Parameter value acquisition device, control device, parameter value acquisition method, and program

Abstract

This parameter value acquisition device samples parameter values in a simulation. For each sampled value obtained, the parameter value acquisition device sets that sampled value in a parameter in the simulation, and acquires a simulation value that is a value calculated in the simulation. Using the sampled values of the parameter in the simulation, the simulation values of each of the sampled values, and a kernel function provided with a partial formula according to which the posterior kernel average has a greater value the closer the parameter value in the simulation is to a predetermined value, the parameter value acquisition device searches for such a parameter value that the value of the posterior kernel average under a target value of the simulation value will be greater.

Description

[Technical Field]

[0001] This disclosure pertains to a parameter value acquisition device. control device , Method for obtaining parameter values ​​and program Regarding. [Background technology]

[0002] Parameter value searches may be performed, such as searching for control parameter values ​​for a device or searching for parameter values ​​in a simulation. For example, Patent Document 1 describes a parameter tuning method using a genetic algorithm (GA) to search for values ​​for multiple parameters. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 08-272761 [Overview of the project] [Problems that the invention aims to solve]

[0004] If there are preferred values ​​for the parameter values, it is preferable to be able to take these preferred values ​​into consideration when searching for parameter values.

[0005] One example of the purpose of this disclosure is a parameter value acquisition device that can solve the above-mentioned problems. control device , Method for obtaining parameter values ​​and program The objective is to provide. [Means for solving the problem]

[0006] According to a first aspect of this disclosure, the parameter value acquisition device includes: sampling means for sampling parameter values ​​in a simulation; simulation value acquisition means for acquiring simulation values, which are values ​​calculated in a simulation in which the sampling value is set as a parameter in the simulation, for each obtained sampling value; and parameter value search means for calculating a posterior kernel average under a target value of the simulation value using the sampling value of the parameter in the simulation, the simulation value for each sampling value, and a kernel function provided with a subexpression such that the value of the posterior kernel average increases as the parameter value in the simulation approaches a predetermined value, and searching for parameter values ​​that increase the value of the posterior kernel average.

[0007] According to a second aspect of this disclosure, the control device includes: sampling means for sampling parameter values ​​in a simulation; simulation value acquisition means for acquiring simulation values, which are values ​​calculated in a simulation, in which the sampling values ​​are set as parameters in the simulation, for each obtained sampling value; parameter value search means for calculating a post-mortem kernel average under target values ​​of simulation values ​​and searching for parameter values ​​that make the post-mortem kernel average larger, using the sampling values ​​of the parameters in the simulation, the simulation values ​​for each sampling value, and a kernel function having a subexpression such that the value of the post-mortem kernel average increases as the parameter values ​​in the simulation approach a predetermined value; and control execution means for performing control on a controlled object using the parameter values ​​obtained in the search. History of this disclosure 3 According to this embodiment, the parameter value acquisition method includes a computer sampling parameter values ​​in a simulation, acquiring simulation values ​​which are values ​​calculated in a simulation in which the sampling values ​​are set as parameters in the simulation for each obtained sampling value, calculating the posterior kernel mean under target values ​​of the simulation values ​​using the sampling values ​​of the parameters in the simulation, the simulation values ​​for each sampling value, and a kernel function which has a subexpression that increases the value of the posterior kernel mean as the parameter values ​​in the simulation are closer to a predetermined value, and searching for parameter values ​​that make the value of the posterior kernel mean larger.

[0008] History of this disclosure 4 According to the manner, programThis is a program to cause a computer to perform the following: sample parameter values ​​in a simulation; for each obtained sample value, acquire a simulation value which is the value calculated in the simulation when that sample value is set as the parameter in the simulation; use the sample values ​​of the parameters in the simulation, the simulation value for each sample value, and a kernel function which has a subexpression that increases the value of the posterior kernel mean as the parameter value in the simulation approaches a predetermined value, calculate the posterior kernel mean under a target value of the simulation value, and search for parameter values ​​that make the posterior kernel mean larger. That is the case. [Effects of the Invention]

[0009] According to this disclosure, if there is a preferred value for a parameter, the search for the parameter value can be performed while taking that preferred value into consideration. [Brief explanation of the drawing]

[0010] [Figure 1] This figure shows an example of the configuration of a parameter value acquisition device according to the first embodiment. [Figure 2] This figure shows an example of what to simulate. [Figure 3] This figure shows an example of the relationship between parameter values ​​and simulation values ​​in a simulation. [Figure 4] This figure shows a first example of the posterior kernel mean in an experiment according to the first embodiment. [Figure 5] This figure shows a second example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 6] This figure shows a third example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 7] This figure shows a fourth example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 8] This figure shows a fifth example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 9] This figure shows a sixth example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 10] This figure shows the seventh example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 11] This figure shows the eighth example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 12] This figure shows the ninth example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 13] This figure shows the tenth example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 14] This figure shows the 11th example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 15] This figure shows the 12th example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 16] This figure shows the 13th example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 17] This figure shows the 14th example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 18] This figure shows the 15th example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 19] This figure shows 16 examples of the posterior kernel mean in an experiment according to the first embodiment. [Figure 20] This figure shows the 17th example of the posterior kernel mean in the experiment according to the first embodiment. [Figure 21] This figure shows 18 examples of the posterior kernel mean in the experiment according to the first embodiment. [Figure 22] This figure shows an example of the procedure for processing performed by the parameter value acquisition device according to the first embodiment. [Figure 23] This figure shows a first example of the prior distribution in the experiment according to the second embodiment. [Figure 24] This figure shows a first example of the posterior kernel mean in an experiment according to the second embodiment. [Figure 25] This figure shows a second example of the prior distribution in the experiment according to the second embodiment. [Figure 26] This figure shows a second example of the posterior kernel mean in the experiment according to the second embodiment. [Figure 27] This figure shows a third example of the prior distribution in the experiment according to the second embodiment. [Figure 28] This figure shows a third example of the posterior kernel mean in the experiment according to the second embodiment. [Figure 29] This figure shows a fourth example of the prior distribution in the experiment according to the second embodiment. [Figure 30] This figure shows a fourth example of the posterior kernel mean in the experiment according to the second embodiment. [Figure 31] This figure shows a fifth example of the prior distribution in the experiment according to the second embodiment. [Figure 32] This figure shows a fifth example of the posterior kernel mean in the experiment according to the second embodiment. [Figure 33] This figure shows a sixth example of the prior distribution in the experiment according to the second embodiment. [Figure 34] This figure shows a first example of the procedure for processing performed by the parameter value acquisition device according to the second embodiment. [Figure 35] This figure shows a second example of the procedure for processing performed by the parameter value acquisition device according to the second embodiment. [Figure 36] This figure shows an example of the posterior kernel mean in an experiment according to the third embodiment. [Figure 37] This figure shows an example of a Gaussian distribution as a second prior distribution. [Figure 38] This figure shows an example of the relationship between the second prior distribution and the posterior kernel mean. [Figure 39] This figure shows an example of a second prior distribution in which the interval of parameter values ​​with relatively high probability densities is divided into multiple intervals. [Figure 40]This figure shows an example of the posterior kernel mean when using a second prior distribution in which the interval of parameter values ​​with relatively high probability density is divided into multiple intervals. [Figure 41] This figure shows a first example of the procedure for processing performed by the parameter value acquisition device according to the third embodiment. [Figure 42] This figure shows a second example of the procedure for processing performed by the parameter value acquisition device according to the third embodiment. [Figure 43] This figure shows an example of the configuration of a parameter value acquisition device according to the fourth embodiment. [Figure 44] This figure shows a first example of the procedure for processing performed by the parameter value acquisition device according to the fourth embodiment. [Figure 45] This figure shows a second example of the procedure for processing performed by the parameter value acquisition device according to the fourth embodiment. [Figure 46] This figure shows an example of the configuration of the control device according to the fifth embodiment. [Figure 47] This figure shows an example of the configuration of a control device according to the sixth embodiment. [Figure 48] This figure shows an example of the configuration of a parameter value acquisition device according to the seventh embodiment. [Figure 49] This figure shows an example of the processing procedure in the parameter value acquisition method according to the 10th embodiment. [Figure 50] This is a schematic block diagram showing the configuration of a computer according to at least one embodiment. [Modes for carrying out the invention]

[0011] The embodiments described below are not intended to limit the claims of the invention. Furthermore, not all combinations of features described in the embodiments are necessarily essential to the solution of the invention. In the following, characters with an overline or macron may be represented by adding a ￣ symbol after them. For example, a θ with an overline or macron may also be written as θ￣. Additionally, characters with a circumflex may be represented by adding a ^ symbol after them. For example, a μ with a circumflex may also be written as μ^.

[0012] <First Embodiment> Figure 1 shows an example of the configuration of a parameter value acquisition device according to the first embodiment. In the configuration shown in Figure 1, the parameter value acquisition device 100 comprises a communication unit 110, a display unit 120, an operation input unit 130, a storage unit 180, and a processing unit 190. The processing unit 190 comprises a sampling unit 191, a simulation value acquisition unit 192, and a parameter value search unit 193.

[0013] The parameter value acquisition device 100 searches for parameter values ​​in the simulation. In particular, the parameter value acquisition device 100 searches for parameter values ​​so that the simulation values ​​approach their target values ​​as closely as possible, and so that the parameter values ​​in the simulation approach their target values ​​as closely as possible. The simulation values ​​referred to here are the values ​​calculated in the simulation. The simulation values ​​correspond to examples of simulation results. The parameter value acquisition device 100 may be configured using a computer such as a personal computer (PC) or a workstation (WS).

[0014] In the following explanation, we will use the case where the simulator outputs simulation values ​​as an example, and the variable that indicates the simulation values ​​will also be referred to as the output in the simulation. However, the simulator may store the simulation values ​​within the simulator itself, and the parameter value acquisition device 100 may read the simulation values ​​from the simulator.

[0015] The subject of the simulation, the parameters in the simulation, and the output of the simulation are not limited to any specific example. For example, the subject of the simulation may be a system such as a production system, and the parameters in the simulation may be parameters that represent values ​​related to the size of the system. Furthermore, the output of the simulation may be an output that indicates the performance of the system. In this case, the parameter value acquisition device 100 can search for the smallest possible system size that allows the system to achieve its performance target.

[0016] Alternatively, the target of the simulation may be a controlled object such as a system or device, and the parameters in the simulation may be parameters that indicate control commands for which desirable values ​​are assumed, such as speed command values ​​for the controlled object. For example, it is possible that a smaller speed command value for the controlled object is preferable, such as lower energy consumption or lower noise generation. Furthermore, the output of the simulation may be an output that indicates the performance of the controlled object. In this case, the parameter value acquisition device 100 can search for a control command value that is as close as possible to a desirable value among the control command values ​​that enable the controlled object to achieve the performance target value.

[0017] Alternatively, the target of the simulation may be an observed object such as the natural environment, and the parameters in the simulation may be parameters that represent values ​​related to the observed object, such as temperature. Furthermore, the output of the simulation may be a parameter that represents another value related to the observed object, such as the growth rate of plants.

[0018] In this case, the parameter value acquisition device 100 can search for conditions that can achieve target values ​​related to the observed object, such as searching for the upper or lower temperature limit, or both, that can achieve the target value of the growth rate. Alternatively, the parameter value acquisition device 100 can be used to search for the upper or lower temperature limits, or both, at which the observed growth rate is achieved, thereby exploring the conditions under which the observed event occurs for the observed object.

[0019] The communication unit 110 communicates with other devices. For example, if the simulator is configured as an external device to the parameter value acquisition device 100, the communication unit 110 may send data for simulation execution to the simulator and receive simulation values.

[0020] The display unit 120 includes a display screen such as a liquid crystal panel or an LED (Light Emitting Diode) panel, and displays various images. For example, the display unit 120 may display the parameter values ​​acquired by the parameter value acquisition device 100 through a search. Alternatively, the parameter value acquisition device 100 may generate a heatmap showing the posterior kernel average for each possible value of the parameter during the parameter value search. The display unit 120 may then display the generated heatmap.

[0021] The operation input unit 130 includes, for example, input devices such as a keyboard and a mouse, and accepts user input. For example, the operation input unit 130 may be configured to accept user input specifying a target value for the simulation value.

[0022] The storage unit 180 stores various types of data. For example, the storage unit 180 may store data that allows the parameter value acquisition device 100 to search for parameter values, such as data showing the prior distribution of parameter values ​​for sampling parameter values ​​in the simulation, sampled parameter values ​​in the simulation, and simulation values ​​obtained based on each sampled value. The storage unit 180 is configured using the storage device provided by the parameter value acquisition device 100.

[0023] The processing unit 190 controls various parts of the parameter value acquisition device 100 to perform various processes. The functions of the processing unit 190 may also be performed by the CPU (Central Processing Unit) of the parameter value acquisition device 100 reading a program from the storage unit 180 and executing it.

[0024] The sampling unit 191 samples parameter values ​​in the simulation. Specifically, the sampling unit 191 samples parameter values ​​based on a predetermined prior distribution. That is, the sampling unit 191 samples parameter values ​​when the parameter values ​​follow a predetermined probability distribution. The sampling unit 191 is an example of a sampling means. The following explanation uses a uniform distribution as the prior distribution for parameter values ​​as an example. However, the prior distribution used by the parameter value acquisition device 100 is not limited to a specific type of distribution. For example, the user may be able to specify the prior distribution for parameter values.

[0025] The simulation value acquisition unit 192 acquires simulation values ​​for each sampling value obtained by the sampling unit 191 by setting that sampling value as a parameter in the simulation. The simulation value acquisition unit 192 is an example of a simulation value acquisition means. The simulation values ​​obtained for each sampling value by setting that sampling value as a parameter in the simulation are also referred to as simulation values ​​for each sampling value. The simulator used by the simulation value acquisition unit 192 may be configured as part of the parameter value acquisition device 100, or it may be configured as an external device to the parameter value acquisition device 100.

[0026] The parameter value search unit 193 searches for parameter values ​​based on the sampled values ​​obtained by the sampling unit 191, the simulation values ​​obtained by the simulation value acquisition unit 192 for each sampled value, and a predetermined target value for the simulation values. In particular, the parameter value search unit 193 uses a kernel function that includes a subexpression such that the value of the posterior kernel mean increases as the parameter value in the simulation approaches a predetermined value, and searches for parameter values ​​that maximize the posterior kernel mean based on the simulation values ​​for each sampled value under the target value for the simulation values ​​(i.e., searches for parameter values ​​that maximize the posterior kernel mean). The parameter value search unit 193 is an example of a parameter value search means.

[0027] The parameter value search performed by the parameter value search unit 193 can be considered a type of kernel ABC (Approximate Bayesian Computation). Searching for parameter values ​​that maximize the posterior kernel mean under the target value of the simulation also leads to searching for parameter values ​​that bring the simulation value as close to the target value as possible.

[0028] Here, as described above, the parameter value search unit 193 searches for parameter values ​​using a kernel function that includes a subexpression such that the value of the posterior kernel mean increases as the parameter value in the simulation approaches a predetermined value. This allows the parameter value search unit 193 to search for parameter values ​​that are as close as possible to the predetermined value and as close as possible to the target value in the simulation. A subexpression in which the kernel mean increases as the parameter value approaches a predetermined value is also called a parameter tuning subexpression. A kernel function with a parameter tuning subexpression is also called an extended kernel function.

[0029] The portion of an extended kernel function excluding the parameter tuning portion is also called the base kernel function or original kernel function. A kernel function that does not include the parameter tuning portion (i.e., a kernel function other than an extended kernel function) is also called the base kernel function or original kernel function. Both extended kernel functions and base kernel functions are sometimes simply referred to as kernel functions.

[0030] The following explanation uses the example of a case where the parameter takes a value greater than or equal to 0, and the predetermined value to which we want to approach the parameter value is 0, and therefore, we want to make the parameter value as small as possible. The process of making the kernel mean larger as the parameter value decreases is also called regularization. The subexpression that makes the kernel mean larger as the parameter value decreases is also called the regularization part. In this case, a kernel function with a regularization part is an example of an extended kernel function.

[0031] The parameter value search unit 193 searches for parameter values ​​in the simulation for each hyperparameter setting value used to adjust the degree of influence of the regularization part, and selects one of the parameter values ​​obtained through the search. For example, the parameter value search unit 193 may set each of the parameter values ​​obtained through the search as a parameter in the simulation, perform a simulation, and select the smallest parameter value among the parameter values ​​for which the simulation value becomes the target value.

[0032] If the influence of the regularization part in the extended kernel function is too small, the parameter values ​​obtained through the search may not be small. On the other hand, if the influence of the regularization part in the extended kernel function is too large, the simulation values ​​obtained by setting the parameter values ​​obtained through the search as the parameters in the simulation may not be close to the target values.

[0033] Accordingly, as described above, the parameter value search unit 193 selects any one of the parameter values obtained in simulations under various setting values of hyperparameters. This is expected to make it possible to obtain a parameter value such that the parameter value is as small as possible and the simulation value is as close to the target value as possible.

[0034] Hereinafter, a parameter in simulation is represented by θ. n θ is a positive integer, and the parameter θ is n θ can be a dimensional vector. For example, the parameter θ may be n θ may be configured as a combination of individual scalar parameters. Further, letting j be a positive integer, a sampled value of the parameter θ is denoted by θ̄ j represented by . Here, j is an identification number for identifying a sampled value. If m is the number of samples of the parameter θ (the number of sampled values), j can be an integer satisfying 1≦j≦m.

[0035] Further, an output in simulation is represented by Y. That is, let Y be a variable representing a simulation value. n Y is a positive integer, and the output Y is n Y can be a dimensional vector. For example, if the simulation value is n Y when represented by individual scalar values, the output Y is n Y may be a variable representing a combination of individual scalar values. Alternatively, when a simulation value represents one scalar value or vector value for each time step, the output Y may be a variable representing time-series data of simulation values.

[0036] Further, the sampled value θ̄ j a simulation value when is set as a parameter in simulation is Ȳ j represented by . The simulation value acquisition unit 192 acquires the sampled value θ̄ as a parameter in simulation jBy setting and running the simulation, the simulation value Y￣ j Alternatively, the simulation value acquisition unit 192 may use a method to estimate the simulation value for the parameter value, such as using a trained neural network, to obtain the simulation value Y￣. j You may also try to obtain an estimated value of Y. * It is represented as follows.

[0037] The parameter value search unit 193 calculates the posterior kernel mean μ^ θ|Y* This can be expressed as shown in equation (1).

[0038]

number

[0039] The left-hand side of equation (1) is the posterior kernel mean μ^, estimated using the sampled parameters and simulation values. θ|Y* However, the simulation value is the target value Y * Under the condition that the value of the parameter θ is Y, the posterior distribution p(θ|Y * This indicates the kernel mean of the simulation, i.e., the posterior kernel mean. The posterior kernel mean under the condition that the simulation value is the target value is also called the posterior kernel mean under the target value of the simulation. m is a positive integer representing the number of samples for the parameter θ.

[0040] k θ This represents a kernel function that takes the value of parameter θ as an argument. Kernel function k θ As such, the base kernel function (i.e., a kernel function that does not include the regularization part) can be used. Below, the kernel function k θ Let's take the example of using a Gaussian kernel (also called a radial basis function kernel). However, the kernel function k θTherefore, various kernel functions can be used, not just the Gaussian kernel. The Gaussian kernel RBF is expressed as shown in equation (2).

[0041]

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[0042] σ represents a hyperparameter in the Gaussian kernel. kernel function k θ When using a Gaussian kernel, the hyperparameter σ is σ θ Represented by σ. Hyperparameter σ θ The value of this parameter may be pre-set by the user, for example.

[0043] k θ (·,θ￣ j The "·" in ")" represents any value of the parameter θ. θ (·,θ￣ j The function ) behaves as a function that accepts the value of the parameter θ as input in the "·" part. As mentioned above, θ j This represents the j-th sampling value of the parameter θ.

[0044] H Θ This represents the reproducing kernel Hilbert space of parameter θ. w j This is the j-th sampling value of parameter θ θ￣ j The kernel function k is input θ (·,θ￣ j This is the scalar weight coefficient for ). j This can be expressed as shown in equation (3).

[0045]

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[0046] A superscript T before a matrix or vector indicates its transpose. ε is the inverse matrix (G+mεI m ) -1 This represents a scalar constant that enables the calculation of ε. The value of ε is, for example, pre-set by the user. I m This represents an m x m identity matrix. R m This represents the m-dimensional real number space. G is an m x m real matrix, expressed as shown in equation (4).

[0047]

number

[0048] j and j' both represent identification numbers that identify the simulation values. j is an integer between 1 and m (1 ≤ j ≤ m). j' is an integer between 1 and m (1 ≤ j' ≤ m). R m×m This represents an m x m dimension real number space. k Y This represents a kernel function that takes the output Y value in the simulation as an argument. In the first embodiment, the kernel function k Y The extended kernel function is used as follows. The parameter value search unit 193 searches for the extended kernel function k Y Alternatively, the function shown in equation (5) may be used.

[0049]

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[0050] θ j , θ j’ These are all variables that indicate the value of the parameter θ. j is the variable θ j This variable shows the simulation value when the parameter value indicated by is set as a parameter in the simulation. j’ is the variable θ j’ This variable indicates the simulation value when the parameter value shown is set as the parameter in the simulation. The "k" in equation (5) Y ((Y j ,θ j ),(Y j’ ,θ j’ ))」 is the extended kernel function k shown in equation (5) Y (Y j ,Y j’ In ) the variable θ j and θ j’ This indicates that it is used explicitly.

[0051] k' Y k' represents the base kernel function. Y You may also choose to use a Gaussian kernel. Base kernel function k' Y When using a Gaussian kernel, the hyperparameter σ in the Gaussian kernel is σ Y Represented by σ. Hyperparameter σ Y The value of this parameter may be pre-set by the user, for example.

[0052] "|| ||" represents a norm. Any norm can be used as "|| ||". For example, you can use the L1 norm or the L2 norm as "|| ||". exp(-β(||θ j ||+||θ j’ ||))」 corresponds to an example of the regularization part. As will be discussed later, the closer the value of parameter θ is to the zero vector, the greater the posterior kernel mean μ^ θ|Y* The experimental results showed that the value of [the variable] increased.

[0053] exp(-β(||θ j ||+||θ j’ The value of ||)) is the sampling value θ j The norm of ||θ j The closer || is to 0, the larger it becomes, and the sampling value θ j’ The norm of ||θ j’The value of exp(-||a||) increases as || approaches 0. Here, the norm can only take values ​​of 0 or greater, so the value of exp(-||a||) increases as the value of a approaches the zero vector. Therefore, the closer the value of the parameter θ is to the zero vector, the larger exp(-β(||θ) becomes. j ||+||θ j’ The value of ||)) becomes large, and the posterior kernel mean μ^ θ|Y* The value of becomes larger. β is a hyperparameter that takes a constant value to adjust the degree of influence of the regularization part.

[0054] When using the L1 norm as "|| ||", exp(-β(||θ) j ||+||θ j’ The expression "||))" can be considered a subexpression for L1 regularization. When using the L2 norm as "|| ||", the expression "exp(-β(||θ)" is used. j ||+||θ j’ The expression "||))" can be considered a subexpression for L2 regularization. Here, regularization means preventing the parameter value from becoming too large.

[0055] The regularization part used by the parameter value search unit 193 is not limited to a specific one. The smaller the parameter value in the simulation, the more the posterior kernel mean μ^ θ|Y* Various regularization parts can be used that increase the value of . For example, the parameter value search unit 193 is "exp(-β(||θ j ||-||θ j’ You may also use the regularization part represented by ||))」. As will be discussed later, in this case as well, the closer the value of parameter θ is to the zero vector, the greater the posterior kernel mean μ^ θ|Y* The experimental results showed that the value of [the variable] increased.

[0056] If you want to bring the value of parameter θ closer to a value other than the zero vector, the value you want to bring it closer to may be explicitly stated in the parameter adjustment section. For example, if A is a constant vector and you want to bring the value of parameter θ closer to A, the parameter value search unit 193 will say, "exp(-β(||θ j -A||+||θ j’A parameter adjustment portion represented by -A||)) may also be used.

[0057] Alternatively, the parameter value search unit 193 may be configured to perform conversion of parameter values. For example, let the parameter in simulation be θ sim and the parameter θ sim Consider a case where it is desired to bring the value of closer to A. Further, let the parameter value used for calculating the posterior kernel mean μ^ θ|Y* be represented by variable θ kf .

[0058] In this case, the parameter value search unit 193 converts, based on θ kf = θ sim - A, the conversion from the value of θ sim to the value of θ kf and the conversion from the value of θ kf to the value of θ sim . Thereby, the closer the value of θ sim is to A, the closer the value of θ kf is to a zero vector. Accordingly, the parameter value search unit 193 can calculate the posterior kernel mean μ^ kf,j ||+||θ kf,j’ ||)) as in "exp(-β(||θ kf by using a partial expression that makes the value of the posterior kernel mean μ^ θ|Y* larger as the value of the variable θ θ|Y* gets closer to the zero vector. Here, both θ sim,j and θ sim,j’ are sampling values of the parameter θ sim in simulation, and let θ kf,j = θ sim,j - A, θ kf,j’ = θ sim,j’ - A.

[0059] When the extended kernel function shown in equation (5) is applied to the extended kernel function k Y (Ȳ j , Ȳ j’ ) of equation (4), the extended kernel function k Y (Ȳj ,Y￣ j’ ) can be expressed as shown in equation (6).

[0060]

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[0061] k in equation (3) Y (Y * ) can be expressed as shown in equation (7).

[0062]

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[0063] The extended kernel function "k" in equation (7) Y (Y￣ j ,Y * In ) (where j is an integer between 1 and j) the target value of the simulation Y * This is input as an argument to the kernel function. In this case, the parameter value search unit 193 uses "exp(-β(||θ)" as the regularization part. j You may also use the subexpression shown by ||)). This is the target value Y of the simulation value. * The parameter value θ from which the value can be obtained * This is equivalent to setting the parameter value to the zero vector, which is the value we want to approach. The extended kernel function shown in equation (5) is the extended kernel function k in equation (7). Y (Y￣ j ,Y * When applied to ), the extended kernel function k Y (Y￣ j ,Y * ) can be expressed as shown in equation (8).

[0064]

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[0065] Next, we will describe an experiment concerning the operation of the parameter value acquisition device 100. In the experiment, we assumed the following simulation target and obtained the posterior kernel mean μ^ for each possible value of the parameter θ. θ|Y* The value was calculated.

[0066] Figure 2 shows an example of a simulation target. Figure 2 shows a production line that completes a product through a process of assembling a product consisting of three parts: a top, a bottom, and a screw, and a process of inspecting the assembled product. The time taken for the assembly process is denoted as parameter θ1 in the simulation. The time taken for the inspection process is denoted as parameter θ2 in the simulation. The simulator is assumed to have these two parameters. That is, parameter θ is assumed to be a vector whose elements are these two parameters θ1 and θ2. Furthermore, the number of products produced per unit time is defined as the output Y in the simulation.

[0067] Figure 3 shows an example of the relationship between parameter values ​​and simulation values ​​in a simulation. Figure 3 shows an example of the relationship between the values ​​of parameters θ1 and θ2 in the simulation and the value of the simulation output Y in the example in Figure 2. The horizontal axis in Figure 3 represents the value of parameter θ1. The vertical axis represents the value of parameter θ2. In Figure 3, the output Y value is shown for each combination of integer values ​​from 0 to 10 for parameter θ1 and integer values ​​from 0 to 10 for parameter θ2.

[0068] Furthermore, the target value Y of the output in the simulation. * Y * Set = 36 and target value Y *It is desired to reduce the values of parameters θ1 and θ2 as much as possible within a range that can achieve the objective. In other words, it is desired to bring both the values of parameters θ1 and θ2 as close to 0 as possible. For example, in order to reduce capital investment or labor costs required for the assembly process and inspection process as much as possible, it is conceivable to reduce the values of parameters θ1 and θ2 as much as possible. For example, the target value Y * represents the target production volume per unit time. (θ1,θ2)=(0,0) corresponds to an example of a predetermined value to which the parameter values are to be brought close.

[0069] In the experiment, assuming that the parameter value acquisition apparatus 100 searches for parameter values in the above case, the posterior kernel mean μ^ obtained using the extended kernel function shown in equation (5) for the range of 0≦θ1≦10 and 0≦θ2≦10 θ|Y* was calculated and a heat map was created. In the search for parameter values by the parameter value acquisition apparatus 100, the posterior kernel mean μ^ θ|Y* is used to search for a combination of values of θ1 and θ2 that makes the value as large as possible.

[0070] Regarding hyperparameter values, the kernel function k in equation (1) θ is the hyperparameter σ of the Gaussian kernel used θ was set to σ θ = 1.9. The base kernel function k' in equation (5) Y is the hyperparameter σ of the Gaussian kernel used Y was set to σ Y = 3.3. The value of the constant ε in equation (1) was set to ε=10 -2 .

[0071] Note that referring to FIG. 3, when the value of parameter θ1 is 5, the value of output Y is equal to the target value Y * of 36 regardless of whether the value of parameter θ2 is any value from 0 to 6. From the perspective of making parameter values as small as possible, it is considered preferable to bring the value of parameter θ1 close to 5 and the value of parameter θ2 close to 0.

[0072] Figure 4 shows a first example of the posterior kernel mean in an experiment according to the first embodiment. Figure 4 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (5) is used and the value of the hyperparameter β is set to 0. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 4, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0073] Setting the value of the hyperparameter β to 0 can be understood as not performing regularization in the kernel function. In the example in Figure 4, when the value of parameter θ1 is approximately 4.6 and the value of parameter θ2 is approximately 6, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0074] Figure 5 shows a second example of the posterior kernel mean in the experiment according to the first embodiment. Figure 5 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (5) is used and the value of the hyperparameter β is set to 0.0001. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 5, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0075] Point P12 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. The heatmap in the example in Figure 5 is approximately the same as the heatmap in the example in Figure 4. In the example in Figure 5, when the value of parameter θ1 is approximately 4.6 and the value of parameter θ2 is approximately 6, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0076] Figure 6 shows a third example of the posterior kernel mean in the experiment according to the first embodiment. Figure 6 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (5) is used and the value of the hyperparameter β is set to 0.001. θ|Y*The values ​​are shown in the form of a heatmap. In the heatmap in Figure 6, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0077] Point P13 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. The heatmap in the example in Figure 6 is approximately the same as the heatmaps in the examples in Figures 4 and 5. In the example in Figure 6, when the value of parameter θ1 is approximately 4.6 and the value of parameter θ2 is approximately 6, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0078] Figure 7 shows a fourth example of the posterior kernel mean in the experiment according to the first embodiment. Figure 7 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (5) is used and the value of the hyperparameter β is set to 0.01. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 7, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0079] Point P14 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. The heatmap in the example in Figure 7 has contour lines with a shape roughly similar to those in the examples in Figures 4 to 6, and the posterior kernel mean μ^ θ|Y* The values ​​of parameters θ1 and θ2 that maximize the value of are approximately the same as in the examples in Figures 4 to 6. In the example in Figure 7, when the value of parameter θ1 is approximately 4.6 and the value of parameter θ2 is approximately 5.9, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0080] Figure 8 shows a fifth example of the posterior kernel mean in the experiment according to the first embodiment. Figure 8 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (5) is used and the value of the hyperparameter β is set to 0.1. θ|Y*The values ​​are shown in the form of a heatmap. In the heatmap in Figure 8, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0081] Point P15 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. In the example in Figure 8, the heatmap shows the posterior kernel mean μ^ θ|Y* The point where the value of is maximized is located lower (on the side with smaller parameter θ2 values) than in the examples in Figures 4 to 7. In the example in Figure 8, when the value of parameter θ1 is approximately 5 and the value of parameter θ2 is approximately 3.1, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0082] Figure 9 shows a sixth example of the posterior kernel mean in the experiment according to the first embodiment. Figure 9 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (5) is used and the value of the hyperparameter β is set to 0.5. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 9, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0083] Point P16 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. In the example in Figure 9, the heatmap shows the posterior kernel mean μ^ θ|Y* The point where the value of is maximized is located even lower (on the side with smaller parameter θ2 values) than in the example in Figure 8. In the example in Figure 9, when the value of parameter θ1 is approximately 5.1 and the value of parameter θ2 is approximately 1.1, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0084] Figure 10 shows the seventh example of the posterior kernel mean in the experiment according to the first embodiment. Figure 10 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (5) is used and the value of the hyperparameter β is set to 1. θ|Y*the value of is shown in the form of a heat map. The horizontal axis of the heat map in FIG. 10 represents the value of parameter θ1. The vertical axis represents the value of parameter θ2.

[0085] Point P17 is the posterior kernel average μ^ θ|Y* represents the point at which the value of is the largest. In the heat map of the example in FIG. 10, the posterior kernel average μ^ θ|Y* the point at which the value of is maximum is located further lower (the side where the value of parameter θ2 is smaller) than in the example of FIG. 9. In the example of FIG. 10, when the value of parameter θ1 is approximately 5.1 and the value of parameter θ2 is approximately 0.6, the posterior kernel average μ^ θ|Y* the value of is the largest.

[0086] FIG. 11 is a diagram showing an eighth example of the posterior kernel average in an experiment according to the first embodiment. In FIG. 11, when the extended kernel function shown in Formula (5) is used and the value of hyperparameter β is set to 5, the posterior kernel average μ^ θ|Y* the value of is shown in the form of a heat map. The horizontal axis of the heat map in FIG. 11 represents the value of parameter θ1. The vertical axis represents the value of parameter θ2.

[0087] Point P18 is the posterior kernel average μ^ θ|Y* represents the point at which the value of is the largest. In the heat map of the example in FIG. 11, the posterior kernel average μ^ θ|Y* the point at which the value of is maximum is located further to the left (the side where the value of parameter θ1 is smaller) than in the example of FIG. 10. In the example of FIG. 11, when the value of parameter θ1 is approximately 0.2 and the value of parameter θ2 is approximately 0.3, the posterior kernel average μ^ θ|Y* the value of is the largest.

[0088] FIG. 12 is a diagram showing a ninth example of the posterior kernel average in an experiment according to the first embodiment. In FIG. 12, when the extended kernel function shown in Formula (5) is used and the value of hyperparameter β is set to 10, the posterior kernel average μ^ θ|Y*The values ​​are shown in the form of a heatmap. In the heatmap in Figure 11, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0089] Point P19 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. The heatmap in the example in Figure 12 is approximately the same as the heatmap in the example in Figure 11. In the example in Figure 12, when the value of parameter θ1 is approximately 0 and the value of parameter θ2 is approximately 0.4, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0090] Among the extended kernel functions shown in equation (5), the base kernel function "k' Y (Y j ,Y j’ )" means that the value of output Y in the simulation is the target value Y * This can be seen as the part that evaluates how close it is to the given value. Also, the regularization part "exp(-β(||θ j ||+||θ j’ The part "||))" can be understood as the part that evaluates how close the values ​​of parameter θ1 and parameter θ2 are to the predetermined value 0. Furthermore, as mentioned above, the hyperparameter β in equation (5) is a constant value used to adjust the degree of influence of the regularization part. The larger the value of β, the greater the degree of influence of the regularization part.

[0091] In the examples shown in Figures 4 to 7, the value of β is relatively small, ranging from 0 to 0.01, and it is thought that the influence of the regularization part is small, which is why the parameter values ​​(especially the value of parameter θ2) have not become very small. In the examples shown in Figures 8 through 10, the value of parameter θ2 decreases as the value of β increases. In the examples from Figures 11 to 12, the β value is relatively large, ranging from 5 to 10, and the influence of the base kernel function is small, so the simulation value is equal to the target value Y. * It is thought to be far away from [the source].

[0092] Referring to Figure 3, in the example shown in Figure 10 among the examples from Figures 4 to 12, the value of parameter θ1 is approximately 5.1 and the value of parameter θ2 is approximately 0.6, which corresponds to the target value Y * This approach is best suited to the objective of minimizing the values ​​of parameter θ1 and parameter θ2 while maintaining the range that achieves =36.

[0093] The parameter value acquisition device 100 changes the value of β and then calculates the posterior kernel mean μ^ θ|Y* Set the parameter value that maximizes this value in the simulator to set the target value Y of the simulation value. * Check whether or not the target value Y can be achieved. * One possible approach is to select the smallest parameter value that can achieve the desired result.

[0094] Furthermore, as the value of β increases, the posterior kernel mean μ^ θ|Y* The point where this is maximized approaches (θ1,θ2)=(0,0). At this point, the regularization part of equation (5) "exp(-β(||θ j ||+||θ j’ ||))」 indicates that the closer the parameter values ​​in the simulation are to the predetermined values, the more the posterior kernel mean μ^ θ|Y* This is an example of a subexpression that increases the value of .

[0095] The parameter value search unit 193 finds "exp(-β(||θ j ||-||θ j’ Experiments were also conducted on the case where the regularization part represented by "||))" is used. In this case, the extended kernel function is expressed as shown in equation (9).

[0096]

number

[0097] The extended kernel function shown in equation (9) is the extended kernel function k in equation (4). Y (Y￣ j ,Y￣ j’ When applied to ), the extended kernel function kY (Y￣ j ,Y￣ j’ ) can be expressed as shown in equation (10).

[0098]

number

[0099] Furthermore, the extended kernel function shown in equation (9) is the same as the extended kernel function k in equation (7). Y (Y￣ j ,Y * When applied to (5), the regularization part is "exp(-β(||θ)" as described above for the case of equation (5). j You may also use the subexpression shown by ||))」. In this case, the extended kernel function shown in equation (9) is the extended kernel function k in equation (7). Y (Y￣ j ,Y * Applies to ) and the extended kernel function k Y (Y￣ j ,Y * ) can be expressed as shown in equation (8) above.

[0100] The experimental conditions, including the subject of the simulation, the relationship between the parameter values ​​and the simulation values ​​in the simulation, the target value of the output in the simulation, the predetermined value to which the parameter values ​​should be approached, and the hyperparameter values, were the same as those described above when using the extended kernel function shown in equation (5).

[0101] Figure 13 shows the tenth example of the posterior kernel mean in the experiment according to the first embodiment. Figure 13 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (9) is used and the value of the hyperparameter β is set to 0. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 13, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0102] Point P21 is the posterior kernel mean μ^ θ|Y*This represents the point with the largest value. The heatmap in the example in Figure 13 is similar to the heatmap in the example in Figure 4. In the example in Figure 13, when the value of parameter θ1 is approximately 4.6 and the value of parameter θ2 is approximately 6, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0103] Figure 14 shows an eleventh example of the posterior kernel mean in an experiment according to the first embodiment. Figure 14 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (9) is used and the value of the hyperparameter β is set to 0.0001. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 14, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0104] Point P22 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. The heatmap in the example in Figure 14 is approximately the same as the heatmap in the example in Figure 13. In the example in Figure 14, when the value of parameter θ1 is approximately 4.6 and the value of parameter θ2 is approximately 6, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0105] Figure 15 shows the 12th example of the posterior kernel mean in the experiment according to the first embodiment. Figure 15 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (9) is used and the value of the hyperparameter β is set to 0.001. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 15, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0106] Point P23 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. The heatmap in the example in Figure 15 is approximately the same as the heatmaps in the examples in Figures 13 and 14. In the example in Figure 15, when the value of parameter θ1 is approximately 4.6 and the value of parameter θ2 is approximately 5.8, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0107] Figure 16 shows the 13th example of the posterior kernel mean in the experiment according to the first embodiment. Figure 16 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (9) is used and the value of the hyperparameter β is set to 0.01. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 16, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0108] Point P24 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. The heatmap in the example in Figure 16 shows the posterior kernel mean μ^ θ|Y* The point where the value of is maximized is located lower (on the side with smaller parameter θ2 values) than in the examples in Figures 13 to 15. In the example in Figure 16, when the value of parameter θ1 is approximately 5.1 and the value of parameter θ2 is approximately 2.3, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0109] Figure 17 shows the 14th example of the posterior kernel mean in the experiment according to the first embodiment. Figure 17 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (9) is used and the value of the hyperparameter β is set to 0.1. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 17, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0110] Point P25 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. In the example shown in Figure 17, the heatmap shows the posterior kernel mean μ^ θ|Y* The point where the value of is maximized is located even lower (on the side with smaller parameter θ2 values) than in the example in Figure 16. In the example in Figure 17, when the value of parameter θ1 is approximately 5.1 and the value of parameter θ2 is approximately 1.1, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0111] Figure 18 shows the 15th example of the posterior kernel mean in the experiment according to the first embodiment. Figure 18 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (9) is used and the value of the hyperparameter β is set to 0.5. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 18, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0112] Point P26 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. In the example shown in Figure 18, the heatmap shows the posterior kernel mean μ^ θ|Y* The point where the value of is maximized is located even lower (on the side with smaller parameter θ2 values) than in the example in Figure 17. In the example in Figure 17, when the value of parameter θ1 is approximately 5.1 and the value of parameter θ2 is approximately 0.6, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0113] Figure 19 shows the 16th example of the posterior kernel mean in the experiment according to the first embodiment. Figure 19 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (9) is used and the value of the hyperparameter β is set to 1. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 19, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0114] Point P27 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. The heatmap in the example in Figure 19 is approximately the same as the heatmap in the example in Figure 18. In the example in Figure 19, when the value of parameter θ1 is approximately 5 and the value of parameter θ2 is approximately 0.5, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0115] Figure 20 shows the 17th example of the posterior kernel mean in the experiment according to the first embodiment. Figure 20 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (9) is used and the value of the hyperparameter β is set to 5. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 20, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0116] Point P28 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. In the example in Figure 20, the heatmap shows the posterior kernel mean μ^ θ|Y* The point where the value of is maximized is located to the left (towards the side where the value of parameter θ1 is smaller) compared to the example in Figure 19. In the example in Figure 20, when the value of parameter θ1 is approximately 0.1 and the value of parameter θ2 is approximately 0.1, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0117] Figure 21 shows the 18th example of the posterior kernel mean in the experiment according to the first embodiment. Figure 21 shows the posterior kernel mean μ^ when the extended kernel function shown in equation (9) is used and the value of the hyperparameter β is set to 10. θ|Y* The values ​​are shown in the form of a heatmap. In the heatmap in Figure 21, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0118] Point P29 is the posterior kernel mean μ^ θ|Y* This represents the point with the largest value. The heatmap in the example in Figure 21 is roughly the same as the heatmap in the example in Figure 20. In the example in Figure 21, when the value of parameter θ1 is approximately 0.2 and the value of parameter θ2 is approximately 0.4, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0119] Among the extended kernel functions shown in equation (9), the base kernel function "k' Y (Y j ,Y j’ )" means that the value of output Y in the simulation is the target value Y * This can be seen as the part that evaluates how close it is to the given value. Also, the regularization part "exp(-β(||θ j ||-||θ j’ The part "||))" can be understood as the part that evaluates how close the values ​​of parameter θ1 and parameter θ2 are to the predetermined value 0. Also, as in equation (5), the hyperparameter β takes a constant value to adjust the degree of influence of the regularization part. The larger the value of β, the greater the degree of influence of the regularization part.

[0120] In the examples in Figures 13 to 15, the value of β is relatively small, ranging from 0 to 0.001, and the influence of the regularization part is small, resulting in the posterior kernel mean μ^ θ|Y* It is thought that the parameter value that maximizes this value (especially the value of parameter θ2) is not getting too small. In the examples from Figures 16 to 19, as the value of β increases, the posterior kernel mean μ^ θ|Y* The value of the parameter θ2 that maximizes the value of is decreasing. In the example from Figures 20 to 21, the β value is relatively large, ranging from 5 to 10, and the influence of the base kernel function is small, so the simulation value is equal to the target value Y. * It is thought to be far away from [the source].

[0121] Referring to Figure 3, in the example shown in Figure 19 among the examples from Figures 13 to 21, the value of parameter θ1 is approximately 5 and the value of parameter θ2 is approximately 0.5, which corresponds to the target value Y *This approach is best suited to the objective of minimizing the values ​​of parameter θ1 and parameter θ2 while maintaining the range that achieves =36.

[0122] Even when using the extended kernel function shown in equation (9), the parameter value acquisition device 100 changes the value of β and calculates the posterior kernel mean μ^ θ|Y* Set the parameter value that maximizes this value in the simulator to set the target value Y of the simulation value. * Check whether or not the target value Y can be achieved. * One possible approach is to select the smallest parameter value that can achieve the desired result.

[0123] Furthermore, as the value of β increases, the posterior kernel mean μ^ θ|Y* The point where this is maximized approaches (θ1,θ2)=(0,0). At this point, the regularization part of equation (9) "exp(-β(||θ j ||-||θ j’ ||))」 indicates that the closer the parameter values ​​in the simulation are to the predetermined values, the more the posterior kernel mean μ^ θ|Y* This is an example of a subexpression that increases the value of .

[0124] Figure 22 is a diagram showing an example of the processing procedure performed by the parameter value acquisition device 100 according to the first embodiment. In the process shown in Figure 22, the parameter value search unit 193 initializes the value of the hyperparameter β (step S101). For example, the storage unit 180 may pre-store a series of values ​​to be set for the hyperparameter β. The parameter value search unit 193 may then read the initial value from the series of values ​​stored in the storage unit 180 and set it for the hyperparameter β.

[0125] Next, the sampling unit 191 samples the value of the parameter θ in the simulation based on the prior distribution until it reaches a predetermined number of samples (step S102). For example, a uniform distribution may be used as the prior distribution here. Alternatively, the user may set the prior distribution in advance.

[0126] Next, the simulation value acquisition unit 192 executes the simulation for each parameter sampling value (step S103). Specifically, for each sampling value acquired by the sampling unit 191 in step S102, the simulation value acquisition unit 192 sets that sampling value as a parameter in the simulation and executes the simulation. In this way, the simulation value acquisition unit 192 acquires simulation values ​​for each sampling value.

[0127] Next, the parameter value search unit 193 uses the extended kernel function to calculate the posterior kernel mean μ^ θ|Y* The parameter value is searched based on (step S104). Specifically, the parameter value search unit 193 searches based on equations (1), (3), (4), and (7), and the kernel function k in equations (4) and (7). Y Using an extended kernel function, the target value Y of the simulation value is... * Under these conditions, the sampling value θ￣ by the sampling unit 191 j , and the sampling value θ￣ obtained by the simulation value acquisition unit 192 j Each simulation value Y j Based on the posterior kernel mean μ^ θ|Y* Calculate the posterior kernel mean μ^ θ|Y* We search for a value for the parameter θ that maximizes the result.

[0128] The method by which the parameter value search unit 193 searches for parameter values ​​is not limited to a specific method. For example, the parameter value search unit 193 calculates the posterior kernel mean μ^ for each possible value of the parameter θ. θ|Y* The value of can also be calculated. Then, the parameter value search unit 193 calculates the posterior kernel mean μ^ θ|Y* Of the parameter values ​​(values ​​of parameter θ) for which the value of was calculated, the posterior kernel mean μ^ θ|Y* Alternatively, the system may detect the parameter value that maximizes the value of [the parameter]. In this case, the parameter value search unit 193 may generate a heatmap as illustrated in Figures 4 to 21, and display the generated heatmap on the display unit 120.

[0129] Alternatively, the parameter value search unit 193 calculates the posterior kernel mean μ^ as a function. θ|Y* The following steps are performed: first, the parameter values ​​are determined based on known solution search methods such as gradient descent, the determination of search points continues until a predetermined termination condition is met, and the posterior kernel mean μ^ at the search points is calculated. θ|Y* You can repeat the calculation of the value.

[0130] Next, the processing unit 190 determines whether the termination conditions for the loop in steps S104, S105, and S106 are met (step S105). The termination conditions here are not limited to any specific conditions. For example, if the storage unit 180 has previously stored a series of values ​​to be set as hyperparameters β, the processing unit 190 may determine whether or not it has set all of the series of values ​​stored in the storage unit 180 as hyperparameters β and performed the process in step S104.

[0131] Alternatively, if the parameter value search unit 193 monotonically increases the value of the hyperparameter β in step S106, the processing unit 190 may determine in the determination in step S105 whether the simulation value achieved when the newly obtained parameter value in step S104 is set as the parameter in the simulation achieves the target value. The processing unit 190 may then repeatedly execute the loop of steps S104, S105, and S106 until the simulation value no longer achieves the target value.

[0132] If the processing unit 190 determines in step S105 that the termination condition is not met (step S105: NO), the parameter value search unit 193 updates the value of the hyperparameter β (step S106). For example, if the storage unit 180 has already stored a series of values ​​to be set as the hyperparameter β, the parameter value search unit 193 may read the series of values ​​stored in the storage unit 180 in order and set them as the hyperparameter β. After step S106, the process returns to step S104.

[0133] On the other hand, if the processing unit 190 determines in step S105 that the termination condition is met (step S105: YES), the parameter value search unit 193 determines the parameter value to be adopted (step S107). For example, the parameter value search unit 193 may select from the parameter values ​​obtained in step S104 for each hyperparameter β setting value the parameter value that is closest to a predetermined value that the simulation value will achieve, among the parameter values ​​that achieve the target value. After step S107, the parameter value acquisition device 100 terminates the process shown in Figure 22.

[0134] As described above, the sampling unit 191 samples the parameter values ​​in the simulation. The simulation value acquisition unit 192 acquires simulation values ​​for each obtained sampling value by setting that sampling value as a parameter in the simulation. Simulation values ​​are values ​​calculated in the simulation. The parameter value search unit 193 uses a kernel function that includes a subexpression that increases the value of the posterior kernel mean as the parameter value in the simulation approaches a predetermined value, to search for parameter values ​​that maximize the posterior kernel mean based on the simulation value for each sampling value, under the target value of the simulation value.

[0135] The parameter value acquisition device 100 allows for the search for parameter values ​​while taking into account preferred values ​​when available. In particular, the parameter value acquisition device 100 uses a kernel function that includes a subexpression such that the value of the posterior kernel mean increases as the parameter value in the simulation approaches a predetermined value. This allows for the search for parameter values ​​that are as close as possible to the predetermined value and as close as possible to the target value in the simulation.

[0136] Furthermore, the parameter value search unit 193 searches for parameter values ​​in the simulation for each hyperparameter setting value used to adjust the degree of influence of the regularization part, and selects one of the parameter values ​​obtained through the search. Here, if the influence of the regularization part in the extended kernel function is too small, the parameter values ​​obtained through the search may not be close to the predetermined values. On the other hand, if the influence of the regularization part in the extended kernel function is too large, the simulation values ​​obtained when the parameter values ​​obtained through the search are set as the parameters in the simulation may not be close to the target values.

[0137] In contrast, the parameter value acquisition device 100 is expected to select one of the parameter values ​​obtained in the simulation under various hyperparameter settings, thereby obtaining parameter values ​​that are as close as possible to a predetermined value and that are as close as possible to a target value.

[0138] <Second Embodiment> In addition to using an extended kernel function to bring the parameter values ​​in the simulation closer to predetermined values, the parameter value acquisition device may also use a prior distribution that has a peak at the value to which the parameter values ​​are to be approached. This point will be explained in the second embodiment.

[0139] The configuration of the parameter value acquisition device according to the second embodiment is the same as that of the parameter value acquisition device according to the first embodiment, and Figure 1 will be used in the description of the second embodiment as well. The parameter value acquisition device 100 according to the second embodiment differs from the parameter value acquisition device 100 according to the first embodiment in that, instead of using an extended kernel function, it uses a prior distribution having a peak at the value to which the parameter value is to be approached.

[0140] Specifically, the sampling unit 191 samples the parameter values ​​in the simulation using a prior distribution that has a peak at the value to which the parameter value is to be approached. In addition, the parameter value search unit 193 searches for the kernel function k in equation (4). Y , and the kernel function k in equation (7) Y For example, an extended kernel function may be used, or a base kernel function (a kernel function that does not include the regularization part) may be used. In other respects, the parameter value acquisition device 100 according to the second embodiment is the same as the parameter value acquisition device 100 according to the first embodiment.

[0141] The prior distribution used by the sampling unit 191 is not limited to a specific type of distribution, but can be any distribution having a peak. For example, the prior distribution used by the sampling unit 191 may be a Laplace distribution or a Gaussian distribution, but is not limited to these.

[0142] Next, an experiment concerning the operation of the parameter value acquisition device 100 according to the second embodiment will be described. In the experiment, the same simulation target as in the experiment described in the first embodiment was assumed, and the post-kernel mean μ^ for each possible value of the parameter θ was calculated. θ|Y* The value was calculated. Furthermore, the Laplace distribution was used as the prior distribution for the parameters in the simulation. The Laplace distribution is shown in equation (11).

[0143]

number

[0144] In equation (11), μ and η represent hyperparameters in the Laplace distribution, respectively. The hyperparameter μ is the Location Parameter, indicating the location of the peak in the distribution. The hyperparameter η is the Scale Parameter, an example of a hyperparameter used to adjust the uniformity of the distribution. The smaller the value of the hyperparameter η (closer to 0), the more uniform the distribution; the larger the value of the hyperparameter η, the more biased the distribution becomes towards the peak indicated by the hyperparameter μ.

[0145] In the experiment, the simulation parameters θ1 and θ2 were sampled based on a Laplace distribution. μ=0 was set for both parameters θ1 and θ2. (θ1,θ2)=(0,0) represents the peak position of the prior distribution. For the value of η, the same value was set for parameters θ1 and θ2, and the posterior kernel mean μ^ was calculated for each of η=0.001, η=0.01, η=0.5, η=1, and η=3. θ|Y* We attempted to generate a heatmap. However, when η=3, the simulation value was similar for all sampling values, and the posterior kernel mean μ^ θ|Y* The calculation could not be performed.

[0146] The domains of both parameters θ1 and θ2 were set to (0,10). Sampling results that did not fall within the domain were discarded, and the parameter values ​​were resampled. The sample size was set to 1000, and sampling continued until the number of sampled values ​​for parameter θ2 reached the sample size.

[0147] Furthermore, the kernel function k in equation (4) Y , and the kernel function k in equation (7) Y The base kernel function was used. Specifically, the kernel function k in equation (4) Y , the kernel function k in equation (7)Y Both used a Gaussian kernel.

[0148] Also, the kernel function k in equation (1) θ The hyperparameter σ of the Gaussian kernel used as θ The value of σ θ = 1.9 was set. The kernel function k in equation (4) Y , and the kernel function k in equation (7) Y The hyperparameter σ of the Gaussian kernel used as Y The value of σ Y =3.3. The value of the constant ε in equation (1) is set to ε = 10 -2 That's what I decided. Similar to the experiment described in the first embodiment, it is considered preferable in the experiment in the second embodiment to bring the value of parameter θ1 closer to 5 and the value of parameter θ2 closer to 0.

[0149] Figure 23 shows a first example of the prior distribution in the experiment according to the second embodiment. Figure 23 shows the sampling results for parameter θ in the simulation when the hyperparameter η is set to 0. In Figure 23, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2. Setting the value of the hyperparameter η to 0 can be seen as using a uniform distribution as the prior distribution. In the example in Figure 23, the parameter values ​​are sampled approximately uniformly within the ranges 0 < θ1 < 10 and 0 < θ2 < 10.

[0150] Figure 24 shows a first example of the posterior kernel mean in an experiment according to the second embodiment. In Figure 24, the posterior kernel mean μ^ calculated using the sampling values ​​shown in Figure 23 is shown. θ|Y* The values ​​are shown in the form of a heatmap. Therefore, Figure 24 shows the posterior kernel mean μ^ when η=0. θ|Y* This shows a heatmap. In the heatmap in Figure 24, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2. Point P31 is the posterior kernel mean μ^ θ|Y* This represents the point where the value of is the largest. In the example in Figure 24, when the value of parameter θ1 is approximately 4.6 and the value of parameter θ2 is approximately 6.0, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0151] Figure 25 shows a second example of the prior distribution in the experiment according to the second embodiment. Figure 25 shows the sampling results for parameter θ in the simulation when the hyperparameter η is set to 0.001. In Figure 25, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0152] Figure 26 shows a second example of the posterior kernel mean in an experiment according to the second embodiment. In Figure 26, the posterior kernel mean μ^ calculated using the sampling values ​​shown in Figure 25 is shown. θ|Y* The values ​​are shown in the form of a heatmap. Therefore, Figure 26 shows the posterior kernel mean μ^ when η = 0.001. θ|Y* This shows a heatmap. In the heatmap in Figure 26, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2. Point P32 is the posterior kernel mean μ^ θ|Y* This represents the point where the value of is the largest. In the example in Figure 26, when the value of parameter θ1 is approximately 4.5 and the value of parameter θ2 is approximately 6.5, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0153] Figure 27 shows a third example of the prior distribution in the experiment according to the second embodiment. Figure 27 shows the sampling results for parameter θ in the simulation when the hyperparameter η is set to 0.01. In Figure 27, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0154] Figure 28 shows a third example of the posterior kernel mean in the experiment according to the second embodiment. In Figure 28, the posterior kernel mean μ^ calculated using the sampling values ​​shown in Figure 27 is shown. θ|Y* The values ​​are shown in the form of a heatmap. Therefore, Figure 28 shows the posterior kernel mean μ^ when η = 0.01. θ|Y* The heatmap is shown. In the heatmap in Figure 28, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2. Point P33 is the posterior kernel mean μ^ θ|Y* This represents the point where the value of is the largest. In the example in Figure 28, when the value of parameter θ1 is approximately 4.1 and the value of parameter θ2 is approximately 7.9, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0155] Figure 29 shows a fourth example of the prior distribution in the experiment according to the second embodiment. Figure 29 shows the sampling results for parameter θ in a simulation when the hyperparameter η is set to 0.5. In Figure 29, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0156] Figure 30 shows a fourth example of the posterior kernel mean in the experiment according to the second embodiment. In Figure 30, the posterior kernel mean μ^ calculated using the sampling values ​​shown in Figure 29 is shown. θ|Y* The values ​​are shown in the form of a heatmap. Therefore, Figure 30 shows the posterior kernel mean μ^ when η = 0.5. θ|Y* This shows a heatmap. In the heatmap of Figure 30, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2. Point P34 is the posterior kernel mean μ^ θ|Y* This represents the point where the value of is the largest. In the example in Figure 30, when the value of parameter θ1 is approximately 4.1 and the value of parameter θ2 is approximately 1.7, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0157] Figure 31 shows a fifth example of the prior distribution in the experiment according to the second embodiment. Figure 31 shows the sampling results for parameter θ in a simulation when the value of the hyperparameter η is set to 1. In Figure 31, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2.

[0158] Figure 32 shows a fifth example of the posterior kernel mean in the experiment according to the second embodiment. In Figure 32, the posterior kernel mean μ^ calculated using the sampling values ​​shown in Figure 31 is shown. θ|Y* The values ​​are shown in the form of a heatmap. Therefore, Figure 32 shows the posterior kernel mean μ^ when η=1. θ|Y* This shows a heatmap. In the heatmap in Figure 32, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2. Point P35 is the posterior kernel mean μ^ θ|Y* This represents the point where the value of is the largest. In the example in Figure 32, when the value of parameter θ1 is approximately 5.0 and the value of parameter θ2 is approximately 1.0, the posterior kernel mean μ^ θ|Y* The value of this is the largest.

[0159] Figure 33 shows a sixth example of the prior distribution in the experiment according to the second embodiment. Figure 33 shows the sampling results for parameter θ in a simulation when the hyperparameter η is set to 3. In Figure 33, the horizontal axis represents the value of parameter θ1, and the vertical axis represents the value of parameter θ2. As mentioned above, when η=3, the simulation value is the same for all the sampling values ​​shown in Figure 33, and the posterior kernel mean μ^ θ|Y* The calculation could not be performed.

[0160] In the examples in Figures 23 to 28, the value of η is relatively small, ranging from 0 to 0.01, and the distribution of the sampled values ​​is relatively uniform. Therefore, the search was not focused on points where the parameter value was relatively small, and as a result, the posterior kernel mean μ^θ|Y* It appears that the parameter value that maximizes this value (especially the value of parameter θ2) is not getting too small.

[0161] In the examples from Figures 29 to 32, as the value of η increases, the distribution of the sampled values ​​becomes skewed towards (θ1,θ2)=(0,0). Therefore, as the value of η increases, points where the parameter value is relatively small are searched for more intensively, and this results in the posterior kernel mean μ^ θ|Y* It is thought that the parameter value that maximizes the value of (especially the value of parameter θ2) is becoming smaller. In the example in Figure 33, the distribution of the sampled values ​​is biased towards (θ1,θ2)=(0,0). As mentioned above, when η=3, the simulation value is similar for all the sampled values ​​shown in Figure 33, and the posterior kernel mean μ^ θ|Y* The calculation could not be performed.

[0162] Referring to Figure 3, among the examples in Figures 23 to 33, the values ​​of parameter θ1 approximately 5.0 and parameter θ2 approximately 1.0, as shown in the examples in Figures 31 and 32, correspond to the target value Y * This approach is best suited to the objective of minimizing the values ​​of parameter θ1 and parameter θ2 while maintaining the range that achieves =36.

[0163] In the second embodiment as well, the parameter value acquisition device 100 changes the value of η and then calculates the post-kernel mean μ^ θ|Y* Set the parameter value that maximizes this value in the simulator to set the target value Y of the simulation value. * Check whether or not the target value Y can be achieved. * One possible approach is to select the smallest parameter value that can achieve the desired result.

[0164] Figure 34 shows a first example of the processing procedure performed by the parameter value acquisition device 100 according to the second embodiment. Figure 34 shows the parameter value acquisition device 100 according to the second embodiment performing the processing procedure of the kernel function k in equations (4) and (7). YThis shows an example of the processing procedure when using the base kernel function (i.e., a kernel function that does not include the regularization part).

[0165] In the process shown in Figure 34, the sampling unit 191 initializes the value of the hyperparameter η for adjusting the uniformity of the prior distribution (step S201). For example, the storage unit 180 may store a series of values ​​to be set as the hyperparameter η in advance. The sampling unit 191 may then read the initial value from the series of values ​​stored in the storage unit 180 and set it as the hyperparameter η.

[0166] Next, the sampling unit 191 samples the value of the parameter θ in the simulation based on the prior distribution until it reaches a predetermined number of samples (step S202). Here, the sampling unit 191 samples the value of the parameter θ using a prior distribution that has a peak at the value to which the parameter θ is to be approached, and also has a hyperparameter η.

[0167] Step S203 is the same as step S103 in Figure 22. After step S203, the parameter value search unit 193 calculates the posterior kernel mean μ^ θ|Y* The parameter value is searched based on (step S204). In step S204, the parameter value search unit 193 searches for the kernel function k in equations (4) and (7). Y The base kernel function is used. In all other respects, step S204 is the same as step S104 in Figure 22.

[0168] Next, the processing unit 190 determines whether the termination condition for the loop from steps S202 to S206 is met (step S205). The termination condition here is not limited to any specific condition. For example, if the memory unit 180 has previously stored a series of values ​​to be set as hyperparameters η, the processing unit 190 may determine whether or not it has set all of the series of values ​​stored in the memory unit 180 as hyperparameters η and performed the processing from steps S202 to S204.

[0169] Alternatively, if the parameter value search unit 193 monotonically increases the value of the hyperparameter η in step S206, the processing unit 190 may determine in the determination in step S205 whether the simulation value achieved when the newly obtained parameter value in step S204 is set as the parameter in the simulation achieves the target value. The processing unit 190 may then repeatedly execute the loop from steps S202 to S206 until the simulation value no longer achieves the target value.

[0170] If the processing unit 190 determines in step S205 that the termination condition is not met (step S205: NO), the sampling unit 191 updates the value of the hyperparameter η (step S206). For example, if the storage unit 180 has already stored a series of values ​​to be set as the hyperparameter η, the sampling unit 191 may read the series of values ​​stored in the storage unit 180 in order and set them as the hyperparameter η. After step S206, the process returns to step S202.

[0171] On the other hand, if the processing unit 190 determines in step S205 that the termination condition is met (step S205: YES), the parameter value search unit 193 determines the parameter value to be adopted (step S207). For example, the parameter value search unit 193 may select from the parameter values ​​obtained in step S204 for each hyperparameter setting value the parameter value that is closest to a predetermined value that the simulation value will reach the target value. After step S207, the parameter value acquisition device 100 completes the process shown in Figure 34.

[0172] Figure 35 shows a second example of the processing procedure performed by the parameter value acquisition device 100 according to the second embodiment. Figure 34 shows the parameter value acquisition device 100 according to the second embodiment performing the processing of the kernel function k in equations (4) and (7). Y This shows an example of the processing procedure when using an extended kernel function. The processing in Figure 35 can be described as a process that combines the use of an extended kernel function in the first embodiment with sampling the parameter values ​​in the simulation based on a prior distribution having a peak at a predetermined value, as in the second embodiment.

[0173] In the process shown in Figure 35, the parameter value search unit 193 initializes the value of the hyperparameter β, and the sampling unit 191 initializes the value of the hyperparameter η for adjusting the uniformity of the prior distribution (step S211). The process by which the parameter value search unit 193 initializes the value of the hyperparameter β is the same as the process in step S101 in Figure 1. The process by which the sampling unit 191 initializes the value of the hyperparameter η is the same as the process in step S201 in Figure 34.

[0174] Step S212 is the same as step S202 in Figure 34. Steps S213 to S214 are the same as steps S103 to S104 in Figure 22.

[0175] After step S214, the processing unit 190 determines whether the termination condition of the loop from steps S212 to S216 is met (step S215). The termination condition here is not limited to any specific condition. For example, if the memory unit 180 has pre-stored a series of values ​​that are combinations of the value to be set as the hyperparameter β and the value to be set as the hyperparameter η, the processing unit 190 may determine whether or not it has set all of the series of values ​​stored in the memory unit 180 as the hyperparameter β and hyperparameter η and performed the processing from steps S212 to S214.

[0176] Alternatively, if in step S216 the parameter value search unit 193 monotonically increases the value of the hyperparameter β and the sampling unit 191 monotonically increases the value of the hyperparameter η, then in the determination in step S215 the processing unit 190 may determine whether the simulation value achieved when the newly obtained parameter value in step S214 is set as the parameter in the simulation achieves the target value. The processing unit 190 may then repeatedly execute the loop from steps S212 to S216 until the simulation value no longer achieves the target value.

[0177] If the processing unit 190 determines in step S215 that the termination condition is not met (step S215: NO), the parameter value search unit 193 updates the value of the hyperparameter β, and the sampling unit 191 updates the value of the hyperparameter η (step S216). For example, if the storage unit 180 has previously stored a series of values ​​that are combinations of the value to be set for the hyperparameter β and the value to be set for the hyperparameter η, the parameter value search unit 193 and the sampling unit 191 may sequentially read the series of values ​​stored in the storage unit 180 and set them as the hyperparameters β and η. After step S216, the process returns to step S112.

[0178] On the other hand, if the processing unit 190 determines in step S215 that the termination condition is met (step S215: YES), the parameter value search unit 193 determines the parameter value to be adopted (step S217). For example, the parameter value search unit 193 may select, from the parameter values ​​obtained in step S214 for each combination of the hyperparameter β setting value and the hyperparameter η setting value, the parameter value that is closest to a predetermined value that the simulation value will achieve the target value of. After step S217, the parameter value acquisition device 100 terminates the process shown in Figure 35.

[0179] As described above, the sampling unit 191 samples the parameter values ​​in the simulation based on a prior distribution having a peak at a predetermined value. The simulation value acquisition unit 192 acquires simulation values ​​for each obtained sampling value by setting that sampling value as a parameter in the simulation. Simulation values ​​are values ​​calculated in the simulation. The parameter value search unit 193 searches for parameter values ​​that maximize the posterior kernel mean value based on the simulation values ​​for each sampling value, under the target value of the simulation values.

[0180] The parameter value acquisition device 100 allows for the search for parameter values ​​while taking into account preferred values ​​when such preferred values ​​exist. In particular, the parameter value acquisition device 100 allows for the search for parameter values ​​that are as close as possible to the predetermined values ​​and as close as possible to the target values, by sampling the parameter values ​​in the simulation based on a prior distribution having a peak at a predetermined value.

[0181] Furthermore, the sampling unit 191 samples the parameter values ​​in the simulation for each hyperparameter setting value used to adjust the uniformity of the prior distribution. The simulation value acquisition unit 192 acquires simulation values ​​for each sampling value for each hyperparameter setting value used to adjust the uniformity of the prior distribution. The parameter value search unit 193 searches for parameter values ​​in the simulation for each hyperparameter setting value used to adjust the uniformity of the prior distribution, and selects one of the parameter values ​​obtained through the search.

[0182] Here, if the bias of the prior distribution is too small (if the prior distribution is too close to a uniform distribution), the parameter values ​​obtained through exploration may not be close to the predetermined values. On the other hand, if the bias of the prior distribution is too large, the simulation values ​​obtained by setting the parameter values ​​obtained through exploration as the parameters in the simulation may not be close to the target values.

[0183] In contrast, the parameter value acquisition device 100 is expected to select one of the parameter values ​​obtained in the simulation under various hyperparameter settings, thereby obtaining parameter values ​​that are as close as possible to a predetermined value and that are as close as possible to a target value.

[0184] <Third Embodiment> The parameter value acquisition device may be configured to calculate the posterior kernel mean based on the kernel Bayes' rule (KBR). This will be explained in the third embodiment. The configuration of the parameter value acquisition device according to the third embodiment is the same as that of the parameter value acquisition device according to the first embodiment, and Figure 1 will also be used in the description of the third embodiment.

[0185] The parameter value acquisition device 100 according to the third embodiment differs from the parameter value acquisition device 100 according to the first embodiment and the parameter value acquisition device 100 according to the second embodiment in that it calculates the posterior kernel mean based on the kernel Bayes rule. In all other respects, the parameter value acquisition device 100 according to the third embodiment is the same as the parameter value acquisition device 100 according to the first embodiment and the parameter value acquisition device 100 according to the second embodiment.

[0186] The kernel Bayes rule, as used here, is a method for calculating the posterior kernel mean when the parameter values ​​in a simulation follow a distribution different from the distribution of a given distribution, using a combination of sampled parameter values ​​in a simulation based on a given distribution and simulation values ​​based on those sampled values.

[0187] The sampling unit 191 samples parameter values ​​in the simulation, as in the first embodiment. In the third embodiment, the prior distribution to which the parameter values ​​follow when the parameter value acquisition device 100 samples the parameter values ​​in the simulation is referred to as the first prior distribution. The first prior distribution is not limited to any particular type of distribution. For example, a uniform distribution may be used as the first prior distribution, but is not limited to this.

[0188] The sampling unit 191 may further sample parameter values ​​in the simulation based on a second prior distribution. However, it is not mandatory for the sampling unit 191 to sample parameter values ​​in the simulation based on a second prior distribution. The following section will explain the case where the sampling unit 191 samples parameter values ​​in the simulation based on a second prior distribution, and then explain the case where the sampling unit 191 does not perform sampling based on the second prior distribution.

[0189] The second prior distribution is not limited to any particular type of distribution. For example, when the parameter value search unit 193 searches for a parameter value that is as close as possible to a predetermined value, the second prior distribution may be a distribution that has a peak at that predetermined value. In this case, the second prior distribution may be a Laplace distribution or a Gaussian distribution, but is not limited to these. Alternatively, when the parameter value search unit 193 searches for parameter values ​​that fall within a predetermined range, it may use a probability distribution with a relatively high probability density within that range as a second prior distribution.

[0190] The simulation value acquisition unit 192 acquires simulation values ​​for each sampling value based on the first prior distribution by setting that sampling value as a parameter in the simulation. In this way, the simulation value acquisition unit 192 acquires simulation values ​​for each sampling value based on the first prior distribution.

[0191] The parameter value search unit 193 uses a combination of sampling values ​​based on a first prior distribution and simulation values ​​for each sampling value to search for parameter values ​​that maximize the posterior kernel mean under the target value of the simulation values, when the parameter values ​​in the simulation are based on a second prior distribution.

[0192] The sampling unit 191 may sample parameter values ​​in the simulation based on a second prior distribution, and the parameter value search unit 193 may calculate the posterior kernel mean using the sampled values ​​based on the second prior distribution. Alternatively, as will be described later, the sampling unit 191 may not sample parameter values ​​in the simulation based on the second prior distribution, and the parameter value search unit 193 may calculate the posterior kernel mean based on the ratio of the probability density in the first prior distribution to the probability density in the second prior distribution. The parameter value search unit 193 calculates the posterior kernel average m^ θ|Y* This is shown in equation (12).

[0193]

number

[0194] kθ T The kernel function k, as explained with reference to equation (1), is shown here. θ (·,θ￣ j This represents the inverted matrix obtained by calculating the matrix in equation (1). Here, θ￣ j This shows the sampling values ​​based on the first prior distribution. k Y (Y * The kernel function k in equation (7) is expressed as shown in equation (7). The parameter value search unit 193 searches for the kernel function k in equation (7). Y Alternatively, you can use an extended kernel function, or you can use the base kernel function (a kernel function that does not include the regularization part). θ|Y* This can be expressed as shown in equation (13).

[0195]

number

[0196] G Y This represents an m x m real matrix similar to that shown in equation (4). The simulation values ​​here correspond to the sampled values ​​based on the first prior distribution. δ m is the inverse matrix ((ΛG Y ) 2 +δ m I m ) -1 This is a hyperparameter that represents a scalar constant that enables the calculation of δ. m The value is pre-set by the user, for example. As mentioned above, m is a positive integer representing the sample size for the parameter θ. Here, m represents the sample size in sampling based on the first prior distribution. As mentioned above, I m This represents an m x m identity matrix. Λ is an element of the vector μ^ i This is a diagonal matrix with the element at the i-th row and i-th column. This can be expressed as in equation (14).

[0197]

number

[0198] The vector μ^ is expressed as shown in equation (15).

[0199]

number

[0200] G θ This represents the Gram matrix of parameter θ. The Gram matrix G in equation (15) θ Therefore, we will use the sampling value based on the first prior distribution as the value of the parameter θ. ε m This is the inverse matrix ((1 / m)G θ +ε m I m ) -1 This is a hyperparameter that represents a scalar constant that enables the calculation of ε. m The value is pre-set by the user, for example. m^ Π This is shown in equation (16) m^ Π,i It is an m-dimensional vector whose i-th element is [element name].

[0201]

number

[0202] In equation (16), i is an integer such that 1 ≤ i ≤ m. l represents the number of samples of parameter θ in sampling based on the second prior distribution. When the parameter value search unit 193 searches for parameter θ for each setting of the scale parameter of the second prior distribution, l represents the number of samples of parameter θ for which the parameter value search unit 193 samples for one setting of the scale parameter. The scale parameter is an example of a hyperparameter used to adjust uniformity.

[0203] θ￣i This represents the i-th sampled value out of m sampled values ​​obtained by sampling based on the first prior distribution. U j This represents the j-th sampled value out of l sampled values ​​obtained by sampling based on the second prior distribution.

[0204] kernel function k θ (θ￣ i , U j The part calculated by ) is θ￣ i and U j It calculates a kind of similarity score to determine how similar the data points are. Therefore, the more similar the data points obtained from sampling based on the first prior distribution and sampling based on the second prior distribution are, the higher the k score. θ (θ￣ i , U j The value of ) becomes larger. γ j This represents the weight of each data point i in sampling based on the second prior distribution. For example, if the second prior distribution is a uniform distribution and sampling is performed from a uniform distribution, all weights are of roughly the same magnitude, i.e., γ j = 1 / l. As will be explained later, for example, if you want to treat something sampled from a uniform distribution as a different distribution, γ j It takes a value that corresponds to the shape of its distribution. Like this m^ Π is the kernel function k θ (θ￣ i , U j ) and γ j This is a vector used to interpret a sample based on a first prior distribution as a sample from a desired prior distribution.

[0205] In addition to searching for parameter values ​​based on the kernel Bayes rule described above, the parameter value search unit 193 may also search for parameter values ​​using the sampled values ​​obtained from sampling based on the first prior distribution and the simulation values ​​acquired by the simulation value acquisition unit 192 for each sampled value. In this case, the parameter value search unit 193 searches for parameter values ​​using the same process as the parameter value search unit 193 in the second embodiment. However, it is not essential that the parameter value search unit 193 searches for parameter values ​​using the sampled values ​​obtained from sampling based on the first prior distribution and the simulation values ​​acquired by the simulation value acquisition unit 192 for each sampled value.

[0206] The same sampling values ​​may be treated as sampling values ​​based on the first and second prior distributions, respectively. In this case, in equation (16), θ￣ i =U i And so, k θ (θ￣ i ,U i ) = 1. Also, if we denote the first prior distribution as p and the second prior distribution as π, then γ in equation (16) j This can be expressed as shown in equation (17).

[0207]

number

[0208] m^ in equation (16) Π,i This can be expressed as shown in equation (18).

[0209]

number

[0210] Thus, the probability density p(θ) in the first prior distribution p is j ) and the probability density π(θ) in the second prior distribution π j) ratio π(θ￣ j ) / p(θ￣ j If it is possible to calculate the posterior kernel mean m^, the parameter value acquisition device 100 will calculate the posterior kernel mean m^ without performing sampling based on the second prior distribution. θ|Y* The value can be calculated.

[0211] Without performing sampling based on a second prior distribution, the posterior kernel mean m^ θ|Y* The method for calculating the value of is expected to require relatively little computation because sampling based on a second prior distribution is not necessary. If we let m be the number of samples in sampling based on the first prior distribution and l be the number of samples in sampling based on the second prior distribution, then calculating equation (16) for each component i will result in a computation time of O(ml). The posterior kernel mean m^ θ|Y* The method for calculating the value is O(m 2 The computational complexity is ). If l is larger than m, a reduction in computational complexity can be expected.

[0212] Furthermore, in the case of distributions that are difficult to sample, it is necessary to calculate the sampled values ​​using methods such as the Markov chain Monte Carlo method (MCMC). In contrast, the posterior kernel mean m^ is calculated without performing sampling based on a second prior distribution. θ|Y* The method for calculating the value is expected to have a low computational load because it does not require calculating the sampling value.

[0213] Furthermore, without performing sampling based on the second prior distribution, the posterior kernel mean m^ θ|Y* The method for calculating the value of eliminates sampling error because it does not require sampling based on a second prior distribution.

[0214] On the other hand, sampling based on a second prior distribution is performed to obtain the posterior kernel mean m^ θ|Y* In the method for calculating the value of the distribution, the ratio π(θ) j ) / p(θ￣ jEven if it is not possible to calculate the posterior kernel mean m^ θ|Y* The value can be calculated.

[0215] Next, an experiment concerning the operation of the parameter value acquisition device 100 according to the third embodiment will be described. In the experiment, the same simulation target as in the experiment described in the first embodiment was assumed, and for the case where the value of parameter θ1 is θ1=5, the posterior kernel average m^ θ|Y* The value was calculated.

[0216] Furthermore, a uniform distribution was used as the first prior distribution. A Laplace distribution was used as the second prior distribution. For the hyperparameter μ of the Laplace distribution shown in equation (11), μ=0 was set. For the hyperparameter η, the posterior kernel mean m^ was used for η=0.01, 0.1, 1, and 10 respectively. θ|Y* The value was calculated.

[0217] The domain of parameter θ2 was set to (0,10), and the number of samples in the sampling based on the first prior distribution was set to 1000. No sampling was performed based on the second prior distribution, and the posterior kernel mean m^ θ|Y* The value was calculated.

[0218] Furthermore, the kernel function k in equation (7) Y The base kernel function was used. Specifically, the kernel function k in equation (7) Y A Gaussian kernel was used. Also, the kernel function k in equation (16) θ The hyperparameter σ of the Gaussian kernel used as θ The value of σ θ = 1.4 was set. The kernel function k in equation (7) Y The hyperparameter σ of the Gaussian kernel used as Y The value of σ Y = 1.7 was set. Hyperparameter δ in equation (13) m The value of is δ m =10 -3The hyperparameter ε in equation (15) was set as follows. m The value of is ε m =10 -5 That's what I decided. Referring to Figure 3, it is considered preferable to bring the value of parameter θ2 closer to 0.

[0219] Figure 36 shows an example of the posterior kernel mean in an experiment according to the third embodiment. In Figure 36, the posterior kernel mean m^ for each value of parameter θ2 is shown for η = 0.01, 0.1, 1, and 10. θ|Y* The values ​​are shown. In the graph in Figure 36, the horizontal axis shows the value of the parameter θ2. The vertical axis shows the posterior kernel mean m^ θ|Y* This shows the value.

[0220] Line L11 represents the posterior kernel mean m^ when η = 0.01. θ|Y* This shows the value of m^. When η = 0.01, the posterior kernel mean m^ is approximately 3 when the value of the parameter θ2 is 3. θ|Y* The value is at its maximum. Furthermore, a uniform distribution is used as the prior distribution, and the posterior kernel mean μ^ is calculated based on kernel ABC using the base kernel function (i.e., a kernel function that does not include the regularization part). θ|Y* This is the posterior kernel mean m^ when η = 0.01. θ|Y* It was similar. In this case, the posterior kernel mean μ^ θ|Y* The graph roughly overlapped with line L11.

[0221] Line L12 represents the posterior kernel mean m^ when η = 0.1. θ|Y* This shows the value of m^. When η=0.1, the posterior kernel mean m^ is approximately 2 when the value of the parameter θ2 is about 2. θ|Y* The value is at its maximum. Line L13 represents the posterior kernel mean m^ when η=1. θ|Y* This shows the value of η=1, and when the value of parameter θ2 is approximately 1, the posterior kernel mean m^ θ|Y* The value is at its maximum. Line L14 represents the posterior kernel mean m^ when η=10. θ|Y*This shows the value of m^. When η=10, the posterior kernel mean m^ is approximately 0 when the value of the parameter θ2 is 0. θ|Y* The value is at its maximum.

[0222] In the example in Figure 36, as the value of η increases, the posterior kernel mean m^ θ|Y* The value of parameter θ2 that maximizes the value of is approaching 0, which is the value of parameter θ2 that we want to approach. The parameter value acquisition device 100 changes the value of η and calculates the post-kernel average m^ θ|Y* Set the parameter value that maximizes this value in the simulator to set the target value Y of the simulation value. * Check whether or not the target value Y can be achieved. * One possible approach is to select the smallest parameter value that can achieve the desired result.

[0223] The position parameter of the second prior distribution can be set to a value that corresponds to the value you want to approximate the parameter value in the simulation to. For example, if a Gaussian distribution is used as the second prior distribution, the mean μ of the Gaussian distribution corresponds to an example of the position parameter, and the variance σ 2 This is an example of a scale parameter. Figure 37 shows an example of a Gaussian distribution as a second prior distribution. Figure 37 shows an example of the probability distribution for each mean when a Gaussian distribution is used as the second prior distribution. In the graph of Figure 37, the horizontal axis represents the value of the parameter θ², and the vertical axis represents the probability density.

[0224] Line L21 shows an example of a Gaussian distribution with a mean of -5. Line L22 shows an example of a Gaussian distribution with a mean of 0. Line L23 shows an example of a Gaussian distribution with a mean of 5. Line L24 shows an example of a Gaussian distribution with a mean of 10. Line L25 shows an example of a Gaussian distribution with a mean of 15.

[0225] Figure 38 shows an example of the relationship between the second prior distribution and the posterior kernel mean. Figure 38 shows the posterior kernel mean m^ for each value of parameter θ2 when each of the Gaussian distributions shown in Figure 37 is used as the second prior distribution in the experiment according to the third embodiment described above. θ|Y* This shows the value. In the graph in Figure 38, the horizontal axis shows the value of the parameter θ2. The vertical axis shows the posterior kernel mean m^ θ|Y* This shows the value.

[0226] Line L31 represents the posterior kernel mean m^ when using a Gaussian distribution with a mean of -5 as the second prior distribution, as shown by line L21 in Figure 37. θ|Y* Examples of values ​​are shown. Line L32 represents the posterior kernel mean m^ when a Gaussian distribution with a mean of 0, as shown by line L22 in Figure 37, is used as the second prior distribution. θ|Y* Examples of values ​​are shown.

[0227] Line L33 represents the posterior kernel mean m^ when using a Gaussian distribution with a mean of 5 as the second prior distribution, as shown by line L23 in Figure 37. θ|Y* Examples of values ​​are shown. Line L34 represents the posterior kernel mean m^ when using a Gaussian distribution with a mean of 10 as the second prior distribution, as shown by line L24 in Figure 37. θ|Y* Examples of values ​​are shown.

[0228] Line L35 represents the posterior kernel mean m^ when using a Gaussian distribution with a mean of 15 as the second prior distribution, as shown by line L25 in Figure 37. θ|Y* Examples of values ​​are shown. Furthermore, line L36 uses a uniform distribution as the prior distribution and is based on kernel ABC, with a posterior kernel mean μ^ θ|Y* When calculating the value of the posterior kernel mean μ^ θ|Y* Examples of values ​​are shown.

[0229] In the example in Figure 38, the smaller the mean of the second prior distribution, the greater the posterior kernel mean m^ θ|Y*The value of parameter θ2 that minimizes the value of is decreasing. If you want to make the value of parameter θ2 as small as possible, you can consider using a Gaussian distribution with a relatively small mean as the second dimensional distribution. On the other hand, if you want to make the value of parameter θ2 as large as possible, you can consider using a Gaussian distribution with a relatively large mean as the second dimensional distribution.

[0230] Furthermore, the second prior distribution is not limited to Laplace distributions or Gaussian distributions, but can be any type of distribution. Figure 39 shows an example of a second prior distribution in which the interval of parameter values ​​with a relatively large probability density is divided into multiple intervals. In Figure 39, the horizontal axis of the graph shows the value of the parameter θ2. The vertical axis shows the probability density. In the example shown in Figure 39, the probability density is relatively high in the intervals 0 < θ² < 2 and 4 < θ² < 6.

[0231] Figure 40 shows the posterior kernel mean m^ when using a second prior distribution in which the interval of parameter values ​​with relatively high probability density is divided into multiple intervals. θ|Y* The figure shows an example of the values. In Figure 40, the horizontal axis of the graph shows the value of the parameter θ2. The vertical axis shows the posterior kernel mean m^ θ|Y* This shows the value.

[0232] Line L41 represents the posterior kernel mean m^ for each value of parameter θ2 when the distribution shown in Figure 39 is used as the second probability distribution in the experiment according to the third embodiment described above. θ|Y* Examples of values ​​are shown. Furthermore, line L42 uses a uniform distribution as the prior distribution and is based on kernel ABC, with a posterior kernel mean μ^ θ|Y* When calculating the value of the posterior kernel mean μ^ θ|Y* Examples of values ​​are shown.

[0233] The posterior kernel mean μ^ shown by line 41 θ|Y*The function has two peaks, one when θ2 is approximately 1 and another when θ2 is approximately 5, and between these two peaks, the posterior kernel mean μ^ θ|Y* The value is relatively small. For example, if we want the parameter θ2 to have a value of 0 < θ2 < 2 or 4 < θ2 < 6, we can consider using the distribution shown in Figure 39 as a second prior distribution.

[0234] Figure 41 shows a first example of the processing procedure performed by the parameter value acquisition device 100 according to the third embodiment. Figure 41 shows that the parameter value search unit 193 calculates the post-kernel average m^ θ|Y* In the calculation, the kernel function k in equation (7) Y An example is shown where the base kernel function is used.

[0235] In the process shown in Figure 41, the sampling unit 191 initializes the values ​​of the hyperparameters of the second prior distribution (step S301). In particular, the sampling unit 191 initializes the values ​​of the hyperparameters for adjusting the uniformity of the second prior distribution. For example, the memory unit 180 may pre-store a series of values ​​to be set as the hyperparameters of the second prior distribution. The sampling unit 191 may then read out the initial values ​​from the series of values ​​stored in the memory unit 180 and set them as the hyperparameters of the second prior distribution.

[0236] Next, the sampling unit 191 samples parameter values ​​based on the first prior distribution until it reaches a preset number of samples (step S302). Next, the simulation value acquisition unit 192 executes a simulation for each sampling value obtained in step S302 (step S303). Specifically, for each sampling value obtained in step S302, the simulation value acquisition unit 192 sets that sampling value as a parameter in the simulation and executes the simulation. In this way, the simulation value acquisition unit 192 acquires a simulation value for each sampling value.

[0237] Next, the parameter value search unit 193 calculates the posterior kernel mean m^ based on the kernel Bayes rule. θ|Y* The parameter values ​​in the simulation are searched for so that the value of is as large as possible (step S304). In step S304, the parameter value search unit 193 searches for the kernel function k in equation (7). Y Using the base kernel function, the posterior kernel mean m^ θ|Y* Calculate the value.

[0238] The method by which the parameter value search unit 193 searches for parameter values ​​is not limited to a specific method. For example, the parameter value search unit 193 calculates the posterior kernel average m^ for each possible value of the parameter θ. θ|Y* The value of can also be calculated. Then, the parameter value search unit 193 calculates the posterior kernel mean m^ θ|Y* Of the parameter values ​​(values ​​of parameter θ) for which the value of was calculated, the posterior kernel mean μ^ θ|Y* Alternatively, the system may detect the parameter value that maximizes the value of [the parameter]. In this case, the parameter value search unit 193 may generate a heatmap as illustrated in Figures 4 to 21, and display the generated heatmap on the display unit 120.

[0239] Alternatively, the parameter value search unit 193 calculates the posterior kernel mean m^ as a function. θ|Y* The following steps are performed: first, the parameter values ​​are determined based on known solution search methods such as gradient descent, the determination of search points continues until a predetermined termination condition is met, and the posterior kernel mean m^ at the search points is calculated. θ|Y* You can repeat the calculation of the value.

[0240] Furthermore, as described above, the sampling unit 191 may perform sampling of parameter values ​​based on a second prior distribution. Then, the parameter value search unit 193 uses the sampled values ​​based on the second prior distribution to calculate the posterior kernel mean m^ θ|Y* You could also calculate it this way. Alternatively, as described above, the parameter value search unit 193 does not directly use the sampling values ​​based on the second prior distribution, but rather the ratio of the distributions π(θ￣ j ) / p(θ￣ j Using ) the posterior kernel mean m^ θ|Y* You could also calculate it this way.

[0241] Next, the processing unit 190 determines whether the termination condition for the loop from steps S304 to S306 is met (step S305). The termination condition here is not limited to any specific condition. For example, if the memory unit 180 has previously stored a series of values ​​to be set as hyperparameters for the second prior distribution, the processing unit 190 may determine whether or not it has set all of the series of values ​​stored in the memory unit 180 as hyperparameters and performed the processing in step S304.

[0242] Alternatively, if the sampling unit 191 updates the hyperparameter values ​​in step S306 so that the bias of the second prior distribution increases (the uniformity decreases), the determination in step S305 may be configured so that the processing unit 190 determines whether the simulation values ​​obtained when the newly obtained parameter values ​​in step S304 are set as the parameters in the simulation achieve the target values. The processing unit 190 may then repeatedly execute the loop from steps S304 to S306 until the simulation values ​​no longer achieve the target values.

[0243] If the processing unit 190 determines in step S305 that the termination condition is not met (step S305: NO), the sampling unit 191 updates the values ​​of the hyperparameters of the second prior distribution (step S306). In particular, the sampling unit 191 updates the values ​​of the hyperparameters for adjusting the uniformity of the second prior distribution.

[0244] For example, if the storage unit 180 has already stored a series of values ​​to be set as hyperparameters, the sampling unit 191 may read the series of values ​​stored in the storage unit 180 in order and set them as hyperparameters. After step S306, the process returns to step S304.

[0245] On the other hand, if the processing unit 190 determines in step S305 that the termination condition is met (step S305: YES), the parameter value search unit 193 determines the parameter value to be adopted (step S307). For example, the parameter value search unit 193 may select from the parameter values ​​obtained in step S304 for each hyperparameter setting value of the second prior distribution the parameter value that is closest to a predetermined value that the simulation value will achieve the target value. After step S307, the parameter value acquisition device 100 terminates the process shown in Figure 41.

[0246] Figure 41 shows an example where a prior distribution with hyperparameters for adjusting uniformity is used as the second prior distribution. If a prior distribution without hyperparameters for adjusting uniformity is used as the second prior distribution, steps S301, S305, and S306 are unnecessary. In step S307, the parameter values ​​obtained in the search in step S304 are determined to be the parameter values ​​to be adopted.

[0247] Figure 42 shows a second example of the processing procedure performed by the parameter value acquisition device 100 according to the third embodiment. Figure 42 shows that the parameter value search unit 193 calculates the post-kernel average m^ θ|Y* In the calculation, the kernel function k in equation (7) Y This shows an example of using extended kernel functions.

[0248] In the process shown in Figure 42, the parameter value search unit 193 initializes the value of the hyperparameter β, and the sampling unit 191 initializes the value of the hyperparameter of the second prior distribution (step S311). The process by which the parameter value search unit 193 initializes the value of the hyperparameter β is the same as in step S101 in Figure 22. The process by which the sampling unit 191 initializes the value of the hyperparameter of the second prior distribution is the same as in step S301 in Figure 41.

[0249] Steps S312 and S313 are the same as steps S302 and S303 in Figure 41. After step S313, the parameter value search unit 193 calculates the posterior kernel mean m^ based on the kernel Bayes rule. θ|Y* The parameter values ​​in the simulation are searched for such that the value of is as large as possible (step S314). In step S314, the parameter value search unit 193 searches for the kernel function k in equation (7). Y Using the extended kernel function, the posterior kernel mean m^ θ|Y* The value of is calculated. In all other respects, step S314 is the same as step S304 in Figure 41.

[0250] Next, the processing unit 190 determines whether the termination condition of the loop from steps S314 to S316 is met (step S315). The termination condition here is not limited to any specific condition. For example, if the memory unit 180 has pre-stored a series of values ​​resulting from combinations of the value to be set as the hyperparameter β and the value to be set as the hyperparameter of the second prior distribution, the processing unit 190 may determine whether or not it has set all of the series of values ​​stored in the memory unit 180 as the hyperparameter β and the hyperparameter of the second prior distribution and performed the processing in step S314.

[0251] Alternatively, in step S316, if the parameter value search unit 193 monotonically increases the value of the hyperparameter β, and the sampling unit 191 updates the hyperparameter value so that the bias of the second prior distribution increases (so that the uniformity decreases), then in the determination in step S315, the processing unit 190 may determine whether the simulation value achieved when the newly obtained parameter value in step S314 is set as the parameter in the simulation achieves the target value. The processing unit 190 may then repeatedly execute the loop from steps S314 to S316 until the simulation value no longer achieves the target value.

[0252] If the processing unit 190 determines in step S315 that the termination condition is not met (step S315: NO), the parameter value search unit 193 updates the value of the hyperparameter β, and the sampling unit 191 updates the value of the hyperparameter of the second prior distribution (step S316). In particular, the sampling unit 191 updates the value of the hyperparameter for adjusting the uniformity of the second prior distribution. The process by which the parameter value search unit 193 updates the value of the hyperparameter β is the same as in step S106 of Figure 22. The process by which the sampling unit 191 updates the value of the hyperparameter for adjusting the uniformity of the second prior distribution is the same as in step S306 of Figure 41. After step S316, the process returns to step S314.

[0253] On the other hand, if the processing unit 190 determines in step S315 that the termination condition is met (step S315: YES), the parameter value search unit 193 determines the parameter value to be adopted (step S317). Step S317 is the same as step S307 in Figure 41. After step S317, the parameter value acquisition device 100 terminates the process shown in Figure 41.

[0254] Figure 42 shows an example where a prior distribution with hyperparameters for adjusting uniformity is used as the second prior distribution. When a prior distribution without hyperparameters for adjusting uniformity is used as the second prior distribution, it is not necessary to set the initial value of the hyperparameter for adjusting the uniformity of the second prior distribution in step S311, or to update the value of the hyperparameter for adjusting the uniformity of the second prior distribution in step S316.

[0255] As described above, the sampling unit 191 samples the parameter values ​​in the simulation based on the first prior distribution. The simulation value acquisition unit 192 acquires simulation values ​​for each obtained sampling value in a simulation in which that sampling value is set as a parameter in the simulation. Simulation values ​​are values ​​calculated in the simulation. The parameter value search unit 193 uses a combination of sampling values ​​based on a first prior distribution and simulation values ​​obtained in a simulation in which that sampling value is set as a parameter in the simulation to search for parameter values ​​that maximize the posterior kernel mean value under the target value of the simulation value when the parameter values ​​in the simulation are based on a second prior distribution.

[0256] The parameter value acquisition device 100 allows for the search for parameter values ​​while taking into account preferred values ​​when such preferred values ​​exist. In particular, when the parameter values ​​in the simulation are based on a second prior distribution, the parameter value acquisition device 100 searches for parameter values ​​based on the posterior kernel mean under the target value of the simulation. This allows for the search for parameter values ​​that are as close as possible to parameter values ​​with a relatively large probability density in the second prior distribution, and that bring the simulation value as close as possible to the target value.

[0257] Furthermore, the parameter value search unit 193 calculates the posterior kernel mean value under the target value of the simulation value when the parameter value in the simulation follows the second prior distribution, using a combination of sampling values ​​based on the first prior distribution and simulation values ​​obtained in a simulation in which those sampling values ​​are set as parameters in the simulation, and the ratio of the probability density in the first prior distribution to the probability density in the second prior distribution.

[0258] The parameter value acquisition device 100 makes it possible to calculate the posterior kernel mean without the need to perform sampling based on a second prior distribution. According to the parameter value acquisition device 100, sampling based on a second prior distribution is unnecessary, which is expected to reduce the computational load. While calculating equation (16) for each component i, where m is the number of samples in sampling based on the first prior distribution and l is the number of samples in sampling based on the second prior distribution, typically results in a computational load of O(ml), the parameter value acquisition device 100 reduces this to O(m). 2 The computational complexity can be kept to ). According to the parameter value acquisition device 100, a reduction in computational complexity can be expected when l is larger than m.

[0259] Furthermore, when sampling distributions that are difficult to sample, it is necessary to calculate the sampled values ​​using methods such as the Markov chain Monte Carlo method. In contrast, the parameter value acquisition device 100 is expected to have a low computational load because it does not require the calculation of sampled values.

[0260] Furthermore, the parameter value acquisition device 100 eliminates the need to perform sampling based on a second prior distribution, thus preventing sampling errors.

[0261] Furthermore, the parameter value search unit 193 searches for parameter values ​​in the simulation for each hyperparameter setting value used to adjust the uniformity of the second prior distribution, and selects one of the parameter values ​​obtained through the search.

[0262] Here, if the bias of the second prior distribution is too small (if the prior distribution is too close to a uniform distribution), the parameter values ​​obtained through exploration may not be close to the predetermined values. On the other hand, if the bias of the second prior distribution is too large, the simulation values ​​obtained when the parameter values ​​obtained through exploration are set as the parameters in the simulation may not be close to the target values.

[0263] In contrast, the parameter value acquisition device 100 is expected to select one of the parameter values ​​obtained in the simulation under various hyperparameter settings, thereby obtaining parameter values ​​that are as close as possible to a predetermined value and that are as close as possible to a target value.

[0264] <Fourth Embodiment> The parameter value acquisition device may also perform parameter value searches based on the posterior kernel mean, assuming that the parameters in the simulation follow a prior distribution of parameter values ​​based on the posterior kernel mean. This point will be explained in the fourth embodiment.

[0265] Figure 43 is a diagram showing an example of the configuration of a parameter value acquisition device according to the fourth embodiment. In the configuration shown in Figure 43, the parameter value acquisition device 200 comprises a communication unit 110, a display unit 120, an operation input unit 130, a storage unit 180, and a processing unit 290. The processing unit 290 comprises a sampling unit 291, a simulation value acquisition unit 192, a parameter value search unit 193, and a kernel average calculation unit 294.

[0266] Of the components shown in Figure 43, the communication unit 110, display unit 120, operation input unit 130, storage unit 180, simulation value acquisition unit 192, and parameter value search unit 193 are the same as in the parameter value acquisition device 100 according to the third embodiment. These components are denoted by the same reference numerals as in Figure 1, and detailed explanations are omitted here.

[0267] The parameter value acquisition device 200 differs from the parameter value acquisition device 100 according to the third embodiment in that it calculates the posterior kernel mean under target values ​​of the simulation values ​​and uses the prior distribution shown by the value of the posterior kernel mean as the first prior distribution to sample parameter values ​​in the simulation. In all other respects, the parameter value acquisition device 200 is the same as the parameter value acquisition device 100 according to the third embodiment.

[0268] The sampling unit 291 samples parameter values ​​in the simulation based on a predetermined prior distribution. This predetermined prior distribution is also referred to as the initial prior distribution. Furthermore, the sampling unit 291 uses the distribution shown by the posterior kernel mean calculated by the kernel mean calculation unit 294 as the first prior distribution, and samples the parameter values ​​in the simulation based on the first prior distribution. The sampling unit 291 is an example of a sampling means.

[0269] The kernel mean calculation unit 294 uses the sampled parameter values ​​in the simulation and the simulation values ​​for each sampled value to calculate the posterior kernel mean under the target value of the simulation values, assuming that the parameter values ​​in the simulation follow the prior distribution at the time of sampling of the sampled values.

[0270] Specifically, the kernel averaging unit 294 uses the sampled values ​​obtained by the sampling unit 291 and the simulation values ​​obtained by the simulation value acquisition unit 192 for each sampled value to calculate the posterior kernel average μ^ based on equation (1). θ|Y* Calculate. The kernel average calculation unit 294 is an example of a kernel average calculation means.

[0271] The processing performed by the combination of the sampling unit 291, the simulation value acquisition unit 192, and the kernel mean calculation unit 294 can be considered as updating the prior distribution. The prior distribution shown by the posterior kernel mean calculated by the kernel mean calculation unit 294 is also called the updated prior distribution. The sampling unit 291, the simulation value acquisition unit 192, and the kernel mean calculation unit 294 may be configured to repeatedly update the prior distribution.

[0272] Specifically, the sampling unit 291 samples the parameter values ​​in the simulation based on the initial prior distribution until it reaches a predetermined number of samples. The simulation value acquisition unit 192 acquires the simulation value for each sampled value based on the initial prior distribution. The kernel mean calculation unit 294 uses the sampled values ​​based on the initial prior distribution and the simulation value for each of those sampled values ​​to calculate the posterior kernel mean μ^ θ|Y* Calculate.

[0273] In the repeated updating of the prior distribution, the sampling unit 291 samples the parameter values ​​in the simulation until a preset number of samples is reached, based on the (latest) prior distribution shown by the posterior kernel mean calculated by the kernel mean calculation unit 294. The simulation value acquisition unit 192 acquires a simulation value for each sampling value based on the (latest) prior distribution shown by the posterior kernel mean. The kernel mean calculation unit 294 uses the sampling values ​​based on the (latest) prior distribution shown by the posterior kernel mean and the simulation values ​​for each of those sampling values ​​to calculate the posterior kernel mean μ^ θ|Y* Calculate. The sampling unit 291, the simulation value acquisition unit 192, and the kernel mean calculation unit 294 may repeat updating the prior distribution multiple times.

[0274] A known method called kernel herding can be used to sample from the (most recent) prior distribution represented by the posterior kernel mean. Kernel herding is a method for sampling from the distribution represented by the kernel mean. The given posterior kernel mean to be sampled is μ^ θ|Y* Let p(θ|Y) be the posterior distribution represented by this kernel mean. * When μ^ θ|Y* We select data points that approximate the posterior distribution p(θ|Y) as closely as possible. The resulting set of selected data points, i.e., the sample, is the posterior distribution p(θ|Y) * This can be considered a sample from ).

[0275] The specific procedure for kernel hardening is as follows: First, μ^ θ|Y* If we choose the point that best approximates it, it would be μ^ θ|Y* The point θ_1 is the point where the value is largest. Next, if we select the point that best approximates one data point θ_1 when it has been sampled, it will be the point where the value of equation (19) is largest.

[0276]

number

[0277] k θ This is the same as in case (1). In this way, we select the point with the largest value for a given kernel mean, and subtract the kernel mean expressed by the data points selected up to that point to use as the next given kernel mean. The first data point θ_1 in the above procedure is expressed as shown in equation (20).

[0278]

number

[0279] Let t be an integer such that t≧2. The t-th data point θ_t can be expressed as shown in equation (21).

number

[0280] Here argmax θ This is a function whose function value is the argument θ that maximizes the value of the expression shown to the right of argmax. That is, equation (20) is μ^ θ|Y* This represents selecting the point that maximizes the value of and designating it as data point θ_1. Similarly, equation (21) represents the kernel mean 1 / tΣ expressed in the t-th sampling of the data points, using the data points selected up to the t-1 sampling. i=2 t-1 k θ (·,θ_i) μ^ θ|Y* This indicates selecting the point that yields the largest value when subtracted from the given value, and designating this point as the data point θ_t. In this way, sampling based on the kernel mean becomes possible.

[0281] The prior distribution update by the sampling unit 291, the simulation value acquisition unit 192, and the kernel average calculation unit 294 is expected to increase the probability density of sampling points and their vicinity where simulation values ​​close to the target value can be obtained. By sampling parameter values ​​using the updated prior distribution, the sampling unit 291 makes it easier to sample parameter values ​​that bring the simulation value closer to the target value, and in this respect, the parameter value search unit 193 is expected to be able to search for parameter values ​​with high accuracy.

[0282] For example, consider a case where parameter θ1 can take real values ​​within the range (0, 10), but the range of values ​​for parameter θ1 that can obtain the desired simulation value is narrow, such as being within the range (4.99, 5.01). Furthermore, assume that the parameter value acquisition device 200 cannot know the value of parameter θ1 that can obtain the desired simulation value in advance (before searching for the parameter value).

[0283] In this case, if the sampling unit 291 samples the value of parameter θ1 based on a uniform distribution, it is conceivable that the number of sampling points where the value of parameter θ1 falls within or near the range of (4.99, 5.01) will be small. In this respect, it is conceivable that the accuracy of the parameter value search performed by the parameter value search unit 193 will be reduced.

[0284] In contrast, the sampling unit 291 samples the value of parameter θ1 based on the updated prior distribution, which is expected to result in a relatively large number of sampling points where the value of parameter θ1 falls within or near the range of (4.99, 5.01). In this respect, the parameter value search unit 193 is expected to be able to search for parameter values ​​with high accuracy.

[0285] The parameter value search unit 193 uses the sampled values ​​based on the updated prior distribution and the simulation values ​​for each sampled value to determine the posterior kernel mean m^ based on equation (12). θ|Y* By calculating and searching for parameter values, it is expected that we can obtain parameter values ​​that satisfy the desired conditions for both the simulation values ​​and the parameter values ​​themselves.

[0286] Figure 44 shows a first example of the processing procedure performed by the parameter value acquisition device 200. Figure 44 shows the parameter value search unit 193 performing the post-kernel average m^ θ|Y* In the calculation, the kernel function k in equation (7) Y An example is shown where the base kernel function is used.

[0287] Step S401 in Figure 44 is the same as step S301 in Figure 41. After step S401, the sampling unit 191 samples the parameter values ​​based on the initial prior distribution until it reaches a preset number of samples (step S402).

[0288] Next, the simulation value acquisition unit 192 performs a simulation for each of the obtained sample values ​​(step S403). When the process transitions from step S402 to S403, the simulation value acquisition unit 192 sets each sampling value obtained in step S402 based on the initial prior distribution as a parameter in the simulation and executes the simulation. In this way, the simulation value acquisition unit 192 acquires simulation values ​​for each sampling value based on the initial prior distribution.

[0289] On the other hand, when the process transitions from step S406 to S403, the simulation value acquisition unit 192 sets each sampling value based on the (latest) prior distribution shown by the posterior kernel mean obtained in step S405 as a parameter in the simulation and executes the simulation. As a result, the simulation value acquisition unit 192 acquires simulation values ​​for each sampling value based on the prior distribution shown by the posterior kernel mean.

[0290] Next, the kernel averaging unit 294 calculates the posterior kernel average (step S404). Specifically, the kernel averaging unit 294 uses the simulation values ​​acquired by the simulation value acquisition unit 192 in step S406 for each sampling value, and the original sampling values ​​from which those simulation values ​​were acquired, to calculate the posterior kernel average μ^ as a function with parameter θ as an argument. θ|Y* Calculate.

[0291] Post-hoc kernel mean μ^ θ|Y* This can be considered as the kernel mean representing the prior distribution. The sampling unit 291 uses the kernel harding described above to sample the parameter values ​​in the simulation based on the kernel mean of the prior distribution shown by the posterior kernel mean (step S405). For example, the sampling unit 291 uses the posterior kernel mean μ^ θ|Y* The parameter values ​​are sampled using the kernel mean, which represents the prior distribution of the parameter values.

[0292] Next, the processing unit 290 determines whether the termination condition for the loop from steps S403 to S406 is met (step S205). The termination condition here is not limited to any specific condition. For example, the termination condition here may be that the number of executions of the loop from step S403 to S406 reaches a predetermined threshold. Alternatively, the termination condition here may be that the sampling value obtained in step S405 is measured by the post-kernel mean μ^ θ|Y* The posterior kernel mean μ^ is calculated by inputting it into the program. θ|Y* The condition may also be that the average value of all sampled values ​​is greater than or equal to a predetermined threshold.

[0293] If the processing unit 290 determines in step S406 that the termination condition is not met (step S406: NO), the process returns to step S403. On the other hand, if the processing unit 290 determines in step S406 that the termination condition is met (step S406: YES), the simulation value acquisition unit 192 performs a simulation for each sampling value obtained in the latest execution in step S405 (step S407). In step S407, the simulation value acquisition unit 192 acquires simulation values ​​for each sampling value, similar to the processing in step S403 when the process transitions from step S406 to S403.

[0294] Next, the parameter value search unit 193 calculates the posterior kernel mean m^ based on the kernel Bayes rule. θ|Y* We search for parameter values ​​in the simulation that maximize the value of (step S408). In step S408, the parameter value search unit 193 uses the sampling values ​​obtained in the most recent execution of step S405 as sampling values ​​based on the first prior distribution, and in step S407, the simulation values ​​obtained for each of these sampling values ​​are used as simulation values ​​for each sampling value based on the first prior distribution, and the post-kernel mean m^ θ|Y* We calculate the parameters and explore their values ​​for the simulation.

[0295] Step S409 is the same as step S305 in Figure 41. If the processing unit 290 determines in step S409 that the termination condition is not met (step S409: NO), the process proceeds to step S410. Step S410 is the same as step S306 in Figure 41. After step S410, the process returns to step S408.

[0296] On the other hand, if the processing unit 290 determines in step S409 that the termination condition is met (step S409: YES), the parameter value search unit 193 determines the parameter value to be adopted (step S411). For example, the parameter value search unit 193 may select from the parameter values ​​obtained in step S408 for each hyperparameter setting value of the second prior distribution the parameter value that is closest to a predetermined value that the simulation value will achieve the target value. After step S411, the parameter value acquisition device 200 completes the process shown in Figure 44.

[0297] Figure 45 shows a second example of the processing procedure performed by the parameter value acquisition device 200. Figure 45 shows the parameter value search unit 193 performing the post-kernel average m^ θ|Y* In the calculation, the kernel function k in equation (7) Y An example of using an extended kernel function is shown. Step S421 in Figure 45 is the same as step S311 in Figure 42. Steps S422 to S427 are the same as steps S402 to S407 in Figure 44.

[0298] After step S427, the parameter value search unit 193 calculates the posterior kernel mean m^ based on the kernel Bayes rule. θ|Y* We search for parameter values ​​in the simulation that maximize the value of (step S428). In step S428, the parameter value search unit 193 uses the sampling values ​​obtained in the most recent execution of step S425 as sampling values ​​based on the first prior distribution, and in step S427, it uses the simulation values ​​obtained for each of these sampling values ​​as simulation values ​​for each sampling value based on the first prior distribution, and similar to the processing in step S314 in Figure 42, it calculates the posterior kernel average m^ θ|Y* We calculate the parameters and explore their values ​​for the simulation.

[0299] Step S429 is the same as step S315 in Figure 41. If the processing unit 290 determines in step S429 that the termination condition is not met (step S429: NO), the process proceeds to step S430. Step S430 is the same as step S316 in Figure 41. After step S430, the process returns to step S428.

[0300] On the other hand, if the processing unit 290 determines in step S429 that the termination condition is met (step S429: YES), the parameter value search unit 193 determines the parameter value to be adopted (step S431). For example, the parameter value search unit 193 may select the parameter value that is closest to a predetermined value that the simulation value will approach from the parameter values ​​obtained in step S428 for each combination of the set value of the hyperparameter β and the set value of the hyperparameter of the second prior distribution. After step S431, the parameter value acquisition device 200 completes the process shown in Figure 45.

[0301] As described above, the sampling unit 291 samples the parameter values ​​in the simulation based on a predetermined prior distribution, and further samples the parameter values ​​in the simulation using the prior distribution shown by the posterior kernel mean calculated by the kernel mean calculation unit 294 as the first prior distribution. The simulation value acquisition unit 192 acquires simulation values ​​for each obtained sampling value by setting that sampling value as a parameter in the simulation. Simulation values ​​are values ​​calculated in the simulation.

[0302] The kernel mean calculation unit 294 uses the sampled parameter values ​​in the simulation and the simulation values ​​for each sampled value to calculate the posterior kernel mean under the target value of the simulation values, assuming that the parameter values ​​in the simulation follow the prior distribution at the time of sampling of the sampled values. The parameter value search unit 193 uses a combination of sampling values ​​based on a first prior distribution and simulation values ​​obtained in a simulation in which those sampling values ​​are set as parameters in the simulation to search for parameter values ​​that maximize the posterior kernel mean under the target value of the simulation values, when the parameter values ​​in the simulation are based on a second prior distribution.

[0303] In the parameter value acquisition device 200, the prior distribution can be updated through processing by the sampling unit 291, the simulation value acquisition unit 192, and the kernel average calculation unit 294, and it is expected that the probability density of sampling points and their vicinity will be relatively large in order to obtain simulation values ​​close to the target value. By sampling parameter values ​​using the updated prior distribution, the sampling unit 291 makes it easier to sample parameter values ​​that will bring the simulation value closer to the target value, and in this respect, it is expected that the parameter value search unit 193 will be able to search for parameter values ​​with high accuracy.

[0304] <Fifth Embodiment> As described above in the first embodiment, the control target may be controlled using the parameter values ​​acquired by the parameter value acquisition device 100 or the parameter value acquisition device 200 through searching. In the fifth embodiment, the case in which the control target is controlled using the parameter values ​​acquired by the parameter value acquisition device 100 through searching will be described.

[0305] Figure 46 is a diagram showing an example of the configuration of a control device according to the fifth embodiment. In the configuration shown in Figure 46, the control device 300 comprises a communication unit 110, a display unit 120, an operation input unit 130, a storage unit 180, and a processing unit 390. The processing unit 390 comprises a sampling unit 191, a simulation value acquisition unit 192, a parameter value search unit 193, and a control execution unit 394.

[0306] Of the components in Figure 46, the communication unit 110, display unit 120, operation input unit 130, storage unit 180, sampling unit 191, simulation value acquisition unit 192, and parameter value search unit 193 are the same as in the case of the parameter value acquisition device 100. These components are denoted by the same reference numerals as in Figure 1, and detailed explanations are omitted here.

[0307] Each of these parts may function in the same way as in the parameter value acquisition device 100 according to the first embodiment. Alternatively, each of these parts may function in the same way as in the parameter value acquisition device 100 according to the second embodiment. Alternatively, each of these parts may function in the same way as in the parameter value acquisition device 100 according to the third embodiment. In the control device 300, the processing unit 390 includes a control execution unit 394 in addition to the parts provided by the processing unit 190 of the parameter value acquisition device 100. In all other respects, the control device 300 is the same as the parameter value acquisition device 100.

[0308] The control execution unit 394 uses the parameter values ​​obtained by the parameter value search unit 193 as control command values ​​to perform control on the controlled object. The control execution unit 394 is an example of a control execution means. According to the control device 300, it is possible to search for a control command value that is as close as possible to a desirable value among the control command values ​​that can achieve the target value of the indicator related to the controlled object.

[0309] <Sixth Embodiment> In the sixth embodiment, we will describe a case in which control is performed on the controlled object using the parameter values ​​acquired by the parameter value acquisition device 200 through searching.

[0310] Figure 47 is a diagram showing an example of the configuration of a control device according to the sixth embodiment. In the configuration shown in Figure 47, the control device 400 comprises a communication unit 110, a display unit 120, an operation input unit 130, a storage unit 180, and a processing unit 490. The processing unit 490 comprises a sampling unit 191, a simulation value acquisition unit 192, a parameter value search unit 193, a kernel average calculation unit 294, and a control execution unit 495.

[0311] Of the components in Figure 47, the communication unit 110, display unit 120, operation input unit 130, storage unit 180, sampling unit 191, simulation value acquisition unit 192, parameter value search unit 193, and kernel average calculation unit 294 are the same as in the case of the parameter value acquisition device 200. These components are denoted by the same reference numerals as in Figure 43, and detailed explanations are omitted here. In the control device 400, the processing unit 490 includes a control execution unit 495 in addition to the parts provided by the processing unit 290 of the parameter value acquisition device 200. In all other respects, the control device 400 is the same as the parameter value acquisition device 200.

[0312] The control execution unit 495 uses the parameter values ​​obtained by the parameter value search unit 193 as control command values ​​to perform control on the controlled object. The control execution unit 495 is an example of a control execution means. The control device 400 can search with relatively high accuracy for a control command value that can achieve the target value of an indicator related to the controlled object, and can also search for a control command value that is as close as possible to a desirable value among the control command values ​​that can achieve the target value of an indicator related to the controlled object.

[0313] <Seventh Embodiment> Figure 48 shows an example of the configuration of a parameter value acquisition device according to the seventh embodiment. In the configuration shown in Figure 48, the parameter value acquisition device 610 comprises a sampling unit 611, a simulation value acquisition unit 612, and a parameter value search unit 613.

[0314] In this configuration, the sampling unit 611 samples the parameter values ​​in the simulation. The simulation value acquisition unit 612 acquires simulation values ​​for each obtained sampling value by setting that sampling value as a parameter in the simulation. The simulation value is a value calculated in the simulation.

[0315] The parameter value search unit 613 uses the sampling values ​​of the parameters in the simulation, the simulation values ​​for each sampling value, and a kernel function that includes a subexpression such that the value of the posterior kernel mean increases as the parameter values ​​in the simulation are closer to a predetermined value. The unit then calculates the posterior kernel mean under target values ​​for the simulation values ​​and searches for parameter values ​​that maximize the posterior kernel mean. The sampling unit 611 is an example of a sampling means. The simulation value acquisition unit 612 is an example of a simulation value acquisition means. The parameter value search unit 613 is an example of a parameter value search means.

[0316] According to the parameter value acquisition device 610 of the seventh embodiment, if there is a preferred value for the parameter value, the parameter value search can be performed while taking the preferred value into consideration. In particular, according to the parameter value acquisition device 610 of the seventh embodiment, the parameter value search is performed using a kernel function that has a subexpression such that the value of the posterior kernel mean increases as the parameter value in the simulation approaches a predetermined value, thereby enabling the search for parameter values ​​that are as close as possible to the predetermined value and as close as possible to the target value in the simulation.

[0317] The sampling unit 611 can be implemented, for example, using the functions of the sampling unit 191 according to the first embodiment. The simulation value acquisition unit 612 can be implemented, for example, using the functions of the simulation value acquisition unit 192 according to the first embodiment. The parameter value search unit 613 can be implemented, for example, using the functions of the parameter value search unit 193 according to the first embodiment.

[0318] <Eighth Embodiment> The configuration of the parameter value acquisition device according to the eighth embodiment is the same as that of the parameter value acquisition device according to the seventh embodiment, and Figure 48 will also be used in the description of the eighth embodiment.

[0319] In the eighth embodiment, the sampling unit 611 samples the parameter values ​​in the simulation based on a prior distribution having a peak at a predetermined value. The simulation value acquisition unit 612 acquires simulation values ​​for each obtained sampling value by setting that sampling value as a parameter in the simulation. Simulation values ​​are values ​​calculated in the simulation.

[0320] The parameter value search unit 613 uses the sampled parameter values ​​in the simulation and the simulation values ​​for each sampled value to calculate the posterior kernel mean under the target value of the simulation value, and searches for parameter values ​​that maximize the posterior kernel mean. The sampling unit 611 is an example of a sampling means. The simulation value acquisition unit 612 is an example of a simulation value acquisition means. The parameter value search unit 613 is an example of a parameter value search means.

[0321] According to the parameter value acquisition device 610 of the eighth embodiment, if there is a preferred value for the parameter value, the search for the parameter value can be performed while taking the preferred value into consideration. In particular, according to the parameter value acquisition device 610 of the eighth embodiment, by sampling the parameter values ​​in the simulation based on a prior distribution having a peak at a predetermined value, it is possible to search for parameter values ​​such that the parameter value is as close as possible to the predetermined value and the simulation value is as close as possible to the target value.

[0322] The sampling unit 611 can be implemented, for example, using the functions of the sampling unit 191 according to the second embodiment. The simulation value acquisition unit 612 can be implemented, for example, using the functions of the simulation value acquisition unit 192 according to the second embodiment. The parameter value search unit 613 can be implemented, for example, using the functions of the parameter value search unit 193 according to the second embodiment.

[0323] <Ninth Embodiment> The configuration of the parameter value acquisition device according to the ninth embodiment is the same as that of the parameter value acquisition device according to the seventh embodiment, and Figure 48 will also be used in the description of the ninth embodiment.

[0324] In the ninth embodiment, the sampling unit 611 samples the parameter values ​​in the simulation based on a first prior distribution. The simulation value acquisition unit 612 acquires simulation values ​​for each obtained sampling value by setting that sampling value as a parameter in the simulation. Simulation values ​​are values ​​calculated in the simulation.

[0325] The parameter value search unit 613 uses the sampled parameter values ​​in the simulation and the simulation values ​​for each sampled value to calculate the posterior kernel mean under the target value of the simulation value, and searches for parameter values ​​that maximize the posterior kernel mean. The sampling unit 611 is an example of a sampling means. The simulation value acquisition unit 612 is an example of a simulation value acquisition means. The parameter value search unit 613 is an example of a parameter value search means.

[0326] According to the parameter value acquisition device 610 of the ninth embodiment, if there is a preferred value for the parameter value, the parameter value search can be performed while taking the preferred value into consideration. In particular, according to the parameter value acquisition device 610 of the ninth embodiment, when the parameter value in the simulation is based on a second prior distribution, the parameter value search can be performed based on the posterior kernel mean under the target value of the simulation value, so that the parameter value is as close as possible to a parameter value where the probability density is relatively large in the second prior distribution, and the simulation value is as close as possible to the target value.

[0327] The sampling unit 611 can be implemented, for example, using the functions of the sampling unit 191 according to the third embodiment. The simulation value acquisition unit 612 can be implemented, for example, using the functions of the simulation value acquisition unit 192 according to the third embodiment. The parameter value search unit 613 can be implemented, for example, using the functions of the parameter value search unit 193 according to the third embodiment.

[0328] <Tenth Embodiment> Figure 49 shows an example of the processing steps in the parameter value acquisition method according to the 10th embodiment. The parameter value acquisition method according to the 10th embodiment includes sampling (step S611), acquiring simulation values ​​(step S612), and searching for parameter values ​​(step S613).

[0329] In step S611, the computer samples parameter values ​​in the simulation. In acquiring simulation values ​​(step S612), the computer acquires simulation values, which are values ​​calculated in the simulation, by setting the obtained sampling values ​​as parameters in the simulation for each sampling value.

[0330] In the step of searching for parameter values ​​(step S613), the computer uses the sampling values ​​of the parameters in the simulation, the simulation values ​​for each sampling value, and a kernel function that has a subexpression that increases the value of the posterior kernel mean as the parameter values ​​in the simulation are closer to predetermined values, to calculate the posterior kernel mean under target values ​​of the simulation values, and searches for parameter values ​​that maximize the value of the posterior kernel mean.

[0331] According to the control method of the 10th embodiment, if there is a preferred value for the parameter value, the parameter value search can be performed while taking the preferred value into consideration. In particular, according to the control method of the 10th embodiment, the parameter value search is performed using a kernel function that has a subexpression such that the value of the posterior kernel mean increases as the parameter value in the simulation approaches a predetermined value, so that the parameter value can be searched for such that the parameter value is as close as possible to the predetermined value and the simulation value is as close as possible to the target value.

[0332] <Embodiment 11> Figure 49 will also be used in the explanation of the parameter value acquisition method according to the 11th embodiment. In the parameter value acquisition method according to the 11th embodiment, in step S611, the computer samples the parameter values ​​in the simulation based on a prior distribution having a peak at a predetermined value.

[0333] In acquiring simulation values ​​(step S612), the computer acquires simulation values, which are values ​​calculated in the simulation, by setting the obtained sampling values ​​as parameters in the simulation for each sampling value.

[0334] In the parameter value search (step S613), the computer uses the sampled parameter values ​​in the simulation and the simulation values ​​for each sampled value to calculate the posterior kernel mean under the target value of the simulation value, and searches for parameter values ​​that maximize the posterior kernel mean.

[0335] According to the control method of the 11th embodiment, if there is a preferred value for the parameter value, the parameter value search can be performed while taking the preferred value into consideration. In particular, according to the control method of the 11th embodiment, by sampling the parameter value in the simulation based on a prior distribution having a peak at a predetermined value, it is possible to search for parameter values ​​such that the parameter value is as close as possible to the predetermined value and the simulation value is as close as possible to the target value.

[0336] <Twelfth Embodiment> Figure 49 will also be used in the explanation of the parameter value acquisition method according to the 12th embodiment. In the parameter value acquisition method according to the 12th embodiment (step S611), the computer samples the parameter values ​​in the simulation based on a first prior distribution.

[0337] In acquiring simulation values ​​(step S612), the computer acquires simulation values, which are values ​​calculated in the simulation, by setting the obtained sampling values ​​as parameters in the simulation for each sampling value.

[0338] In the step of searching for parameter values ​​(step S613), the computer uses sampling values ​​based on a first prior distribution and simulation values ​​for each sampling value to calculate the posterior kernel mean under target values ​​of simulation values, assuming that the parameter values ​​in the simulation follow a second prior distribution different from the first prior distribution, and searches for parameter values ​​that maximize the posterior kernel mean.

[0339] According to the parameter value acquisition method of the 12th embodiment, if there is a preferred value for the parameter, the parameter value search can be performed while taking that preferred value into consideration. In particular, according to the parameter value acquisition method of the 12th embodiment, when the parameter value in the simulation is based on a second prior distribution, the parameter value is searched based on the posterior kernel mean under the target value of the simulation. This makes it possible to search for a parameter value that is as close as possible to a parameter value with a relatively large probability density in the second prior distribution, and that brings the simulation value as close as possible to the target value.

[0340] Figure 50 is a schematic block diagram showing the configuration of a computer according to at least one embodiment. In the configuration shown in Figure 50, the computer 700 comprises a CPU 710, a main memory 720, an auxiliary memory 730, an interface 740, and a non-volatile recording medium 750.

[0341] One or more of the above-mentioned parameter value acquisition devices 100, 200, 300, 400, and 610, or a part thereof, may be implemented in the computer 700. In that case, the operation of each of the above-mentioned processing units is stored in the auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, expands it in the main memory 720, and executes the above-mentioned processing according to the program. The CPU 710 also allocates memory areas in the main memory 720 corresponding to each of the above-mentioned storage units according to the program. Communication between each device and other devices is performed by the interface 740 having a communication function and performing communication according to the control of the CPU 710. The interface 740 also has a port for the non-volatile recording medium 750 and reads information from and writes information to the non-volatile recording medium 750.

[0342] When the parameter value acquisition device 100 is implemented in the computer 700, the operation of the processing unit 190 and each of its parts is stored in auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main memory 720, and executes the above processing according to the program.

[0343] Furthermore, the CPU 710 reserves a memory area for the memory unit 180 in the main memory 720 according to the program. Communication with other devices by the communication unit 110 is performed by the interface 740 having a communication function and operating under the control of the CPU 710. Display of images by the display unit 120 is performed by the interface 740 having a display device and displaying various images under the control of the CPU 710. Acceptance of user operations by the operation input unit 130 is performed by the interface 740 having an input device and accepting user operations under the control of the CPU 710.

[0344] When the parameter value acquisition device 200 is implemented in the computer 700, the operation of the processing unit 290 and each of its parts is stored in auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main memory 720, and executes the above processing according to the program.

[0345] Furthermore, the CPU 710 reserves a memory area for the memory unit 180 in the main memory 720 according to the program. Communication with other devices by the communication unit 110 is performed by the interface 740 having a communication function and operating under the control of the CPU 710. Display of images by the display unit 120 is performed by the interface 740 having a display device and displaying various images under the control of the CPU 710. Acceptance of user operations by the operation input unit 130 is performed by the interface 740 having an input device and accepting user operations under the control of the CPU 710.

[0346] When the control device 300 is implemented in the computer 700, the operation of the processing unit 390 and each of its parts is stored in auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main memory 720, and executes the above processing according to the program.

[0347] Furthermore, the CPU 710 reserves a memory area for the memory unit 180 in the main memory 720 according to the program. Communication with other devices by the communication unit 110 is performed by the interface 740 having a communication function and operating under the control of the CPU 710. Display of images by the display unit 120 is performed by the interface 740 having a display device and displaying various images under the control of the CPU 710. Acceptance of user operations by the operation input unit 130 is performed by the interface 740 having an input device and accepting user operations under the control of the CPU 710.

[0348] When the control device 400 is implemented in the computer 700, the operation of the processing unit 490 and each of its parts is stored in auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main memory 720, and executes the above processing according to the program.

[0349] Furthermore, the CPU 710 reserves a memory area for the memory unit 180 in the main memory 720 according to the program. Communication with other devices by the communication unit 110 is performed by the interface 740 having a communication function and operating under the control of the CPU 710. Display of images by the display unit 120 is performed by the interface 740 having a display device and displaying various images under the control of the CPU 710. Acceptance of user operations by the operation input unit 130 is performed by the interface 740 having an input device and accepting user operations under the control of the CPU 710.

[0350] When the parameter value acquisition device 610 is implemented in the computer 700, the operations of the sampling unit 611, the simulation value acquisition unit 612, and the parameter value search unit 613 are stored in the auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main memory 720, and executes the above processes according to the program.

[0351] Furthermore, the CPU 710 allocates memory in the main memory 720 for processing by the parameter value acquisition device 610 according to the program. Communication between the parameter value acquisition device 610 and other devices is performed by the interface 740 having a communication function and operating under the control of the CPU 710. Interaction between the parameter value acquisition device 610 and the user is performed by the interface 740 having input and output devices, presenting information to the user via the output device and accepting user operations via the input device under the control of the CPU 710.

[0352] One or more of the above-mentioned programs may be recorded on the non-volatile recording medium 750. In this case, the interface 740 may read the program from the non-volatile recording medium 750. The CPU 710 may then either directly execute the program read by the interface 740, or temporarily save it in the main memory 720 or auxiliary memory 730 before executing it.

[0353] Alternatively, a program for executing all or part of the processing performed by the parameter value acquisition device 100, parameter value acquisition device 200, control device 300, control device 400, and parameter value acquisition device 610 may be recorded on a computer-readable recording medium, and the program recorded on this recording medium may be loaded into a computer system and executed to perform the processing of each part. The term "computer system" here includes hardware such as the OS (Operating System) and peripheral devices. Furthermore, "computer-readable recording media" refers to portable media such as flexible disks, magneto-optical disks, ROMs (Read Only Memory), CD-ROMs (Compact Disc Read Only Memory), and storage devices such as hard disks built into computer systems. The above-mentioned program may be intended to implement only a part of the functions described above, and may also be able to implement the above-mentioned functions in combination with programs already recorded in the computer system.

[0354] While embodiments of this disclosure have been described in detail above with reference to the drawings, the specific configuration is not limited to these embodiments and may include designs and other elements that do not depart from the gist of this disclosure.

[0355] Some or all of the above embodiments may also be described as follows, but are not limited to the following:

[0356] (Note 1) A sampling means for sampling parameter values ​​in a simulation, For each obtained sampling value, a simulation value acquisition means acquires a simulation value, which is a value calculated in the simulation, by setting that sampling value as a parameter in the simulation. A parameter value search means calculates the posterior kernel mean under a target value of the simulation value, using the sampling value of the parameters in the simulation, the simulation value for each sampling value, and a kernel function having a subexpression such that the value of the posterior kernel mean increases as the parameter value in the simulation approaches a predetermined value, and searches for parameter values ​​that make the value of the posterior kernel mean larger. A parameter value acquisition device equipped with the following features.

[0357] (Note 2) The parameter value acquisition device described in Appendix 1, wherein the parameter value search means searches for parameter values ​​in the simulation for each hyperparameter setting value for adjusting the degree of influence of the subexpression, and selects one of the parameter values ​​obtained in the search.

[0358] (Note 3) The sampling means samples the parameter values ​​in the simulation based on a prior distribution having a peak at a predetermined value. A parameter value acquisition device as described in Appendix 1 or Appendix 2.

[0359] (Note 4) The sampling means samples the parameter values ​​in the simulation for each hyperparameter setting value for adjusting the uniformity of the prior distribution. The simulation value acquisition means acquires simulation values ​​for each sampling value for each hyperparameter setting value for adjusting the uniformity of the prior distribution. The parameter value search means searches for parameter values ​​in the simulation for each hyperparameter setting value for adjusting the uniformity of the prior distribution, and selects one of the parameter values ​​obtained in the search. The parameter value acquisition device described in Appendix 3.

[0360] (Note 5) The parameter value search means calculates the posterior kernel mean of the simulation values ​​under the target value when the parameter values ​​in the simulation follow a second prior distribution different from the first prior distribution which is the prior distribution at the time of sampling by the sampling means. A parameter value acquisition device as described in Appendix 1 or Appendix 2.

[0361] (Note 6) The parameter value search means calculates the posterior kernel mean value under the target value of the simulation value when the parameter value in the simulation follows the second prior distribution, using the sampling value based on the first prior distribution, the simulation value for each sampling value, and the ratio of the probability density in the first prior distribution to the probability density in the second prior distribution. Parameter value acquisition device as described in Appendix 5.

[0362] (Note 7) The parameter value search means searches for parameter values ​​in the simulation for each hyperparameter setting value for adjusting the uniformity of the second prior distribution, and selects one of the parameter values ​​obtained in the search. A parameter value acquisition device as described in Appendix 5 or Appendix 6.

[0363] (Note 8) The system further comprises a kernel mean calculation means that uses the sampled values ​​of the parameters in the simulation and the simulation values ​​for each sampled value to calculate the posterior kernel mean under the target value of the simulation values, assuming that the parameter values ​​in the simulation follow the prior distribution at the time of sampling of the sampled values. The sampling means samples the parameter values ​​in the simulation based on a predetermined prior distribution, and further samples the parameter values ​​in the simulation using the prior distribution shown by the posterior kernel mean calculated by the kernel mean calculation means as the first prior distribution. A parameter value acquisition device as described in any one of the appendices 5 to 7.

[0364] (Note 9) A sampling means for sampling parameter values ​​in a simulation based on a prior distribution having a peak at a predetermined value, For each obtained sampling value, a simulation value acquisition means acquires a simulation value, which is a value calculated in the simulation, by setting that sampling value as a parameter in the simulation. A parameter value search means calculates the posterior kernel mean under a target value of the simulation value using the sampled values ​​of the parameters in the simulation and the simulation value for each sampled value, and searches for parameter values ​​that make the posterior kernel mean larger. A parameter value acquisition device equipped with the following features.

[0365] (Note 10) The sampling means samples the parameter values ​​in the simulation for each hyperparameter setting value for adjusting the uniformity of the prior distribution. The simulation value acquisition means acquires simulation values ​​for each sampling value for each hyperparameter setting value for adjusting the uniformity of the prior distribution. The parameter value search means searches for parameter values ​​in the simulation for each hyperparameter setting value for adjusting the uniformity of the prior distribution, and selects one of the parameter values ​​obtained in the search. Parameter value acquisition device as described in Appendix 9.

[0366] (Note 11) A sampling means for sampling parameter values ​​in a simulation based on a first prior distribution, For each obtained sampling value, a simulation value acquisition means acquires a simulation value, which is a value calculated in the simulation, by setting that sampling value as a parameter in the simulation. A parameter value search means calculates the posterior kernel mean under target values ​​of the simulation values ​​when the parameter values ​​in the simulation follow a second prior distribution different from the first prior distribution, using the sampling values ​​based on the first prior distribution and the simulation values ​​for each sampling value, and searches for parameter values ​​that make the posterior kernel mean larger. A parameter value acquisition device equipped with the following features.

[0367] (Note 12) The parameter value search means calculates the posterior kernel mean value under the target value of the simulation value when the parameter value in the simulation follows the second prior distribution, using the sampling value based on the first prior distribution, the simulation value for each sampling value, and the ratio of the probability density in the first prior distribution to the probability density in the second prior distribution. Parameter value acquisition device as described in Appendix 11.

[0368] (Note 13) The parameter value search means searches for parameter values ​​in the simulation for each hyperparameter setting value for adjusting the uniformity of the second prior distribution, and selects one of the parameter values ​​obtained in the search. A parameter value acquisition device as described in Appendix 11 or Appendix 12.

[0369] (Note 14) The system further comprises a kernel mean calculation means that uses the sampled values ​​of the parameters in the simulation and the simulation values ​​for each sampled value to calculate the posterior kernel mean under the target value of the simulation values, assuming that the parameter values ​​in the simulation follow the prior distribution at the time of sampling of the sampled values. The sampling means samples the parameter values ​​in the simulation based on a predetermined prior distribution, and further samples the parameter values ​​in the simulation using the prior distribution shown by the posterior kernel mean calculated by the kernel mean calculation means as the first prior distribution. A parameter value acquisition device as described in any one of the appendices 11 to 13.

[0370] (Note 15) A sampling means for sampling parameter values ​​in a simulation, For each obtained sampling value, a simulation value acquisition means acquires a simulation value, which is a value calculated in the simulation, by setting that sampling value as a parameter in the simulation. A parameter value search means calculates the posterior kernel mean under a target value of the simulation value, using the sampling value of the parameters in the simulation, the simulation value for each sampling value, and a kernel function having a subexpression such that the value of the posterior kernel mean increases as the parameter value in the simulation approaches a predetermined value, and searches for parameter values ​​that make the value of the posterior kernel mean larger. A control execution means that performs control on the controlled object using the parameter values ​​obtained through the search, A control device equipped with the following features.

[0371] (Note 16) A sampling means for sampling parameter values ​​in a simulation based on a prior distribution having a peak at a predetermined value, For each obtained sampling value, a simulation value acquisition means acquires a simulation value, which is a value calculated in the simulation, by setting that sampling value as a parameter in the simulation. A parameter value search means calculates the posterior kernel mean under a target value of the simulation value using the sampled values ​​of the parameters in the simulation and the simulation value for each sampled value, and searches for parameter values ​​that make the posterior kernel mean larger. A control execution means that performs control on the controlled object using the parameter values ​​obtained through the search, A control device equipped with the following features.

[0372] (Note 17) A sampling means for sampling parameter values ​​in a simulation based on a first prior distribution, For each obtained sampling value, a simulation value acquisition means acquires a simulation value, which is a value calculated in the simulation, by setting that sampling value as a parameter in the simulation. A parameter value search means calculates the posterior kernel mean under target values ​​of the simulation values ​​when the parameter values ​​in the simulation follow a second prior distribution different from the first prior distribution, using the sampling values ​​based on the first prior distribution and the simulation values ​​for each sampling value, and searches for parameter values ​​that make the posterior kernel mean larger. A control execution means that performs control on the controlled object using the parameter values ​​obtained through the search, A control device equipped with the following features.

[0373] (Note 18) The system further comprises a kernel mean calculation means that uses the sampled values ​​of the parameters in the simulation and the simulation values ​​for each sampled value to calculate the posterior kernel mean under the target value of the simulation values, assuming that the parameter values ​​in the simulation follow the prior distribution at the time of sampling of the sampled values. The sampling means samples the parameter values ​​in the simulation based on a predetermined prior distribution, and further samples the parameter values ​​in the simulation using the prior distribution shown by the posterior kernel mean calculated by the kernel mean calculation means as the first prior distribution. The control device described in Appendix 17.

[0374] (Note 19) Computers Sampling parameter values ​​in the simulation, For each obtained sampling value, a simulation value is obtained in a simulation in which that sampling value is set as a parameter in the simulation, and the value calculated in the simulation is obtained. Using the sampled parameter values ​​in the simulation, the simulation values ​​for each sampled value, and a kernel function that includes a subexpression such that the value of the posterior kernel mean increases as the parameter values ​​in the simulation approach a predetermined value, the posterior kernel mean is calculated under the target values ​​of the simulation values, and parameter values ​​that result in a larger posterior kernel mean are searched for. A method for obtaining parameter values, including the following.

[0375] (Note 20) Computers The parameter values ​​in the simulation are sampled based on a prior distribution having a peak at a predetermined value. For each obtained sampling value, a simulation value is obtained in a simulation in which that sampling value is set as a parameter in the simulation, and the value calculated in the simulation is obtained. Using the sampled parameter values ​​in the simulation and the simulation values ​​for each sampled value, the posterior kernel mean is calculated under the target value of the simulation value, and parameter values ​​that result in a larger posterior kernel mean are searched for. A method for obtaining parameter values, including the following.

[0376] (Note 21) Computers The parameter values ​​in the simulation are sampled based on the first prior distribution. For each obtained sampling value, a simulation value is obtained in a simulation in which that sampling value is set as a parameter in the simulation, and the value calculated in the simulation is obtained. Using the sampling values ​​based on the first prior distribution and the simulation values ​​for each sampling value, the posterior kernel mean is calculated under the target value of the simulation value when the parameter values ​​in the simulation follow a second prior distribution different from the first prior distribution, and parameter values ​​are searched for that result in a larger posterior kernel mean. A method for obtaining parameter values, including the following.

[0377] (Note 22) Computers Sampling parameter values ​​in the simulation, For each obtained sampling value, a simulation value is obtained in a simulation in which that sampling value is set as a parameter in the simulation, and the value calculated in the simulation is obtained. Using the sampled values ​​of the parameters in the simulation, the simulation values ​​for each sampled value, and a kernel function that includes a subexpression such that the value of the posterior kernel mean increases as the parameter values ​​in the simulation approach predetermined values, the posterior kernel mean is calculated under target values ​​of the simulation values, and parameter values ​​that result in a larger posterior kernel mean are searched for. The parameter values ​​obtained through exploration are used to perform control on the controlled object. A control method that includes the following.

[0378] (Note 23) Computers The parameter values ​​in the simulation are sampled based on a prior distribution having a peak at a predetermined value. For each obtained sampling value, a simulation value is obtained in a simulation in which that sampling value is set as a parameter in the simulation, and the value calculated in the simulation is obtained. Using the sampled values ​​of the parameters in the simulation and the simulation values ​​for each sampled value, the posterior kernel mean is calculated under the target value of the simulation value, and parameter values ​​are searched for that make the posterior kernel mean larger. The parameter values ​​obtained through exploration are used to perform control on the controlled object. A control method that includes the following.

[0379] (Note 24) Computers The parameter values ​​in the simulation are sampled based on the first prior distribution. For each obtained sampling value, a simulation value is obtained in a simulation in which that sampling value is set as a parameter in the simulation, and the value calculated in the simulation is obtained. Using the sampling values ​​based on the first prior distribution and the simulation values ​​for each sampling value, the posterior kernel mean under the target value of the simulation value is calculated when the parameter values ​​in the simulation follow a second prior distribution different from the first prior distribution, and parameter values ​​that make the posterior kernel mean larger are searched for. The parameter values ​​obtained through exploration are used to perform control on the controlled object. A control method that includes the following.

[0380] (Note 25) On the computer, Sampling parameter values ​​in a simulation, For each obtained sampling value, a simulation value is obtained, which is the value calculated in the simulation, by setting that sampling value as a parameter in the simulation. Using the sampled parameter values ​​in the simulation, the simulation values ​​for each sampled value, and a kernel function that includes a subexpression such that the value of the posterior kernel mean increases as the parameter values ​​in the simulation approach predetermined values, the posterior kernel mean is calculated under target values ​​for the simulation values, and parameter values ​​that result in a larger posterior kernel mean are searched for. A program to execute.

[0381] (Note 26) On the computer, The parameter values ​​in the simulation are sampled based on a prior distribution having a peak at a predetermined value, For each obtained sampling value, a simulation value is obtained, which is the value calculated in the simulation, by setting that sampling value as a parameter in the simulation. Using the sampled values ​​of the parameters in the simulation and the simulation values ​​for each sampled value, the posterior kernel mean is calculated under the target value of the simulation value, and parameter values ​​are searched for that result in a larger posterior kernel mean. A program to execute.

[0382] (Note 27) On the computer, The parameter values ​​in the simulation are sampled based on a first prior distribution, For each obtained sampling value, a simulation value is obtained, which is the value calculated in the simulation, by setting that sampling value as a parameter in the simulation. Using the sampling values ​​based on the first prior distribution and the simulation values ​​for each sampling value, the posterior kernel mean is calculated under the target value of the simulation value when the parameter values ​​in the simulation follow a second prior distribution different from the first prior distribution, and parameter values ​​are searched for that result in a larger posterior kernel mean. A program to execute.

[0383] (Note 28) On the computer, Sampling parameter values ​​in a simulation, For each obtained sampling value, a simulation value is obtained, which is the value calculated in the simulation, by setting that sampling value as a parameter in the simulation. Using the sampled parameter values ​​in the simulation, the simulation values ​​for each sampled value, and a kernel function that includes a subexpression such that the value of the posterior kernel mean increases as the parameter values ​​in the simulation approach predetermined values, the posterior kernel mean is calculated under target values ​​for the simulation values, and parameter values ​​that result in a larger posterior kernel mean are searched for. Using the parameter values ​​obtained through exploration, control is performed on the controlled object. A program to execute.

[0384] (Note 29) On the computer, The parameter values ​​in the simulation are sampled based on a prior distribution having a peak at a predetermined value, For each obtained sampling value, a simulation value is obtained, which is the value calculated in the simulation, by setting that sampling value as a parameter in the simulation. Using the sampled values ​​of the parameters in the simulation and the simulation values ​​for each sampled value, the posterior kernel mean is calculated under the target value of the simulation value, and parameter values ​​are searched for that result in a larger posterior kernel mean. Using the parameter values ​​obtained through exploration, control is performed on the controlled object. A program to execute.

[0385] (Note 30) On the computer, The parameter values ​​in the simulation are sampled based on a first prior distribution. For each obtained sampling value, a simulation value is obtained, which is the value calculated in the simulation, by setting that sampling value as a parameter in the simulation. Using the sampling values ​​based on the first prior distribution and the simulation values ​​for each sampling value, the posterior kernel mean is calculated under the target value of the simulation value when the parameter values ​​in the simulation follow a second prior distribution different from the first prior distribution, and parameter values ​​are searched for that result in a larger posterior kernel mean. Using the parameter values ​​obtained through exploration, control is performed on the controlled object. A program to execute.

[0386] This application claims priority based on Japanese Patent Application No. 2023-051306, filed on 28 March 2023, and incorporates all of its disclosures herein. [Industrial applicability]

[0387] This disclosure may be applied to a parameter value acquisition device, a parameter value acquisition method, and a recording medium. [Explanation of symbols]

[0388] 100, 200, 610 Parameter Value Acquisition Device 110 Communications Department 120 Display section 130 Operation Input Section 180 Storage section 190, 290, 390, 490 Processing Unit 191, 291 Sampling section 192 Simulation Value Acquisition Unit 193 Parameter Value Search Unit 294 Kernel average calculation unit 394, 495 Control execution unit 300, 400 control devices

Claims

1. A sampling means for sampling parameter values ​​in a simulation, For each obtained sampling value, a simulation value acquisition means acquires a simulation value, which is a value calculated in the simulation, by setting that sampling value as a parameter in the simulation. A parameter value search means calculates the posterior kernel mean under a target value of the simulation value, using the sampling value of the parameters in the simulation, the simulation value for each sampling value, and a kernel function having a subexpression such that the value of the posterior kernel mean increases as the parameter value in the simulation approaches a predetermined value, and searches for parameter values ​​that make the value of the posterior kernel mean larger. A parameter value acquisition device equipped with the following features.

2. The parameter value acquisition device according to claim 1, wherein the parameter value search means searches for parameter values ​​in the simulation for each hyperparameter setting value for adjusting the degree of influence of the subexpression, and selects one of the parameter values ​​obtained in the search.

3. The sampling means samples the parameter values ​​in the simulation based on a prior distribution having a peak at a predetermined value. The parameter value acquisition device according to claim 1.

4. The sampling means samples the parameter values ​​in the simulation for each hyperparameter setting value for adjusting the uniformity of the prior distribution. The simulation value acquisition means acquires simulation values ​​for each sampling value for each hyperparameter setting value for adjusting the uniformity of the prior distribution. The parameter value search means searches for parameter values ​​in the simulation for each hyperparameter setting value for adjusting the uniformity of the prior distribution, and selects one of the parameter values ​​obtained in the search. The parameter value acquisition device according to claim 3.

5. The parameter value search means calculates the posterior kernel mean of the simulation values ​​under the target value when the parameter values ​​in the simulation follow a second prior distribution different from the first prior distribution which is the prior distribution at the time of sampling by the sampling means. The parameter value acquisition device according to claim 1.

6. The parameter value search means calculates the posterior kernel mean value under the target value of the simulation value when the parameter value in the simulation follows the second prior distribution, using the sampling value based on the first prior distribution, the simulation value for each sampling value, and the ratio of the probability density in the first prior distribution to the probability density in the second prior distribution. The parameter value acquisition device according to claim 5.

7. The parameter value search means searches for parameter values ​​in the simulation for each hyperparameter setting value for adjusting the uniformity of the second prior distribution, and selects one of the parameter values ​​obtained in the search. A parameter value acquisition device according to claim 5 or claim 6.

8. A sampling means for sampling parameter values ​​in a simulation, For each obtained sampling value, a simulation value acquisition means acquires a simulation value, which is a value calculated in the simulation, by setting that sampling value as a parameter in the simulation. A parameter value search means calculates the posterior kernel mean under a target value of the simulation value, using the sampling value of the parameters in the simulation, the simulation value for each sampling value, and a kernel function having a subexpression such that the value of the posterior kernel mean increases as the parameter value in the simulation approaches a predetermined value, and searches for parameter values ​​that make the value of the posterior kernel mean larger. A control execution means that performs control on the controlled object using the parameter values ​​obtained through the search, A control device equipped with the following features.

9. Computers Sampling parameter values ​​in the simulation, For each obtained sampling value, a simulation value is obtained in a simulation in which that sampling value is set as a parameter in the simulation, and the value calculated in the simulation is obtained. Using the sampled parameter values ​​in the simulation, the simulation values ​​for each sampled value, and a kernel function that includes a subexpression such that the value of the posterior kernel mean increases as the parameter values ​​in the simulation approach a predetermined value, the posterior kernel mean is calculated under the target values ​​of the simulation values, and parameter values ​​that result in a larger posterior kernel mean are searched for. A method for obtaining parameter values, including the following.

10. On the computer, Sampling parameter values ​​in a simulation, For each obtained sampling value, a simulation value is obtained, which is the value calculated in the simulation, by setting that sampling value as a parameter in the simulation. Using the sampled parameter values ​​in the simulation, the simulation values ​​for each sampled value, and a kernel function that includes a subexpression such that the value of the posterior kernel mean increases as the parameter values ​​in the simulation approach predetermined values, the posterior kernel mean is calculated under target values ​​for the simulation values, and parameter values ​​that result in a larger posterior kernel mean are searched for. A program to execute.

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