Data assimilation apparatus, data assimilation method, data assimilation program, and data assimilation system

Abstract

An acquisition unit (101) acquires an actual measurement value obtained by measuring changes in a data assimilation object in a predetermined environment. A calculation unit (102) uses a provisional initial state and a provisional value of an unknown parameter regarding the data assimilation object to numerically calculate the change in the data assimilation object in the predetermined environment. An update unit (103) calculates the value of an evaluation function representing an error between the actual measurement value and a value obtained from the result of the numerical calculation corresponding to the actual measurement value, and determines an acquisition function from a plurality of combinations of the initial state and unknown parameter values and the value of the evaluation function, and, on the basis of the value of the acquisition function, updates the initial state and the value of the unknown parameter that minimize the value of the evaluation function. An iterative determination unit (104) repeats the processes of the calculating unit (102) and the update unit (103) until a prescribed iteration end condition is satisfied, to thereby estimate the initial state and the value of the unknown parameter regarding the data assimilation object.

Description

[Technical Field]

[0001] The disclosed technologies relate to data assimilation devices, data assimilation methods, data assimilation programs, and data assimilation systems. [Background technology]

[0002] Against the backdrop of digital transformation and Society 5.0, there is an increasing need to improve the prediction accuracy of numerical simulations that analyze and predict complex phenomena based on physics in order to streamline the development and design of industrial products. The prediction accuracy of numerical simulations largely depends on how accurately the material properties and parameters included in the mathematical models used in the numerical simulations are identified from experimental data.

[0003] Traditionally, numerous experiments have been conducted to identify physical properties and parameters that match the obtained experimental results. However, the greater the pursuit of accuracy, the more experimental data is required, leading to an increase in the number of experiments.

[0004] Here, data assimilation, a numerical computation technique that links experiments and numerical simulations based on Bayesian statistics, is known (Higuchi, Tomoyuki; Ueno, Genta; Nakano, Shinya; Nakamura, Kazuyuki; Yoshida, Ryo, "Introduction to Data Assimilation - Next-Generation Simulation Technology," Asakura Shoten, 2011; Awaji, Toshiyuki; Kamachi, Masafumi; Ikeda, Motomi; Ishikawa, Yoichi, "Data Assimilation: An Innovation that Integrates Observation, Experiment and Models," Kyoto University Press, 2009). By using data assimilation, material properties and parameters can be efficiently inversely estimated from experimental results. Furthermore, various unmeasurable data can be inversely estimated from measurable experimental data, allowing for the inverse estimation of states that cannot be directly measured in experiments.

[0005] Data assimilation is already being used in practical applications as a numerical calculation technique to improve forecast accuracy in weather forecasting and typhoon track forecasting (Japan Meteorological Agency, Forecasting Department, "Challenges and Prospects of Ensemble Forecasting for Probabilistic Weather Forecasting," Numerical Weather Prediction Division Report Supplement Vol. 62, 2016, Internet search).<URL:https: / / www.jma.go.jp / jma / kishou / books / nwpreport / 62 / No62_all.pdf> Against the backdrop of the recent boom in data science and machine learning, advancements in hardware such as GPUs and computing performance have boosted the application of data assimilation to engineering fields. [Overview of the project] [Problems that the invention aims to solve]

[0006] However, conventional data assimilation algorithms often have problems, including being difficult to implement in numerical simulations and requiring a large amount of computation.

[0007] The disclosed technology was developed in view of the above points, and aims to provide a data assimilation device, method, program, and data assimilation system that can perform data assimilation with an algorithm that reduces computational costs and is easy to implement. [Means for solving the problem]

[0008] A first aspect of this disclosure is a data assimilation apparatus comprising: an acquisition unit that acquires measured values ​​of changes of a data assimilation target in a predetermined environment; a calculation unit that numerically calculates the changes of the data assimilation target in the predetermined environment using a provisional initial state and provisional values ​​of unknown parameters relating to the data assimilation target; and an update unit that calculates a value of an evaluation function representing the error between the measured values ​​and a value corresponding to the measured values ​​obtained from the results of the numerical calculation, obtains an acquisition function from a plurality of combinations of the initial state, the value of the unknown parameters, and the value of the evaluation function, and updates the initial state and the value of the unknown parameters that minimize the value of the evaluation function based on the value of the acquisition function, wherein the calculation unit performs the numerical calculation again using the initial state and the value of the unknown parameters updated by the update unit, and by repeating the numerical calculation by the calculation unit and the update by the update unit, estimates the initial state and the value of the unknown parameters relating to the data assimilation target and obtains an initial state that improves the prediction accuracy of changes in the predetermined environment.

[0009] A second aspect of this disclosure is a data assimilation method comprising: an acquisition unit acquiring measured values ​​of changes of a data assimilation target in a predetermined environment; a calculation unit numerically calculating the changes of the data assimilation target in the predetermined environment using a provisional initial state and provisional values ​​of unknown parameters related to the data assimilation target; an update unit calculating a value of an evaluation function representing the error between the measured values ​​and a value corresponding to the measured values ​​obtained from the results of the numerical calculation; obtaining an acquisition function from a plurality of combinations of the initial state, the value of the unknown parameters, and the value of the evaluation function; and updating the initial state and the value of the unknown parameters that minimize the value of the evaluation function based on the value of the acquisition function; the calculation unit then performs the numerical calculation again using the value of the initial state and the value of the unknown parameters updated by the update unit; and by repeating the numerical calculation by the calculation unit and the update by the update unit, the calculation unit estimates the initial state and the value of the unknown parameters related to the data assimilation target and obtains an initial state that improves the prediction accuracy of changes in the predetermined environment.

[0010] A third aspect of this disclosure is a data assimilation program for performing the following actions: obtaining measured values ​​of changes in a predetermined environment of a data assimilation target; numerically calculating the changes in the predetermined environment of the data assimilation target using a provisional initial state and provisional values ​​of unknown parameters for the data assimilation target; calculating the value of an evaluation function that represents the error between the measured values ​​and the values ​​corresponding to the measured values ​​obtained from the results of the numerical calculation; determining an acquisition function from a plurality of combinations of the initial state, the values ​​of the unknown parameters, and the value of the evaluation function; and updating the initial state and the values ​​of the unknown parameters that minimize the value of the evaluation function based on the value of the acquisition function, wherein the numerical calculation is performed again using the updated initial state and the values ​​of the unknown parameters; and the numerical calculation and the update are repeated to estimate the initial state and the values ​​of the unknown parameters for the data assimilation target and obtain an initial state that improves the prediction accuracy of changes in the predetermined environment.

[0011] A fourth aspect of this disclosure includes an input unit that inputs measured values ​​of changes in a predetermined environment of the data assimilation target, a provisional initial state of the data assimilation target, and provisional values ​​of unknown parameters; a calculation unit that numerically calculates the changes in the data assimilation target in the predetermined environment using the provisional initial state of the data assimilation target and provisional values ​​of unknown parameters; and a value of an evaluation function that represents the error between the measured values ​​and the values ​​corresponding to the measured values ​​obtained from the results of the numerical calculation, and a plurality of combinations of the initial state, the values ​​of the unknown parameters, and the value of the evaluation function. The system includes an update unit that calculates an acquisition function from the data and updates the initial state and unknown parameter values ​​that minimize the evaluation function based on the value of the acquisition function, and a presentation unit. The calculation unit performs the numerical calculation again using the initial state and unknown parameter values ​​updated by the update unit, and by repeating the numerical calculation by the calculation unit and the update by the update unit, the system estimates the initial state and unknown parameter values ​​related to the data assimilation target, and the presentation unit presents the estimated initial state and unknown parameter values. [Effects of the Invention]

[0012] According to the disclosed technology, an effect can be obtained that data assimilation can be performed with an algorithm that suppresses calculation costs and can be easily implemented.

Brief Description of the Drawings

[0013] [Figure 1] It is a schematic block diagram of an example of a computer that functions as a data assimilation device of this embodiment. [Figure 2] It is a block diagram showing the configuration of the data assimilation device of this embodiment. [Figure 3] It is a flowchart showing a data assimilation processing routine in the data assimilation device of this embodiment. [Figure 4] It is a diagram showing the result of sintering simulation of powder in Example 1. [Figure 5] It is a diagram showing the estimation result inside the sintered body in the data assimilation process in Example 1. [Figure 6] It is a diagram showing the minimization calculation process of the evaluation function compared with the conventional method. [Figure 7] It is a diagram showing an example of experimental data in Example 2. [Figure 8] It is a diagram showing an example of simulation results in Example 2. [Figure 9] It is a cross-sectional view showing the shape and dimensions of the mold and blank used in the experiment in Example 2. [Figure 10] It is a diagram showing the in-situ observation result of the three-dimensional shape change of silver fine particles in Example 3. [Figure 11] It is a graph showing the change in the value of the evaluation function in Example 3. [Figure 12] It is a diagram showing an example of the estimation result of the time change of the three-dimensional shape of silver fine particles during sintering obtained by performing a sintering simulation in Example 3. [Figure 13] It is a conceptual diagram of the process of calculating the posterior distribution from the prior distribution based on Bayes' theorem. [Figure 14]It is a block diagram showing the configuration of a data assimilation system in a modification example of the present embodiment.

Mode for Carrying Out the Invention

[0014] Hereinafter, an example of an embodiment of the disclosed technology will be described with reference to the drawings. In each drawing, the same or equivalent components and parts are given the same reference numerals. Also, the dimensional ratios in the drawings are exaggerated for the convenience of explanation and may be different from the actual ratios.

[0015] <Overview of the Present Embodiment> First, the overview in the present embodiment will be described.

[0016] In data assimilation, as shown in FIG. 13, it is considered that there are always errors in the experimental data y t at time t and the numerical simulation result x t , and both are expressed as probability density functions. Then, based on Bayes' theorem shown in the following formula, if it is determined that the error of the experimental data is smaller than the error of the numerical simulation result, the numerical simulation result is corrected to approach the experimental data. JPEG0007886615000001.jpg991 Here, for example, y 1:t represents all the experimental data from the initial state to time t.

[0017] In FIG. 13, from the likelihood p(y t [[ID=3�]]|x t ) shown by the dotted line and the prior distribution p(x t |y 1:t-1 ), the posterior distribution p(x t |y 1:t ) shown by the broken line is obtained, and it is shown that the numerical simulation result is corrected.

[0018] Mathematically, this means that if the error represented by the variance-covariance matrix of the probability density function (likelihood) representing the experimental data is smaller than that of the probability density function (prior distribution) representing the numerical simulation results, the prior distribution is modified to approximate the experimental data, resulting in the posterior distribution.

[0019] In computer-based numerical computation, conventional data assimilation algorithms can be broadly classified into two types, as follows:

[0020] One type of algorithm uses ensemble approximation of the probability density function. Data assimilation algorithms in this category employ "ensemble approximation of the probability density function," which treats the probability density function as a collection (histogram) of numerous numerical simulation results. Representative algorithms include the Ensemble Kalman Filter (EnKF), Particle Filter (PF), and Marginal Particle Filter (MPF).

[0021] Another type of algorithm is one based on minimizing an evaluation function that represents the error between measured values ​​and numerical simulation results. Data assimilation algorithms in this category are called adjoint methods or variational methods. They define an evaluation function J that represents the error between experimental data and numerical simulation results, and estimate unknown parameters and initial states by solving the problem of minimizing J. Unlike the algorithms mentioned above that use ensemble approximation of probability density functions, this algorithm does not require ensemble approximation of probability density functions. Representative algorithms include the three-dimensional variational method and the four-dimensional variational method (4DVar).

[0022] Here, we will explain the problems with algorithms that use ensemble approximations of probability density functions. Because data assimilation based on this algorithm uses ensemble approximations of probability density functions, it is necessary to perform a large number of numerical simulations. According to K. Sasaki, A. Yamanaka, H. Nagao, S. Ito, Data assimilation for phase-field models based on the ensemble Kalman filter, Computational Materials Science, 141 (2018), pp. 141-152, it has been shown that at least several hundred numerical simulations are necessary to perform data assimilation with good estimation accuracy, which requires a huge amount of computation.

[0023] Next, we will explain the problems with algorithms based on minimizing the evaluation function. This algorithm does not require ensemble approximation of the probability density function, and therefore requires less computation than the algorithms that use ensemble approximation of the probability density function described above.

[0024] However, solving the minimization problem of the evaluation function J requires calculating the gradient of the evaluation function J, and in that calculation process, it is necessary to analytically derive an operator called the adjoint model. Deriving the adjoint model is difficult in numerical simulations dealing with nonlinear phenomena, requiring advanced mathematical knowledge, and is a practical bottleneck. Furthermore, even if the derivation of the adjoint model is successful and the calculation of the gradient of the evaluation function J becomes possible, solving the minimization problem of the evaluation function J, which is often a multimodal function, is generally not easy. There is also the Ensemble 4D Variational Method (En4DVar), which combines the above algorithm using ensemble approximation of probability density functions with an algorithm based on minimization of the evaluation function, but because it is an algorithm that uses ensemble approximation of probability density functions, it ultimately cannot solve problems that require a huge amount of computation.

[0025] This embodiment employs a novel data assimilation algorithm that combines Bayesian optimization (BO), an optimization theory. By applying Bayesian optimization to the minimization calculation of the evaluation function J in this embodiment, the computational complexity can be significantly reduced. Furthermore, by applying Bayesian optimization, the calculation of the gradient of the evaluation function J, which is required in conventional adjoint methods, becomes unnecessary, simplifying implementation (source code creation) and promoting the application of data assimilation to numerical simulations in various fields.

[0026] <Configuration of the data assimilation device according to this embodiment> Figure 1 is a block diagram showing the hardware configuration of the data assimilation device 10 of this embodiment.

[0027] As shown in Figure 1, the data assimilation device 10 includes a CPU (Central Processing Unit) 11, ROM (Read Only Memory) 12, RAM (Random Access Memory) 13, storage 14, input unit 15, display unit 16, and communication interface (I / F) 17. Each component is connected to the others via a bus 19 so as to be able to communicate with each other.

[0028] The CPU 11 is a central processing unit that executes various programs and controls various parts. Specifically, the CPU 11 reads a program from the ROM 12 or storage 14 and executes the program using the RAM 13 as a working area. The CPU 11 controls each of the above components and performs various calculations according to the program stored in the ROM 12 or storage 14. In this embodiment, the ROM 12 or storage 14 stores a data assimilation program for executing data assimilation processing. The data assimilation program may be a single program or a group of programs composed of multiple programs or modules.

[0029] ROM12 stores various programs and data. RAM13 temporarily stores programs or data as a working area. Storage14 consists of an HDD (Hard Disk Drive) or SSD (Solid State Drive) and stores various programs, including the operating system, and various data.

[0030] The input unit 15 includes a pointing device such as a mouse and a keyboard, and is used for various types of input.

[0031] The input unit 15 receives measured values ​​that represent changes in a predetermined environment of the data to be assimilated.

[0032] The display unit 16 is, for example, a liquid crystal display and displays various information. The display unit 16 may also function as an input unit 15 by employing a touch panel system.

[0033] The communication interface 17 is an interface for communicating with other devices, and standards such as Ethernet®, FDDI, and Wi-Fi® can be used.

[0034] Next, the functional configuration of the data assimilation device 10 will be described. Figure 2 is a block diagram showing an example of the functional configuration of the data assimilation device 10.

[0035] Functionally, the data assimilation device 10 is configured to include an acquisition unit 101, a calculation unit 102, an update unit 103, and an iteration determination unit 104, as shown in Figure 2.

[0036] The acquisition unit 101 acquires actual measured values ​​of the data assimilation target, which are input values ​​that measure changes in a predetermined environment. For example, it acquires experimental data consisting of actual measured values ​​of the data assimilation target, which are measured under experimental conditions that represent a predetermined environment.

[0037] The calculation unit 102 numerically calculates the changes of the data assimilation target in a predetermined environment using a provisional initial state of the data assimilation target and provisional values ​​of unknown parameters. The calculation unit 102 also performs numerical calculations again using the initial state and unknown parameter values ​​updated by the update unit 103. For example, a simulation software (which may also be an executable file compiled from source code) that numerically calculates the changes of the data assimilation target in a predetermined environment is given the initial state, unknown parameter values, and data representing the same predetermined environment as the experimental conditions, and the changes of the data assimilation target are numerically calculated to obtain predicted values ​​corresponding to the experimental data.

[0038] The update unit 103 calculates the value of an evaluation function that represents the error between the measured values ​​obtained by the acquisition unit 101 and the predicted values ​​corresponding to the measured values ​​obtained from the numerical calculations performed by the calculation unit 102. The update unit 103 obtains multiple combinations of the initial state, the values ​​of the unknown parameters, and the value of the evaluation function. From these multiple combinations of the initial state, the values ​​of the unknown parameters, and the value of the evaluation function, the update unit 103 derives the initial state and unknown parameter values ​​that minimize the value of the evaluation function using Bayesian optimization based on Gaussian process regression, and updates the initial state and unknown parameter values ​​to the derived values.

[0039] Specifically, the update unit 103 performs regression analysis using Gaussian process regression on multiple combinations of the initial state, unknown parameter values, and evaluation function values ​​to determine the relationship between the initial state, unknown parameter values, and evaluation function values. The update unit 103 calculates the mean and variance of the evaluation function values ​​corresponding to any initial state and unknown parameter values ​​obtained by the regression analysis, and calculates the value of the acquisition function from the mean and variance of the evaluation function values. The update unit 103 updates the initial state and unknown parameter values ​​that are estimated to yield the minimum value of the evaluation function based on the value of the acquisition function.

[0040] Here, we will explain a concrete example of an evaluation function. Starting from the initial state (time t=0), at a certain time t=t end During this time, the experimental data in the time series (represented by the vector y at a given time t) tAssume that a value (represented by ) is obtained. On the other hand, the predicted value at a certain time t obtained by numerical calculation is vector x t This is defined as follows. In this case, the evaluation function J, which represents the error between the experimental data and the numerical simulation results, is defined as follows based on the maximum likelihood estimation method or Maximum a Posterior Estimation (MAP) estimation.

[0041] JPEG0007886615000002.jpg12133 (1)

[0042] Here, x0 is a vector consisting of unknown parameters and initial states that serve as input data for the numerical simulation. b This represents the initial estimate of x0 when the numerical simulation results reproduce the experimental data. B is the background error covariance matrix, R t These are called observation error covariance matrices, and x0 b and y t This represents the magnitude of the error. M(x0) represents the simulation model. H t This is experimental data y t A quantity comparable to the result of a numerical simulation (i.e., x t This is an operator used to extract from ) and is called the observation operator. The x0 that minimizes the evaluation function J in equation (1) should be a vector consisting of the optimal parameters and initial state that we want to find through data assimilation, and this is x0 a This is how it is expressed.

[0043] In contrast, conventional data assimilation algorithms, such as the adjoint method or the variational method, minimize x0 in equation (1). a To find this, we calculate the following equation, which is the gradient of equation (1).

[0044] JPEG0007886615000003.jpg12116 (2)

[0045] Here, H t and M t These can be expressed by the following equations.

[0046] JPEG0007886615000004.jpg2457 (3) JPEG0007886615000005.jpg2359 (4)

[0047] The practical problem is that in order to calculate equation (2), we must calculate equation (4). In other words, since many simulation models are described by partial differential equations with strong nonlinearity, M t Analyzing this is difficult, which is the reason why implementing data assimilation is difficult. Furthermore, even if we obtain equation (4), calculating equation (2) and minimizing the evaluation function J in equation (1) is computationally expensive.

[0048] On the other hand, in this embodiment, by eliminating the need for the calculation in equation (2), the implementation of data assimilation is made easier, and computational costs are significantly reduced.

[0049] The iteration determination unit 104 determines whether or not a predetermined iteration termination condition is met. The iteration determination unit 104 causes the calculation unit 102 to repeat numerical calculations and the update unit 103 to repeat updates until the iteration termination condition is met. The optimal unknown parameter and initial state value obtained at the end is obtained as the result of data identification. Here, the iteration termination condition can be the number of iterations reaching the upper limit, the value of the evaluation function converging, or a user inputting an iteration termination instruction after viewing the data identification result.

[0050] <Operation of the data assimilation device according to this embodiment> Next, the operation of the data assimilation device 10 according to this embodiment will be described.

[0051] Figure 3 is a flowchart showing the flow of data assimilation processing by the data assimilation device 10. The CPU 11 reads the data assimilation program from the ROM 12 or storage 14, expands it into the RAM 13, and executes it to perform data assimilation processing. Experimental data consisting of measured values ​​of changes in the data assimilation target under experimental conditions representing a predetermined environment is input to the data assimilation device 10. It is also assumed that the initial state and initial values ​​of unknown parameters used in numerical calculations, as well as the range of possible values ​​for unknown parameters, are defined.

[0052] First, in step S100, the CPU 11, acting as an acquisition unit 101, acquires experimental data consisting of measured values ​​that represent changes in the data assimilation target under experimental conditions that represent a predetermined environment.

[0053] In the next step, S102, the CPU 11, acting as the calculation unit 102, sets initial values ​​for the initial state and unknown parameters. Specifically, x0 b Set it.

[0054] In step S104, the CPU 11, acting as the calculation unit 102, provides simulation software (which may also be an executable file compiled from source code) that numerically calculates the changes of the data assimilation target in a predetermined environment. The CPU 11 provides the initial state and unknown parameter values, along with data representing the same predetermined environment as the experimental conditions, to numerically calculate the changes of the data assimilation target and obtain values ​​corresponding to the experimental data. Specifically, a numerical simulation is performed with x0(i) being the unknown parameter and initial state values. n values ​​for the initial state and unknown parameter are prepared, and the numerical simulation is performed n times to obtain n values ​​corresponding to the experimental data.

[0055] In step S106, the CPU 11, acting as an update unit 103, calculates the value of an evaluation function that represents the error between the measured value obtained in step S100 and the value corresponding to the measured value obtained from the numerical calculation results in step S104 or S114.

[0056] Specifically, the evaluation function J is calculated according to equation (1) above. At this time, prior information D(1:n) used in the Bayesian optimization calculation is created. For this purpose, in step S102 above, n unknown parameter and initial state values ​​are prepared as x0(i) (where i=1,2,...n) within a predetermined range. Here, n is any integer greater than or equal to 1. The evaluation function for the numerical simulation results performed using x0(i) (where i=1,2,...n) is denoted as J(x0(i)) (where i=1,2,...n).

[0057] If the (n+1)th numerical simulation is performed in step S114, which will be described later, prior information D(1:n+1) is created with the newly added combination of x0(n+1) and J(x0(n+1)).

[0058] In step S108, the CPU 11, acting as an update unit 103, uses prior information D(1:m)(m≧n) to calculate the initial state and unknown parameters from multiple combinations of the initial state and unknown parameter values ​​and the evaluation function J, using Bayesian optimization to minimize the value of the evaluation function J.

[0059] Specifically, following a Bayesian optimization algorithm, the relationship between the initial state, unknown parameter values, and evaluation function values ​​is analyzed using Gaussian process regression from multiple combinations of initial state, unknown parameter values, and evaluation function values. The mean and variance of the evaluation function values ​​corresponding to any given initial state and unknown parameter values ​​obtained from the regression analysis are then calculated. The acquisition function value a(x0) is then determined from the mean and variance of the evaluation function values, and the acquisition function a(x0) that minimizes the evaluation function J in equation (1) is calculated. There are no restrictions on the type of acquisition function, but for example, the Expected Improvement (EI) function can be used. The x0 that maximizes this acquisition function is denoted as x0(n+1).

[0060] In step S110, the CPU 11, acting as an iteration determination unit 104, determines whether or not a predetermined iteration termination condition is met. If the iteration termination condition is not met, the process proceeds to step S112. On the other hand, if the iteration termination condition is met, the process proceeds to step S116.

[0061] In step S112, the CPU 11 changes the initial state and unknown parameter values ​​that the update unit 103 provides to the simulation software (which may also be an executable file compiled from source code) to the initial state and unknown parameter values ​​calculated in step S108.

[0062] In step S114, the CPU 11, acting as the calculation unit 102, provides the simulation software (which may also be an executable file compiled from source code) with the initial state and unknown parameter values ​​changed in step S112, as well as data representing a predetermined environment identical to the experimental conditions. The CPU 11 then numerically calculates the changes in the data assimilation target and determines the values ​​corresponding to the experimental data. The process then returns to step S106.

[0063] In step S116, the CPU 11 displays the optimal initial state and unknown parameter values ​​that minimize the evaluation function as identification results on the display unit 16, saves them in the ROM 12 or storage 14, and terminates the data assimilation process.

[0064] <Example 1> Next, an example in which the data assimilation process of the above embodiment is applied to a powder sintering process will be described.

[0065] Sintering is a materials manufacturing technique that creates a dense solid by heating powder, and it is a fundamental technology in powder metallurgy and the ceramics industry. In particular, it is a technology that has recently become important from the perspective of research and development of 3D printers using laser sintering. Therefore, research on numerical simulations of sintering (hereinafter abbreviated as sintering simulations) that predict crystal changes in the solid that occur during sintering is active, with the aim of controlling the various properties of materials manufactured by sintering. However, experimentally and accurately identifying the physical properties used in sintering simulations and the parameters included in the mathematical models calculated in sintering simulations requires the accumulation of a large amount of experimental data.

[0066] In this embodiment 1, the above embodiment is applied to a sintering simulation using the phase-field method, and numerical experiments demonstrate that it is possible to estimate crystal changes and physical properties / parameters during sintering.

[0067] Here, this numerical experiment does not perform data assimilation (state estimation or parameter estimation) using actual experimental data. Instead, it sets hypothetical true values ​​for the parameters to be estimated, and uses the simulation results obtained with these hypothetical true values ​​as pseudo-experimental data. By performing data assimilation using these simulation results, the data assimilation algorithm is verified. In the field of data assimilation, this is called a twin experiment.

[0068] In this embodiment 1, the material used is silver particles (powder). Furthermore, the computational complexity of the above embodiment is compared with that of the conventional data assimilation algorithm, En4DVar, and it is shown that the computational complexity can be reduced to less than half.

[0069] Table 1 shows the material properties and parameters (true values ​​in numerical experiments) used in the sintering simulation performed to obtain pseudo-experimental data.

[0070] [Table 1]

[0071] Furthermore, Figure 4 shows the results of a sintering simulation performed using the physical properties and parameters shown in Table 1.

[0072] Figure 4(a) shows the surface shape change of the sintered body, illustrating that silver nanoparticles fuse (aggregate) during sintering. Figure 4(b) shows the z-axis center cross-section of the sintered body, indicating the location of each crystal and grain boundary. In the numerical experiment, only the results shown in Figure 4(a) are considered pseudo-observational data.

[0073] Recently, it has become possible to observe the sintering process in situ using an electron microscope, so the surface shape change of the sintered body shown in Figure 4(a) was treated as pseudo-observation data (assuming it is experimental data that can actually be obtained in an experiment). On the other hand, the data in Figure 4(b) was assumed to represent an unknown state that is difficult to measure directly in an experiment, and was used as the target for estimation in the numerical experiment. In other words, in this numerical experiment, if the physical property values ​​and parameter values ​​shown in Table 1 and the state changes shown in Figure 4(b) can be estimated solely from the information on the surface shape change of the sintered body, the validity of the above embodiment will be verified.

[0074] Table 2 shows the initial estimated values ​​of physical properties and parameters in numerical experiments. These are the initial values ​​of physical properties and parameters estimated using this embodiment or En4DVar.

[0075] [Table 2]

[0076] As shown in Table 2 above, the initial value was set to half of the true value shown in Table 1. As shown in Table 3, by using the above embodiment, physical properties and parameters can be estimated with high accuracy.

[0077] [Table 3]

[0078] Figure 5 shows the estimation results for the sintered body using the above embodiment. Compared to Figure 4, there is almost no difference, and the estimation can be performed with good accuracy, including the inside of the sintered body.

[0079] The upper part of Figure 5 shows the error between the pseudo-experimental data shown in Figure 4(a) and the estimation results in the above embodiment. It can be seen that the error decreases and the accuracy of state estimation improves as the evaluation function is minimized from Figure 5(a) to Figure 5(c). The lower part shows the estimation results for the inside of the sintered body, and there is almost no difference compared to Figure 4(b), indicating that the inside of the sintered body can be estimated with high accuracy.

[0080] Figure 6 shows the minimization calculation process of the evaluation function calculated using the above embodiment and En4DVar. The horizontal axis represents the number of sintering simulations performed to minimize the evaluation function. In En4DVar, the ensemble size was set to 50 to ensure the accuracy of data assimilation. That is, in En4DVar, it is necessary to perform 50 sintering simulations before performing the evaluation function minimization calculation. Therefore, the evaluation function decreases from n=50 onwards.

[0081] On the other hand, in the above embodiment, there is no need to perform multiple sintering simulations in advance, and state estimation and physical property / parameter estimation can be performed with less than half the computational load (number of sintering simulations) compared to En4DVar.

[0082] <Example 2> Next, we will describe an example in which the data assimilation process of the above embodiment is applied to a press forming simulation of a metal sheet material.

[0083] Press forming of metal sheets is a crucial production process in manufacturing, most notably in the automotive industry. Numerical simulations of press forming using the finite element method (hereinafter referred to as forming simulations) are being conducted to improve yield and development efficiency during metal sheet press forming, and there is a need to improve the accuracy of these simulations. To improve the accuracy of forming simulations, there is a need for a technique that can inversely identify the parameters of the material model (a mathematical model that describes the deformation behavior of the material) used in the forming simulations from experimental data.

[0084] By using the above embodiment, various experimental data obtained from press forming tests (for example, loads and pressures applied to the die during press forming, and changes in the thickness of the metal sheet measured by sensors installed inside the die) can be incorporated into the forming simulation. This allows for the accurate identification of the material properties and material model parameters of the metal sheet while correcting the forming simulation results. Conventionally, it was necessary to conduct multiple experiments (multiaxial stress tests) to apply various deformations to the material and identify the material properties and material model parameters to match the experimental results. For example, if a biaxial tensile test is used for a metal sheet, typically 18 multiaxial stress tests (9 conditions with changed stress states × 2 tests to ensure reliability) are required. However, by using the data assimilation process of the above embodiment, data assimilation can be performed with less computation, reducing the number of experiments to just one.

[0085] As shown in Figure 7, the deformation of a metal sheet during press forming is continuously captured with a digital camera, and the displacement and strain distributions of the material surface, calculated by processing the captured images using digital image correlation, are incorporated into the forming simulation through data assimilation. Then, while correcting the forming simulation results shown in Figure 8, numerical experiments demonstrate that it is possible to identify the physical properties of the metal sheet and the parameters of the material model with high accuracy.

[0086] To verify the data assimilation process of the above embodiment, numerical experiments were conducted using the following procedures A to D.

[0087] (Procedure A) The true values ​​of the parameters of the material model to be inversely identified using the data assimilation processing method of this embodiment are defined, and a forming simulation is performed using those parameter values. In this embodiment 2, a material model called Yld2000-2d (see Reference 1), which is widely used to analyze the deformation behavior of aluminum alloy sheets, was used, and the true values ​​of its parameters were assumed to be the values ​​shown in Table 4. As an example of forming simulation, a numerical simulation of hole widening (a process in which a circular hole is made in a thin sheet test piece and the circular hole is widened with a cylindrical punch) was performed. [References 1] F. Barlat, JC Brem, JW Yoon, K. Chung, RE Dick, DJ Lege, F. Pourboghrat, SH Choi and E. Chu, Plane stress yield function for aluminum alloy sheets - part 1: theory, International Journal of Plasticity, Vol. 19 (2003), No. 9, pp. 1297-1319.

[0088] [Table 4]

[0089] (Procedure B) The time-series changes in displacement and strain on the specimen surface, obtained as a result of the hole expansion simulation performed in Procedure A, are saved as pseudo-experimental data. When the data assimilation process of the above embodiment is applied to an actual press working experiment, experimental data of the time-series changes in displacement and strain on the specimen surface measured by the digital image correlation method will be used.

[0090] (Procedure C) Assuming that the true values ​​of the parameters defined in Procedure A are unknown, the initial estimated values ​​of the parameters to be de-identified by the data assimilation processing method of the above embodiment are set to the values ​​shown in Table 5.

[0091] (Procedure D) Using the parameters with the values ​​shown in Table 5, a hole widening simulation is performed, and the pseudo-experimental data saved in Procedure B is imported using the data assimilation processing method of the above embodiment. In other words, in the process of correcting the hole widening simulation results based on the pseudo-experimental data, the estimated values ​​of the parameters are corrected, and finally the parameters are identified.

[0092] [Table 5]

[0093] The final identified parameter values ​​are shown in Table 6.

[0094] [Table 6]

[0095] Compared to the parameter values ​​(true values) in Table 4, although errors exist, the accuracy is good for parameter values ​​identified from only one experimental data point. In this embodiment 2, only the parameters of the material model were estimated, but it is possible to estimate the state of the sheet metal, which cannot be directly measured because it is inside the mold, such as the friction coefficient between the mold and the sheet metal, and the temperature of the sheet metal inside the mold.

[0096] Furthermore, the experimental conditions for this second embodiment are as follows.

[0097] First, a metal sheet is cut into a circle with a diameter of 195 mm, and a circular hole with a diameter of 30 mm is drilled in the center (see Figure 9). Hereafter, this will be referred to as the blank. Figure 9 is a cross-sectional view showing the shape and dimensions of the mold and blank used in the experiment.

[0098] Next, spray a random pattern onto the blank.

[0099] Then, a Teflon® sheet coated with petroleum jelly (lubricant) is placed between the blank and the punch die.

[0100] The blank is placed inside the mold and then sandwiched between the upper die and the lower die.

[0101] Next, the punch die is raised in the z-direction. During this time, the load on the punch die is measured using a load cell. In addition, continuous images of the blank surface are taken with two digital cameras.

[0102] Next, when the punch die reaches a predetermined z-coordinate, the punch die is stopped. The digital camera also stops taking pictures.

[0103] The punch die is lowered, and the die is removed sequentially to complete the test.

[0104] Then, the images captured by the digital camera are processed using the digital image correlation method, and the deformation (displacement and strain) that occurred in the blank is calculated by a computer. The calculated results become the experimental data for the data assimilation process of the above embodiment.

[0105] <Example 3> Next, we will describe an example in which the data assimilation process of the above embodiment is applied to a powder sintering process and demonstrated using actual experimental data.

[0106] The objective of this third embodiment is to observe the sintering process of silver nanoparticles in situ using a scanning transmission electron microscope (STEM), and to use the experimental data obtained therefrom, which shows the three-dimensional shape change of the silver nanoparticles, as observational data for data assimilation to estimate the physical properties and parameters (the four values ​​shown in Table 1 above and the stiffness constant k) to be used in sintering simulations.

[0107] To verify the data assimilation process of the above embodiment, the experiment was conducted in the following steps 1 to 3.

[0108] (Procedure 1) Observe the sintering process of silver nanoparticles in situ using an electron microscope. An in-situ heating stage is inserted into the chamber of a scanning transmission electron microscope (STEM), and silver nanoparticles are placed on the stage. The temperature of the in-situ heating stage is raised to 350°C only when sintering is to proceed. When measuring the three-dimensional shape of the silver nanoparticles using tomography, the temperature is lowered to 200°C, a temperature at which sintering does not proceed, before tilting the in-situ heating stage. In this embodiment 3, sintering was carried out at a temperature of 350°C at 5-second intervals, and the three-dimensional shape of the silver nanoparticles was measured each time. Figure 10 shows the result of reconstructing the three-dimensional shape of the silver nanoparticles from experimental data obtained by in-situ observation.

[0109] (Step 2) Estimate physical properties and parameters using the data assimilation method of the present invention. The time evolution of the three-dimensional shape of silver nanoparticles during sintering, obtained in Step 1, was used as observational data to estimate the physical properties and parameters (the four values ​​shown in Table 1 above, plus the stiffness constant k) to be used in the sintering simulation. The data assimilation method used here is a Bayesian optimization method based on a Tree-structured Parzan Estimator (TPE).

[0110] Table 7 shows the search range, initial estimates, and standard deviations of the initial estimates for the physical properties and parameters to be estimated.

[0111] Figure 11 shows the change in the evaluation function J(x0) when estimating material properties and parameters using a data assimilation method based on TPE and Bayesian optimization. The minimum value of the evaluation function was obtained at 73 iterations of the minimization calculation. The material properties and parameters obtained at this point are the optimal estimates, and these are shown in Table 8.

[0112] [Table 7]

[0113] [Table 8]

[0114] (Step 3) Using the estimated physical properties and parameters, estimate the shape of the sintered body through sintering simulation. Figure 12 shows the estimated time evolution of the three-dimensional shape of silver nanoparticles during sintering, obtained by performing a sintering simulation using the optimal estimated physical properties and parameters shown in Table 8 above. Compared with the in-situ observation results shown in Figure 10, it was found that the three-dimensional shape evolution of silver nanoparticles can be estimated with high accuracy.

[0115] As described above, the data assimilation device of this embodiment repeatedly performs numerical calculations of the changes of the data assimilation target in a predetermined environment using a provisional initial state of the data assimilation target and provisional values ​​of unknown parameters, and updates the initial state and unknown parameter values ​​that minimize the value of the evaluation function by Bayesian optimization. In this way, the initial state and unknown parameter values ​​of the data assimilation target are estimated. Therefore, data assimilation can be performed with an algorithm that is computationally cost-effective and easy to implement.

[0116] Furthermore, conventional data assimilation algorithms require enormous computational resources or advanced mathematical knowledge, making them difficult to implement and thus not widely adopted in society, including industry. In contrast, this embodiment overcomes the above problems, and the data assimilation algorithm of this embodiment can be easily implemented if the source code or simulation software for numerical simulation is available. Therefore, numerical simulations that utilize experimental data (data-driven simulations) will become widespread in numerical simulations in various fields.

[0117] Furthermore, a conventional use of Bayesian optimization is the search for the minimum value of a function that cannot be mathematically formulated (a black-box function). On the other hand, 4D variational methods minimize an evaluation function J that is mathematically clearly formulated. Minimizing the evaluation function J can be done using conventional techniques (such as the steepest descent method and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method), but it is necessary to calculate the gradient of the evaluation function J. The more complex (highly nonlinear) the phenomenon dealt with in numerical simulation, that is, the more practical applications are envisioned, the more difficult it becomes to calculate the gradient of the evaluation function J. Therefore, it is more engineering-wise effective to treat the evaluation function J as a function that cannot be mathematically formulated (a black-box function) and apply Bayesian optimization. Thus, by applying Bayesian optimization, we can achieve minimization of the evaluation function J without requiring the calculation of its gradient. Since the calculation of the gradient of the evaluation function J is unnecessary, the computational load is reduced and implementation becomes simpler. Thus, in this embodiment, instead of utilizing the advantages of Bayesian optimization, we focus on overcoming the weaknesses of conventional adjoint methods (or variational methods) and use Bayesian optimization for data assimilation. This allows us to perform data assimilation with an algorithm that is computationally cost-effective and easy to implement.

[0118] Furthermore, the data assimilation device of this embodiment performs regression analysis on the relationship between the initial state, the value of the unknown parameter, and the value of the evaluation function using Gaussian process regression. The data assimilation device calculates the mean and variance of the predicted values ​​of the evaluation function corresponding to an arbitrary initial state and unknown parameter value obtained by the regression analysis, and calculates the value of the acquisition function from the mean and variance of the predicted values ​​of the evaluation function. The data assimilation device then calculates the initial state and unknown parameter values ​​that are estimated to yield the minimum value of the evaluation function from the value of the acquisition function. These steps are repeated. In this way, the value of the evaluation function can be minimized without calculating the gradient of the evaluation function.

[0119] <Variation> It should be noted that the present invention is not limited to the embodiments described above, and various modifications and applications are possible without departing from the spirit of the invention.

[0120] For example, the data assimilation device may be implemented with one or more servers, and an information processing terminal connected via a network may be used to input measured values ​​of changes in a predetermined environment of the data assimilation target, as well as a provisional initial state and provisional values ​​for unknown parameters related to the data assimilation target. In this case, as shown in Figure 14, the data assimilation system 100 comprises a data assimilation device 10, which is a server, and an information processing terminal 50, and the data assimilation device 10 and the information processing terminal 50 are connected via a network N such as the Internet. As shown in Figure 1 above, the information processing terminal 50 has a CPU 11, ROM 12, RAM 13, storage 14, input unit 15, display unit 16, and communication interface 17, similar to the data assimilation device 10. The input unit 15 of the information processing terminal 50 receives measured values ​​of changes in a predetermined environment of the data assimilation target, as well as a provisional initial state and provisional values ​​for unknown parameters related to the data assimilation target, which are input by the user. The information processing terminal 50 transmits to the data assimilation device 10 the measured values ​​of the data assimilation target's changes in a predetermined environment, as well as a provisional initial state and provisional values ​​of unknown parameters related to the data assimilation target. The acquisition unit 101 of the data assimilation device 10 acquires the received measured values ​​of the data assimilation target's changes in a predetermined environment, as well as a provisional initial state and provisional values ​​of unknown parameters related to the data assimilation target. The data assimilation device 10 transmits the estimation results to the information processing terminal 50. The display unit 16 of the information processing terminal 50 presents the estimated initial state and unknown parameter values ​​to the user.

[0121] Furthermore, although the above embodiment described an example where the data assimilation target is a substance or material and the unknown parameters are physical properties of the substance or material, the invention is not limited to this. Since the present invention relates to data assimilation, a numerical computation technique that links experiments and numerical simulations, it can be used in a wide range of fields where numerical simulations are used.

[0122] For example, the data assimilation target may be heat or fluid, and simulations related to heat or fluid may be used, with the parameters related to heat or fluid being treated as unknown parameters.

[0123] Alternatively, electromagnetic waves may be used as the data assimilation target, and simulations related to electromagnetic waves may be used to treat the parameters related to electromagnetic waves as unknown parameters.

[0124] Alternatively, the data assimilation target may be meteorological data, with time-series data of temperature and atmospheric pressure measured by weather satellites or other means being used as actual values, and parameters of the weather simulation model may be estimated using weather simulations.

[0125] Alternatively, the data assimilation target could be the infection phenomenon of an infectious disease, the daily number of infected people could be measured, and the infection rate parameters necessary for the simulation could be estimated using a simulation of fluctuations in the number of patients with an infectious disease.

[0126] Alternatively, the data assimilation target may be stock prices, daily stock price data may be used as actual values, and the parameters of the stock price fluctuation simulation may be estimated using stock price fluctuation simulations related to financial engineering. For example, daily stock price fluctuations can be predicted by numerical simulation using the Black-Scholes model or similar.

[0127] In the above embodiment, the use of Bayesian optimization based on Gaussian process regression was described as a specific method of Bayesian optimization, but it is not limited to this. For example, Bayesian optimization based on a Tree-structured Parzan Estimator (TPE) may be used. In this case, even when using a TPE, data assimilation can be performed without calculating the gradient of the evaluation function. Specifically, the update unit 103 calculates the value of an evaluation function that represents the error between the measured values ​​obtained by the acquisition unit 101 and the values ​​corresponding to the measured values ​​obtained from the numerical calculations performed by the calculation unit 102. The update unit 103 classifies multiple combinations of the initial state, unknown parameter values, and evaluation function values ​​into upper and lower groups. The update unit 103 estimates the probability density function for the upper group and the probability density function for the lower group, and obtains the value of the acquisition function from the ratio of the probability density function for the upper group and the probability density function for the lower group. The data assimilation device updates the initial state and unknown parameter values ​​that are estimated to yield the minimum value of the evaluation function based on the value of the acquisition function.

[0128] More specifically, in TPE-based Bayesian optimization, an evaluation function is calculated, similar to Bayesian optimization based on Gaussian process regression. Then, the data obtained up to that point (combinations of the initial input state and parameters and the output evaluation function) is classified into two groups, an upper group and a lower group, based on the magnitude of the evaluation function and a set threshold. Kernel density estimation is then performed on the data in each of the upper and lower groups, and two probability density functions are calculated. The relative magnitudes of the acquisition function are then calculated from the ratio of these two probability density functions. Subsequent operations are similar to Bayesian optimization based on Gaussian process regression: the initial state and parameters are updated by referencing the maximum value of the acquisition function, and the optimal estimate is obtained by minimizing the evaluation function through repeated updates.

[0129] Furthermore, the various processes that the CPU reads and executes in each of the above embodiments may be executed by various processors other than the CPU. Examples of such processors include PLDs (Programmable Logic Devices) such as FPGAs (Field-Programmable Gate Arrays) whose circuit configuration can be changed after manufacturing, and dedicated electrical circuits that are processors with circuit configurations specifically designed to execute specific processes, such as ASICs (Application Specific Integrated Circuits). In addition, the data assimilation process may be executed by one of these various processors, or by a combination of two or more processors of the same or different types (for example, multiple FPGAs, and a combination of a CPU and an FPGA). More specifically, the hardware structure of these various processors is an electrical circuit that combines circuit elements such as semiconductor elements.

[0130] Furthermore, although the above embodiments describe a configuration in which the data assimilation program is pre-stored (installed) in the storage 14, the invention is not limited to this configuration. The program may be provided in a form stored on a non-transitory storage medium such as a CD-ROM (Compact Disk Read Only Memory), DVD-ROM (Digital Versatile Disk Read Only Memory), or USB (Universal Serial Bus) memory. Alternatively, the program may be provided in a form downloaded from an external device via a network.

[0131] The following additional information is disclosed regarding the embodiments described above.

[0132] (Additional note 1) Memory and At least one processor connected to the memory, Includes, The aforementioned processor, We obtain measured values ​​that represent changes in a predetermined environment for the data to be assimilated. Using the provisional initial state of the data assimilation target and provisional values ​​of the unknown parameters, the changes of the data assimilation target in the predetermined environment are numerically calculated. The value of an evaluation function representing the error between the measured value and the value corresponding to the measured value obtained from the numerical calculation is calculated. An acquisition function is determined from multiple combinations of the initial state, the unknown parameter value, and the evaluation function value. Based on the value of the acquisition function, the initial state and the unknown parameter value that minimize the evaluation function value are updated. A data assimilation device configured as follows: In the aforementioned numerical calculation, the numerical calculation is performed again using the updated initial state and the unknown parameter values. By repeating the above numerical calculations and updates, the initial state and unknown parameter values ​​related to the data assimilation target are estimated. Data assimilation device.

[0133] (Additional note 2) A non-temporary storage medium that stores a program executable by a computer to perform data assimilation processing, The aforementioned data assimilation process is, We obtain measured values ​​that represent changes in a predetermined environment for the data to be assimilated. Using the provisional initial state of the data assimilation target and provisional values ​​of the unknown parameters, the changes of the data assimilation target in the predetermined environment are numerically calculated. This includes calculating the value of an evaluation function that represents the error between the measured value and the value corresponding to the measured value obtained from the numerical calculation, determining an acquisition function from a plurality of combinations of the initial state, the value of the unknown parameter, and the value of the evaluation function, and updating the initial state and the value of the unknown parameter that minimize the value of the evaluation function based on the value of the acquisition function. In the aforementioned numerical calculation, the numerical calculation is performed again using the updated initial conditions and the unknown parameter values. By repeating the above numerical calculations and updates, the initial state and unknown parameter values ​​related to the data assimilation target are estimated. Non-transitory storage medium.

[0134] The disclosure of Japanese application 2021-150483 is incorporated herein by reference in its entirety.

[0135] All documents, patent applications, and technical standards described herein are incorporated by reference to the same extent as if each individual document, patent application, and technical standard were specifically and individually described as being incorporated by reference.

Claims

1. An acquisition unit that acquires measured values ​​of changes in a data assimilation target, which is a substance or material, in a predetermined environment, A calculation unit that numerically calculates the changes of the data assimilation target in the predetermined environment, using a provisional initial state which is the state value at time t=0 in the numerical calculation of the data assimilation target, the parameters of the simulation model, and provisional values ​​of unknown parameters including the physical properties of the substance or material. An update unit calculates the value of an evaluation function that represents the error between the measured value and the value corresponding to the measured value obtained from the numerical calculation; determines an acquisition function from a plurality of combinations of the initial state, the unknown parameter value, and the evaluation function value; and updates the initial state and the unknown parameter value that minimize the evaluation function value based on the acquisition function value. Includes, The calculation unit then performs the numerical calculation again using the initial state and the unknown parameter values ​​updated by the update unit. By repeatedly performing the numerical calculation by the calculation unit and updating by the update unit, the initial state and unknown parameter values ​​related to the data assimilation target are estimated. Data assimilation device.

2. The data assimilation apparatus according to claim 1, wherein the update unit calculates a value of an evaluation function that represents the error between the measured value and a value corresponding to the measured value obtained from the results of the numerical calculation, performs regression analysis of the relationship between the initial state, the value of the unknown parameter, and the value of the evaluation function using Gaussian process regression from a plurality of combinations of the initial state, the value of the unknown parameter, and the value of the evaluation function, obtains the mean and variance of the value of the evaluation function corresponding to an arbitrary initial state and value of the unknown parameter obtained by the regression analysis, obtains the value of the acquisition function from the mean and variance, and updates the initial state and value of the unknown parameter that is estimated to yield the minimum value of the evaluation function from the value of the acquisition function.

3. The update unit calculates a value of an evaluation function that represents the error between the measured value and a value corresponding to the measured value obtained from the results of the numerical calculation, classifies a plurality of combinations of the initial state, the value of the unknown parameter, and the value of the evaluation function into upper and lower groups, each consisting of a combination of the initial state, the value of the unknown parameter, and the value of the evaluation function, based on a predetermined threshold for the value of the evaluation function, estimates the value of the probability density function for the upper group and the value of the probability density function for the lower group, determines the value of the acquisition function from the ratio of the value of the probability density function for the upper group and the value of the probability density function for the lower group, and updates the initial state and the value of the unknown parameter that is estimated to yield the minimum value of the evaluation function from the value of the acquisition function, as described in claim 1.

4. The data assimilation apparatus according to claim 1, wherein the measured value is a measured value obtained by digital image correlation or a measured value obtained by observing surface shape changes.

5. The data assimilation apparatus according to claim 1, wherein the change in the predetermined environment is a change due to press working of the material.

6. The data assimilation apparatus according to claim 1, wherein the change in the predetermined environment is a change due to the sintering process of the material.

7. The acquisition unit acquires measured values ​​of the data assimilation target, which is a substance or material, by measuring its changes in a predetermined environment. The calculation unit numerically calculates the changes of the data assimilation target in the predetermined environment, using a provisional initial state which is the state value at time t=0 in the numerical calculation, the parameters of the simulation model, and provisional values ​​of unknown parameters including the physical properties of the substance or material. The update unit calculates a value of an evaluation function that represents the error between the measured value and the value corresponding to the measured value obtained from the numerical calculation result, determines an acquisition function from multiple combinations of the initial state, the unknown parameter value and the evaluation function value, and updates the initial state and the unknown parameter value that minimizes the evaluation function value based on the value of the acquisition function. This includes, The calculation unit then performs the numerical calculation again using the initial state and the unknown parameter values ​​updated by the update unit. By repeatedly performing the numerical calculation by the calculation unit and updating by the update unit, the initial state and unknown parameter values ​​related to the data assimilation target are estimated. Data assimilation methods.

8. Obtain measured values ​​of changes in a data assimilation target, which is a substance or material, in a predetermined environment, Using a provisional initial state, which is the state value at time t=0 in the numerical calculation, and provisional values ​​of unknown parameters including the parameters of the simulation model and the physical properties of the substance or material, the changes of the data assimilation target in the predetermined environment are numerically calculated. The value of an evaluation function representing the error between the measured value and the value corresponding to the measured value obtained from the numerical calculation is calculated. An acquisition function is determined from multiple combinations of the initial state, the unknown parameter value, and the evaluation function value. Based on the value of the acquisition function, the initial state and the unknown parameter value that minimize the evaluation function value are updated. A data assimilation program that causes a computer to perform the following action: In the aforementioned numerical calculation, the numerical calculation is performed again using the updated initial state and the unknown parameter values. By repeating the above numerical calculations and updates, the initial state and unknown parameter values ​​related to the data assimilation target are estimated. Data assimilation program.

9. An input unit that inputs measured values ​​of changes in a data assimilation target, which is a substance or material, in a predetermined environment, and a provisional initial state and provisional values ​​of unknown parameters relating to the data assimilation target, A calculation unit that numerically calculates the changes of the data assimilation target in the predetermined environment using a provisional initial state which is the state value at time t=0 in numerical calculations, the parameters of the simulation model, and provisional values ​​of unknown parameters including the physical properties of the substance or material, An update unit calculates the value of an evaluation function that represents the error between the measured value and the value corresponding to the measured value obtained from the numerical calculation; determines an acquisition function from a plurality of combinations of the initial state, the unknown parameter value, and the evaluation function value; and updates the initial state and the unknown parameter value that minimize the evaluation function value based on the acquisition function value. The presentation section and, Includes, The calculation unit then performs the numerical calculation again using the initial state and the unknown parameter values ​​updated by the update unit. By repeatedly performing the numerical calculation by the calculation unit and updating by the update unit, the initial state and unknown parameter values ​​related to the data assimilation target are estimated. The display unit presents the estimated initial state and the values ​​of the unknown parameters. Data assimilation block.

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