subroutine will be described later.

[0060] The control unit 21 determines whether the quality of the surrogate model training data 419 is sufficient (step S507). If it determines that the quality is insufficient (NO in step S507), the control unit 21 generates an additional input dataset 411, for example, based on user instructions (step S508). The control unit 21 creates a configuration file 413 corresponding to the generated input dataset 411 (step S509). The control unit 21 returns to step S504.

[0061] If it is determined that the data is sufficient (YES in step S507), the control unit 21 starts the surrogate model generation subroutine (step S510). The surrogate model generation subroutine generates a CFD surrogate model 36 based on the training data. The processing flow of the surrogate model generation subroutine will be described later.

[0062] The control unit 21 starts an active learning subroutine (step S511). The active learning subroutine is a subroutine that performs additional learning on the generated CFD surrogate model 36. The processing flow of the active learning subroutine will be described later. After that, the control unit 21 terminates its processing.

[0063] Figure 4 is a flowchart illustrating the processing flow of the CFD subroutine. The CFD subroutine is the subroutine that executes the CFD simulation.

[0064] The control unit 21 acquires an input dataset 411 corresponding to one sampling point (step S521). The control unit 21 acquires a configuration file 413 corresponding to the input dataset 411 acquired in step S521 (step S522).

[0065] The control unit 21 inputs the input dataset 411 and the configuration file 413 into the CFD simulation software 31 (step S523). The control unit 21 inputs each input dataset 411 into the CFD simulation software 31, and the configuration file 413 associated with the input dataset 411 may be automatically read during the execution of the CFD simulation software 31.

[0066] The CFD simulation software 31 performs iterative calculations according to the conditions recorded in the configuration file 413 and outputs a CFD output dataset 415 and a residual history. Here, the residuals refer to the difference in values ​​such as velocity, pressure, and density calculated at each node for each loop of the iterative calculation.

[0067] The control unit 21 determines whether the CFD output dataset 415 has converged (step S524). Specifically, the control unit 21 determines whether the residuals have converged to a threshold such as 1E-5 based on the residual history output from the CFD simulation software 31.

[0068] If convergence is determined, the control unit 21 extracts target variables, such as central velocity and vortex center coordinates, from the CFD output dataset 415 for each iteration. The control unit 21 then determines, for example, whether the rate of change of the target variables during the most recent hundred iterations is below a threshold, such as 0.1 percent.

[0069] If the residuals converge to below a threshold and the rate of change of the target variable is below a threshold, the control unit 21 determines that the CFD output dataset 415 has converged (YES in step S524). If the above conditions are not met, the control unit 21 determines that the CFD output dataset 415 has not converged (NO in step S524).

[0070] If the control unit 21 determines that the CFD output dataset 415 has not converged (NO in step S524), it modifies the configuration file 413 (step S525). Specifically, the control unit 21 makes changes that contribute to the convergence of the CFD output dataset 415, such as making the mesh resolution setting for dividing the computation target space finer, shortening the computation time interval, or changing the discretization scheme to a more stable one, among the parameters recorded in the configuration file 413. The control unit 21 returns to step S523.

[0071] If the control unit 21 determines that the CFD output dataset 415 has converged (YES in step S524), it adds metadata to the input dataset 411, the configuration file 413, and the CFD output dataset 415, respectively, and records them in the data lake 18 (step S526). The metadata includes, for example, the coordinates of the sampling points, the value of the target variable, the resources used for the calculation, and the convergence evaluation results of the iterative calculation. By appropriately adding metadata, the control unit 21 can retrieve the necessary data from the data lake 18 at any time.

[0072] Table 1 lists specific examples of metadata. The metadata assigned by the control unit 21 is not limited to those exemplified in Table 1.

[0073] [Table 1]

[0074] The control unit 21 determines whether it has finished processing the input dataset 411 corresponding to all sampling points (step S527). If it determines that it has not finished (NO in step S527), the control unit 21 returns to step S521. If it determines that it has finished (YES in step S527), the control unit 21 terminates processing.

[0075] Figure 5 is a flowchart illustrating the processing flow of the training data evaluation subroutine. The training data evaluation subroutine evaluates the quality of the surrogate model training data 419.

[0076] The control unit 21 determines whether or not outliers are included in the target variable extracted from the CFD output dataset 415 (step S641). Specifically, the control unit 21 performs principal component analysis on the target variable and extracts multiple principal components. The target variable can be plotted on a space where the extracted principal components are coordinates. The control unit 21 performs cluster analysis and extracts normal clusters where the target variable is clustered together.

[0077] The control unit 21 calculates the distance between the center coordinates of a normal cluster and the target variable not included in the normal cluster, for example, using the Mahalanobis distance. The control unit 21 determines that any target variable whose distance exceeds a predetermined threshold is an outlier. The control unit 21 preferably excludes the CFD dataset 41 containing the outliers from the surrogate model training data 419 used to generate the CFD surrogate model 36.

[0078] If the control unit determines that the target variable contains outliers (YES in step S641), it outputs information about the CFD dataset 41, which includes the CFD output dataset 415 in which the outliers were detected and the corresponding input dataset 411 (step S642). For example, the control unit 21 adds metadata indicating that the CFD dataset 41 containing the outliers is an outlier and outputs it to the data lake 18. The control unit 21 may also notify the user of the outliers by outputting information about the CFD dataset 41 containing the outliers to the display unit 25.

[0079] If it is determined that no outliers have been detected (NO in step S641), or after the completion of step S642, the control unit 21 determines whether the distribution of sampling points across the entire parameter space is appropriate (step S643). Specifically, the control unit 21 calculates quantitative indicators such as the minimum distance between sampling points and the coverage rate of the sampling points, and determines whether the sampling points are appropriately distributed within the parameter space by comparing each indicator with a predetermined threshold. Appropriate distribution of sampling points within the parameter space means that they are distributed evenly and with sufficient density throughout the entire parameter space.

[0080] If the control unit 21 determines that the sampling point arrangement is inappropriate (NO in step S643), it outputs information regarding the inappropriate arrangement (step S644). For example, the control unit 21 outputs information to the data lake 18 regarding which parts of the parameter space are lacking sampling points. The control unit 21 may also notify the user of the inappropriate sampling point arrangement by outputting information regarding which parts of the parameter space are lacking sampling points to the display unit 25.

[0081] If the arrangement of sampling points is determined to be appropriate (YES in step S643), or after the completion of step S644, the control unit 21 determines whether or not there is a bias in the sampling points across the entire parameter space (step S645). Specifically, the control unit 21 determines whether or not there is a bias in the sampling points using kernel density estimation for a portion of the parameter space, such as a range of a specific Reynolds number.

[0082] If the control unit 21 determines that there is a bias in the sampling points (YES in step S645), it outputs information regarding the bias (step S646). For example, the control unit 21 outputs information to the data lake 18 regarding areas where sampling points should be added to reduce the bias, i.e., areas with sparse sampling points. The control unit 21 may also notify the user of the bias in the sampling points by outputting information regarding areas with sparse sampling points in the parameter space to the display unit 25.

[0083] If it is determined that there is no bias in the sampling points (NO in step S645), or after the completion of step S646, the control unit 21 determines whether the CFD dataset 41 is consistent with known physical laws (step S647). For example, if the product shape is cylindrical and the Reynolds number is around 30, but the CFD output dataset 415 contains vortices, the control unit 21 determines that the CFD dataset 41 is not consistent with physical laws. The control unit 21 may also determine whether the CFD dataset 41 is consistent with physical laws based, for example, on a comparison of the CFD output dataset 415 with existing wind tunnel experiment data.

[0084] If the control unit 21 determines that there is a CFD dataset 41 that does not conform to the laws of physics (NO in step S647), it outputs information about the CFD dataset 41 that does not conform to the laws of physics (step S648). For example, the control unit 21 outputs the CFD dataset 41 that does not conform to the laws of physics to the data lake 18 with metadata on how it does not conform to the laws of physics. The control unit 21 may also notify the user by outputting information about the CFD dataset 41 that does not conform to the laws of physics to the display unit 25. It is preferable for the control unit 21 to exclude the CFD dataset 41 that does not conform to the laws of physics from the surrogate model training data 419 used to generate the CFD surrogate model 36.

[0085] If the control unit 21 determines that there are no CFD datasets 41 that do not conform to the laws of physics (YES in step S647), or after the completion of step S648, the control unit 21 terminates processing.

[0086] Figure 6 is a flowchart illustrating the processing flow of the surrogate model generation subroutine. The surrogate model generation subroutine generates a surrogate model based on the training data.

[0087] The control unit 21 divides the calculated sampling points of the CFD dataset 41 equally into, for example, five groups (step S561). The control unit 21 uses one group as the validation dataset and the remaining four groups as the training dataset. In other words, the control unit 21 divides the surrogate model training data 419 into five groups. The control unit 21 uses each training dataset to perform the processes from steps S562 to S564, which will be described below.

[0088] The control unit 21 selects a model architecture to be used for generating the CFD surrogate model 36 (step S562). In the initial stages of generating the CFD surrogate model 36, it is preferable for the control unit 21 to select a Gaussian process model in step S562.

[0089] In step S562, which is performed when the amount of data has increased during the active learning process, the control unit 21 may select, for example, PINNs (Physics-Informed Neural Networks) or a Transformer-based model. The control unit 21 may also accept a user's selection of the model architecture to be used.

[0090] The control unit 21 generates a CFD surrogate model 36 that outputs the target variable when explanatory variables are input, using the model architecture selected in step S562 (step S563). Details of how to generate the CFD surrogate model 36 using the respective model architectures of the Gaussian process model, PINNs, and Transformer model are omitted from this explanation.

[0091] The control unit 21 optimizes the hyperparameters of the CFD surrogate model 36 (step S564). For example, if the model architecture selected in step S561 is a Gaussian process model, the hyperparameters to be optimized include the kernel function and length scale. The control unit 21 can optimize the hyperparameters by using a hyperparameter optimization framework such as Optuna®.

[0092] The control unit 21 evaluates the performance of each generated CFD surrogate model 36 using a validation dataset (step S565). For example, the control unit 21 evaluates the performance of each generated CFD surrogate model 36 using evaluation metrics such as RMSE (Root Mean Square Error) or R^2 (Coefficient of Determination). The control unit 21 uses the CFD surrogate model 36 with the highest evaluation for subsequent processing.

[0093] The control unit 21 records each generated CFD surrogate model 36, information about the sampling points that make up the group used for generation, and the evaluation results in the data lake 18 (step S566). The control unit 21 then terminates the process.

[0094] Figure 7 is a flowchart illustrating the processing flow of the active learning subroutine. The active learning subroutine is a subroutine that performs additional training on the generated CFD surrogate model 36.

[0095] The control unit 21 calculates the predictive variance of the CFD surrogate model 36 in the parameter space (step S581). The predictive variance represents the uncertainty of the target variable output by the CFD surrogate model 36 for each coordinate in the parameter space. Details of how to calculate the predictive variance of the CFD surrogate model 36 generated using the respective model architectures of the Gaussian process model, PINNs, and Transformer model are omitted.

[0096] The control unit 21 determines whether there is a region in the parameter space with a large prediction variance, i.e., a region where the prediction by the CFD surrogate model 36 is uncertain (step S582). If it determines that there is such a region (YES in step S582), the control unit 21 generates additional sampling points in the region where the prediction was determined to be uncertain (step S583).

[0097] If the control unit 21 determines that there are no regions where the prediction by the CFD surrogate model 36 is uncertain (NO in step S582), it selects a region in the parameter space with a large gradient relative to the target variable (step S584). A region with a large gradient relative to the target variable means a region where the target variable changes significantly when the coordinates of the sampling points are changed. Adding sampling points in such a region is expected to contribute significantly to improving the performance of the CFD surrogate model 36.

[0098] The control unit 21 generates additional sampling points in the selected region (step S585). Here, the control unit 21 may expand the parameter space by generating additional sampling points outside the range of the parameter space.

[0099] In other words, in steps S584 and S585, the control unit 21 implements an Upper Confidence Bound (UCB) algorithm-like strategy and an information criterion-based strategy for generating additional sampling points. Here, the UCB algorithm contributes to efficiently improving the model by selecting sampling points from the parameter space that have not yet been sufficiently learned and have high uncertainty.

[0100] After the completion of step S583 or step S585, the control unit 21 generates an additional input dataset 421 corresponding to the additional sampling points (step S586). The control unit 21 creates a configuration file 413 corresponding to the generated additional input dataset 421 (step S587).

[0101] The control unit 21 inputs the additional input dataset 421 and the configuration file 413 to the CFD simulation software 31 (step S588). The CFD simulation software 31 performs iterative calculations according to the conditions recorded in the configuration file 413 and outputs the additional CFD output dataset and the residual history.

[0102] The control unit 21 determines whether the additional CFD output dataset has converged (step S589). Specifically, the control unit 21 determines whether the residuals have converged to a threshold such as 1E-5 based on the residual history output from the CFD simulation software 31.

[0103] If convergence is determined, the control unit 21 extracts target variables, such as central velocity and vortex center coordinates, from the additional CFD output dataset for each iteration. The control unit 21 then determines, for example, whether the rate of change of the target variables during the most recent hundred iterations is below a threshold, such as 0.1 percent.

[0104] If the residuals converge to below the threshold and the rate of change of the target variable is below the threshold, the control unit 21 determines that the additional CFD output dataset has converged (YES in step S589). Otherwise, the control unit 21 determines that the additional CFD output dataset has not converged (NO in step S589).

[0105] If the control unit determines that the additional CFD output dataset has not converged (NO in step S589), the control unit 21 modifies the configuration file 413 (step S590). Specifically, the control unit 21 makes changes that contribute to the convergence of the additional CFD output dataset, such as making the mesh resolution setting for dividing the computation target space finer, or shortening the computation time interval, among the parameters recorded in the configuration file 413. The control unit 21 returns to step S588.

[0106] If the control unit 21 determines that the additional CFD output dataset has converged (YES in step S589), it extracts the target variable from the additional CFD dataset 42. The control unit 21 updates the CFD surrogate model 36 based on the explanatory variables corresponding to the additional sampling points and the extracted target variable (step S591). Details of the method for updating the existing CFD surrogate model 36 based on the additional data are omitted.

[0107] The control unit 21 evaluates the updated CFD surrogate model 36 using a validation dataset (step S592). For example, the control unit 21 evaluates the degree of improvement of an evaluation metric such as RMSE or R^2. The control unit 21 records information about the updated CFD surrogate model 36, the additional input dataset 421 used for the update, the configuration file 413, and the additional CFD output dataset, as well as the evaluation results, in the data lake 18 (step S593).

[0108] The control unit 21 determines whether or not to terminate the process (step S594). For example, the control unit 21 determines to terminate the process if the evaluation index exceeds a predetermined threshold, if the degree of improvement in the evaluation index has saturated, or if there is little prospect of further performance improvement even if updates are continued. The control unit 21 may also determine to terminate the process if, for example, the number of times the loop from step S582 to step S594 is executed exceeds a predetermined threshold.

[0109] If it is determined that the process should not be terminated (NO in step S594), the control unit 21 returns to step S582. If it is determined that the process should be terminated (YES in step S594), the control unit 21 terminates the process.

[0110] The control unit 21 may generate multiple additional sampling points in steps S583 and S585. If there are multiple unprocessed sampling points and it is determined that processing should not be terminated (NO in step S594), the control unit 21 returns to step S586.

[0111] In the processing from step S581 to step S582, the control unit 21 may use the standard deviation of the predicted values ​​output by the CFD surrogate model 36 instead of the predicted variance of the CFD surrogate model 36. The control unit 21 may also use any parameter related to the uncertainty of the predicted values ​​output by the CFD surrogate model 36, such as the ensemble variance or the UCB (Upper Confidence Bound) index.

[0112] The control unit 21 preferably performs the processing from steps S586 to S591 for the multiple additional sampling points in parallel. When performing parallel processing, the control unit 21 may dynamically allocate computing resources based on the information value and computational cost of each additional sampling point.

[0113] Here, informational value refers to the expected contribution of the calculation results corresponding to the additional sampling points to the improvement of the CFD surrogate model 36. When the input dataset 411 corresponding to the additional sampling points is input to the CFD simulation software 31, if the uncertainty of the prediction regarding the CFD output dataset 415 output from the CFD simulation software 31 is high, then calculating the CFD output dataset 415 and adding it to the surrogate model training data 419 can be expected to contribute significantly to the improvement of the CFD surrogate model 36. In other words, a CFD dataset 41 with high informational value is obtained.

[0114] The computational cost refers to the amount of computation required to input the input dataset 411 into the CFD simulation software 31 and obtain the CFD output dataset 415. For example, when using the same control unit 21, the longer the control unit 21 is used, the higher the computational cost.

[0115] Let's explain with a concrete example. Note that information value and computational cost are expressed as dimensionless relative values. Assume that sampling point A has an information value of 0.9 and a computational cost of 100, and sampling point B has an information value of 0.4 and a computational cost of 5. The efficiency of each sampling point is defined as information value / computational cost.

[0116] Efficiency of sampling point A = 0.9 / 100 = 0.009 Efficiency of sampling point B = 0.4 / 5 = 0.080 Therefore, the control unit 21 prioritizes allocating computational resources to the highly efficient sampling point B. Specifically, the control unit 21 prioritizes inputting the input dataset 411 corresponding to the highly efficient sampling point to the CFD simulation software 31 over other input datasets 411.

[0117] By prioritizing the allocation of computational resources to highly efficient additional sampling points, the rate of improvement of the CFD surrogate model 36 is expected to increase.

[0118] If the CFD surrogate model 36 is generated using a Gaussian process model intended for the initial stage, and the control unit 21 determines that the process should be terminated (YES in step S594), it is preferable to recreate the CFD surrogate model 36 using a model architecture such as PINNs or a Transformer model, and continue active learning.

[0119] The CFD surrogate model 36 is completed through the series of processes described using Figures 3 to 7. Figure 8 is a flowchart illustrating the processing flow of the program at the stage where the CFD surrogate model is used.

[0120] The following explanation uses the case where the CFD surrogate model 36 is used with the information processing device 20 that generated the CFD surrogate model 36 as an example. The CFD surrogate model 36 may be distributed to other information processing devices, for example, via a network, and executed there.

[0121] The control unit 21 receives instructions from the user regarding calculation conditions such as simulation (step S601). The conditions are specified by a combination of explanatory variables. The control unit 21 determines whether or not to use the CFD surrogate model 36 (step S602). For example, the control unit 21 determines to use the CFD surrogate model 36 if the combination of explanatory variables received in step S601 is within or near the range of sampling points used to generate the CFD surrogate model 36.

[0122] If it is determined that the CFD surrogate model 36 should be used (YES in step S602), the control unit 21 inputs the explanatory variables received in step S601 into the CFD surrogate model 36 and obtains the target variable output from the CFD surrogate model 36. The control unit 21 outputs the obtained target variable (step S603).

[0123] If it is determined that the CFD surrogate model 36 will not be used (NO in step S602), the control unit 21 notifies the user that the CFD simulation software 31 must be used because the CFD surrogate model 36 is within the usable range (step S604). After the completion of step S603 or step S604, the control unit 21 determines whether or not to terminate the process (step S605).

[0124] If it is determined that the process should not be terminated (NO in step S605), the control unit 21 returns to step S601. If it is determined that the process should be terminated (YES in step S605), the control unit 21 terminates the process.

[0125] In step S604, the control unit 21 may, for example, start the CFD simulation software 31 and accept the input of the input dataset 411. A program can be provided that allows seamless use of the CFD surrogate model 36 and the CFD simulation software 31.

[0126] In step S604, it is desirable for the control unit 21 to record the explanatory variables specified by the user. The recorded data can be used to define the specifications when creating a new CFD surrogate model 36.

[0127] According to this embodiment, by creating the CFD surrogate model 36 almost automatically, an environment is made that makes it easy for users other than fluid analysis experts to utilize CFD simulations. Active learning of the CFD surrogate model 36 generates a highly reliable CFD surrogate model 36.

[0128] By automatically determining whether or not the CFD surrogate model 36 is applicable, it is possible to prevent users with limited expertise from mistakenly using the CFD surrogate model 36 and obtaining inappropriate calculation results.

[0129] [Embodiment 2] This embodiment relates to a configuration in which an information processing system 10 is realized by operating a general-purpose computer 90 in combination with a program 97. Parts common to Embodiment 1 will not be described.

[0130] Figure 9 is an explanatory diagram illustrating the configuration of the information processing system in Embodiment 2. The computer 90 includes the control unit 21, main memory 22, auxiliary memory 23, communication unit 24, display unit 25, input unit 26, and bus mentioned above, as well as a reading unit 29.

[0131] Program 97 is recorded on a portable recording medium 96. The control unit 21 reads Program 97 via the reading unit 29 and saves it to the auxiliary storage device 23. The control unit 21 may also read Program 97 stored in a semiconductor memory 98, such as flash memory, implemented in the computer 90. Furthermore, the control unit 21 may download Program 97 from another server computer (not shown) connected via the communication unit 24 and a network (not shown) and save it to the auxiliary storage device 23.

[0132] Program 97 is installed as a control program for the computer 90, loaded into the main memory 22, and executed. Thus, the information processing system 10 described in Embodiment 1 is realized.

[0133] Program 97 is an example of a program product. Program 97 may be provided on a recording medium or distributed from an external computer. Computer programs can be deployed to run on a single computer, at a single site, or distributed across multiple sites and interconnected by a communication network.

[0134] The technical features (constituent elements) described in each embodiment are combinable with each other, and by combining them, new technical features can be formed. The embodiments disclosed herein should be considered in all respects to be illustrative and not restrictive. The scope of the present invention is indicated by the claims, not in the sense described above, and all modifications within the sense and scope equivalent to the claims are intended to be included.

[0135] The independent and dependent claims described in the claims can be combined with each other in any combination, regardless of the form of reference. Furthermore, while the claims use a multi-claim format in which claims refer to two or more other claims (multi-claim format), this is not the only option. Claims may also be described using a multi-claim format in which at least one multi-claim is referenced (multi-multi-claim format). [Explanation of symbols]

[0136] 10 Information Processing Systems 18 Data Lakes 20 Information Processing Devices 21 Control Unit 22 Main storage 23 Auxiliary storage device 24 Communications Department 25 Display section 26 Input section 29 Reading section 31 CFD Simulation Software 36 CFD Surrogate Models 41 CFD datasets 411 input datasets 413 Configuration file 415 CFD output datasets 419 Surrogate Model Training Data 42 Additional CFD datasets 421 Additional Input Datasets 90 Computer 96 Portable recording media 97 Programs 98 Semiconductor memory

Claims

1. Multiple sets of input datasets are generated, each defined within its respective input range, for use in a CFD (Computational Fluid Dynamics) simulation. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The surrogate model training data, which includes multiple combinations of the input dataset and the corresponding CFD output dataset, is divided into multiple groups. Using each group, multiple CFD surrogate models are generated. Based on the performance of each of the multiple CFD surrogate models, a specific CFD surrogate model is selected. An information processing method in which a computer performs the processing.

2. Multiple sets of input datasets are generated, each defined within its respective input range, for use in CFD simulations. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. A CFD surrogate model is generated based on the combination of each input dataset and the corresponding CFD output dataset. Obtain the predicted variance of the CFD surrogate model, The input dataset corresponding to the region with large predictive variance is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The CFD surrogate model is updated based on the combination of the input dataset and the CFD output dataset. An information processing method in which a computer performs the processing.

3. Based on the contribution of the input dataset to the improvement of the CFD surrogate model and the computational cost, the efficiency of the input dataset is determined. The input dataset that has been determined to be highly efficient is given priority over other input datasets and input to the CFD simulation. The information processing method according to claim 2.

4. Multiple sets of input datasets are generated, each defined within its respective input range, for use in CFD simulations. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. A CFD surrogate model is generated based on the combination of each input dataset and the corresponding CFD output dataset. The region of explanatory variables with a large gradient relative to the objective variable of the CFD surrogate model is obtained. The input dataset corresponding to the aforementioned region is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The CFD surrogate model is updated based on the combination of the input dataset and the CFD output dataset. An information processing method in which a computer performs the processing.

5. Based on the contribution of the input dataset to the improvement of the CFD surrogate model and the computational cost, the efficiency of the input dataset is determined. The input dataset that has been determined to be highly efficient is given priority over other input datasets and input to the CFD simulation. The information processing method according to claim 4.

6. Multiple sets of input datasets are generated, each defined within its respective input range, for use in CFD simulations. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. A CFD surrogate model is generated based on the combination of each input dataset and the corresponding CFD output dataset. The performance of the CFD surrogate model is determined, If the aforementioned performance does not meet the predetermined conditions, An additional input dataset, different from the input dataset used to generate the CFD surrogate model, is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The CFD surrogate model is updated using the combination of the additional input dataset and the corresponding CFD output dataset. An information processing method in which a computer performs the processing.

7. Determine whether the acquired CFD output dataset satisfies predetermined conditions. If it is determined that the condition is not met, Modify the configuration file that contains the settings for running the aforementioned CFD simulation. The input dataset corresponding to the CFD output dataset is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained using the modified configuration file. The information processing method according to any one of claims 1 to 6.

8. If the calculation results of the CFD simulation do not converge, The configuration file containing the settings for executing the CFD simulation is modified to contribute to the convergence of the CFD output dataset. The input dataset corresponding to the CFD output dataset is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained using the modified configuration file. The information processing method according to any one of claims 1 to 6.

9. A CFD surrogate model is generated using a CFD output dataset that does not contain outliers from the CFD output dataset. The information processing method according to any one of claims 1 to 6.

10. Determining whether the CFD output dataset is consistent with physical laws. The information processing method according to any one of claims 1 to 6.

11. Calculate an index relating to the arrangement of multiple input datasets in the parameter space corresponding to the input range. The information processing method according to any one of claims 1 to 6.

12. Multiple sets of input datasets are generated, each defined within its respective input range, for use in CFD simulations. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The surrogate model training data, which includes multiple combinations of the input dataset and the corresponding CFD output dataset, is divided into multiple groups. Using each group, multiple CFD surrogate models are generated. Based on the performance of each of the multiple CFD surrogate models, a specific CFD surrogate model is selected. A program that instructs a computer to perform a process.

13. Multiple sets of input datasets are generated, each defined within its respective input range, for use in CFD simulations. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. A CFD surrogate model is generated based on the combination of each input dataset and the corresponding CFD output dataset. Obtain the predicted variance of the CFD surrogate model, The input dataset corresponding to the region with large predictive variance is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The CFD surrogate model is updated based on the combination of the input dataset and the CFD output dataset. A program that instructs a computer to perform a process.

14. Multiple sets of input datasets are generated, each defined within its respective input range, for use in CFD simulations. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. A CFD surrogate model is generated based on the combination of each input dataset and the corresponding CFD output dataset. The region of explanatory variables with a large gradient relative to the objective variable of the CFD surrogate model is obtained. The input dataset corresponding to the aforementioned region is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The CFD surrogate model is updated based on the combination of the input dataset and the CFD output dataset. A program that instructs a computer to perform a process.

15. Multiple sets of input datasets are generated, each defined within its respective input range, for use in CFD simulations. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. A CFD surrogate model is generated based on the combination of each input dataset and the corresponding CFD output dataset. The performance of the CFD surrogate model is determined, If the aforementioned performance does not meet the predetermined conditions, An additional input dataset, different from the input dataset used to generate the CFD surrogate model, is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The CFD surrogate model is updated using the combination of the additional input dataset and the corresponding CFD output dataset. A program that instructs a computer to perform a process.

16. An information processing device comprising a control unit, The control unit, Multiple sets of input datasets are generated, each defined within its respective input range, for use in CFD simulations. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The surrogate model training data, which includes multiple combinations of the input dataset and the corresponding CFD output dataset, is divided into multiple groups. Using each group, multiple CFD surrogate models are generated. Based on the performance of each of the multiple CFD surrogate models, a specific CFD surrogate model is selected. An information processing device that performs processing.

17. An information processing device comprising a control unit, The control unit, Multiple sets of input datasets are generated, each defined within its respective input range, for use in CFD simulations. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. A CFD surrogate model is generated based on the combination of each input dataset and the corresponding CFD output dataset. Obtain the predicted variance of the CFD surrogate model, The input dataset corresponding to the region with large predictive variance is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The CFD surrogate model is updated based on the combination of the input dataset and the CFD output dataset. An information processing device that performs processing.

18. An information processing device comprising a control unit, The control unit, Multiple sets of input datasets are generated, each defined within its respective input range, for use in CFD simulations. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. A CFD surrogate model is generated based on the combination of each input dataset and the corresponding CFD output dataset. The region of explanatory variables with a large gradient relative to the objective variable of the CFD surrogate model is obtained. The input dataset corresponding to the aforementioned region is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The CFD surrogate model is updated based on the combination of the input dataset and the CFD output dataset. An information processing device that performs processing.

19. An information processing device comprising a control unit, The control unit, Multiple sets of input datasets are generated, each defined within its respective input range, for use in CFD simulations. Each of the generated input datasets is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. A CFD surrogate model is generated based on the combination of each input dataset and the corresponding CFD output dataset. The performance of the CFD surrogate model is determined, If the aforementioned performance does not meet the predetermined conditions, An additional input dataset, different from the input dataset used to generate the CFD surrogate model, is input to the CFD simulation, and the CFD output dataset output from the CFD simulation is obtained. The CFD surrogate model is updated using the combination of the additional input dataset and the corresponding CFD output dataset. An information processing device that performs processing.

Images