Information processing device, information processing method, and program

Abstract

To further improve the accuracy of generating a physical phenomenon model.SOLUTION: An information processing device includes a storage unit. a nonlinear function generation unit, a regression equation generation unit, an estimation unit, a calculation unit, a correction unit, and an output control unit. The storage unit stores time-series data including at least one of dependent and independent variables. The nonlinear function generation unit generates a plurality of nonlinear functions by a plurality of methods based on at least one of the dependent and independent variables. The regression equation generation unit mixes the plurality of nonlinear functions to generate a linear regression equation used as a basis function. The estimation unit estimates a coefficient of the linear regression equation. The calculation unit calculates, for a nonlinear function generated by one of the plurality of methods, a product of the coefficient and a maximum value of the basis function corresponding to the coefficient as a degree of influence. The correction unit corrects the coefficient based on the degree of influence. An output control unit outputs the linear regression equation represented by the corrected coefficient.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] An embodiment of the present invention relates to an information processing device, an information processing method, and a program. [Background technology]

[0002] Techniques for modeling physical phenomena have been known for some time. For example, there is a technique for acquiring a mathematical model that describes a physical phenomenon from time-series data by applying a function identification problem, which is a type of machine learning. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2022-167097 [Patent Document 2] Japanese Patent Publication No. 2022-167093 [Patent Document 3] Japanese Patent Publication No. 2022-75213 [Non-patent literature]

[0004] [Non-Patent Document 1] SLBrunton, JLProctor, JNKutz, “Discovering governing equations from data by sparse identification of nonlinear dynamical systems”, Proc. Natl. Acad. Sci., 113 (2016), pp. 3932-3937 [Non-patent document 2] Suzuki, T., Kano, A., Hirohata, K. (2021).Deriving Thermal Model From Data by Sparse Identification Based on Physical Laws, Proceedings of the ASME 2021 International Mechanical Engineering Congress and Exposition,IMECE2021,November 1-5, 2021,IMECE2021-70639 Summary of the Invention [Problem to be solved by the invention]

[0005] However, with conventional techniques, it has been difficult to further improve the accuracy of generating models of physical phenomena. [Means for solving the problem]

[0006] According to an embodiment, an information processing device includes a storage unit, a nonlinear function generation unit, a regression equation generation unit, an estimation unit, a calculation unit, a correction unit, and an output control unit. The storage unit stores time-series data including at least one of a dependent variable and an independent variable. The nonlinear function generation unit generates a plurality of nonlinear functions using a plurality of methods based on at least one of the dependent variable and the independent variable. The regression equation generation unit combines the plurality of nonlinear functions to generate a linear regression equation using the combined nonlinear functions as a basis function. The estimation unit estimates coefficients of the linear regression equation. The calculation unit calculates, as an influence, the product of the coefficient and the maximum value of the basis function corresponding to the coefficient for the nonlinear function generated by any one of the plurality of methods. The correction unit corrects the coefficient based on the influence. The output control unit outputs the linear regression equation represented by the corrected coefficients. [Brief explanation of the drawings]

[0007] [Figure 1] FIG. 10 is a diagram showing an example of a temperature prediction formula generated from time-series data. [Figure 2]FIG. 10 is a diagram showing an example of the left side of a linear regression equation. [Figure 3] FIG. 10 is a diagram showing an example of a candidate component of one basis function on the right-hand side of a linear regression equation. [Figure 4] FIG. 2 is a diagram showing an example of the functional configuration of the information processing apparatus according to the embodiment. [Figure 5] 1 is a flowchart illustrating an example of a model generation method according to an embodiment. [Figure 6] FIG. 10 is a diagram showing Example 1 of the effect of the embodiment. [Figure 7] FIG. 10 is a diagram showing Example 2 of the effect of the embodiment. [Figure 8] FIG. 1 is a diagram illustrating an example of a hardware configuration of an information processing apparatus according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0008] Hereinafter, embodiments of an information processing device, an information processing method, and a program will be described in detail with reference to the accompanying drawings.

[0009] There is a method for easily simulating phenomena by dividing a complex product or system into multiple elements and modeling the relationships between each element. This method applies equivalent circuits, which are used to solve electrical circuits, to heat and fluid problems. For example, in the case of heat, this is called the thermal network method, and the conservation of energy at each node is expressed by the following equation (1).

[0010]

number

[0011] Here, C is the heat capacity, R is the thermal resistance, Q is the amount of heat generated, and N is the number of nodes. By transforming the above formula (1), the differential equation shown in the following formula (2) is obtained.

[0012]

number

[0013] When constructing the above formula (2) deductively, the actual phenomenon or structure is simplified from a physical perspective, and thermal resistance, heat capacity, etc. are set. Thermal resistance depends on the shape and physical properties as well as state quantities such as its own temperature and speed. In many cases, there is no theoretical formula, and in those cases, it is necessary to select a formula that is appropriate for the subject from a huge number of empirical formula candidates.

[0014] Sparse Identification of Nonlinear Dynamics (SINDy), which is an extension of the function identification problem, assumes that the true model can be expressed as a linear combination of nonlinear functions, and the time derivative of the variable vector X is given in the form of the following equation (3).

[0015]

number

[0016] Here, X is an m×n matrix, where m is the number of time samples and n is the dimension of the variable X. θ(X) is called the library and consists of candidate nonlinear functions. Ξ is a sparse vector of coefficients. Coefficients (Ξ components) corresponding to nonlinear functions not selected as basis functions are represented as 0.

[0017] If the library is constructed in a form proportional to any of the terms in equation (2) above, then by applying sparse identification of nonlinear dynamics (SINDy), a temperature prediction formula (equation (2) above) that differs for each object can be generated from time series data using equation (4) below.

[0018]

number

[0019] FIG. 1 is a diagram showing an example of a temperature prediction formula generated from time series data. For example, B is data based on data set B obtained from detailed simulation B. Time series data T B The rows of correspond to the time samples. BThe columns correspond to the nodes for which the temperature is to be predicted.

[0020] The left side of the temperature prediction equation indicates the time derivative for each node of the temperature prediction target. Each component of θ(X) is represented by a number m that identifies the time sample, a number n that identifies the node, a number l that identifies the data set, and a number p that identifies the basis function candidate. The column vectors included in θ(X) are the basis function candidates. Ξ is a vector that determines the coefficients of the basis functions.

[0021] However, the desired equation cannot be obtained from the above equation (2), which is generated from the time derivative of X calculated from time series data and θ(X) by the sequential thresholded least-squares algorithm (STLS), which is a sparse estimation method proposed in Non-Patent Document 1. The following are some of the reasons why the desired equation cannot be obtained.

[0022] Cause 1: When time series data is converted into the form of an ordinary differential equation, each piece of data is treated independently, which causes errors to accumulate when making long-term forecasts. Cause 2: The effects of multicollinearity make it impossible to perform efficient sparse estimation, resulting in unstable equations. Cause 3: In basis function selection, it is difficult to optimize thresholds that differ for each equation (e.g., equations for each temperature node).

[0023] Cause 1 can be solved by Patent Document 1, and causes 2 and 3 can be solved by Patent Document 2. However, a highly accurate formula cannot be generated by simply combining Patent Documents 1 and 2. Here, we consider time-series data of basis functions when data from different preprocessing methods are mixed (Patent Document 1).

[0024] FIG. 2 shows an example of the left side of the linear regression equation. FIG. 3 shows an example of a candidate component of one basis function on the right side of the linear regression equation. FIG. 2 shows example data for 14 detailed analysis cases for the left side of the linear regression equation when training data was created based on Patent Document 1. FIG. 3 shows example data for 14 detailed analysis cases for one candidate basis function on the right side of the linear regression equation when training data was created based on Patent Document 1. The detailed analysis is a transient analysis until the state quantity (temperature) stabilizes, and outputs the state quantity for each time. This analysis covers 14 cases with different boundary conditions, initial conditions, etc. The horizontal axis of FIGS. 2 and 3 indicates a number identifying the data (a combination of the detailed analysis number and time). The data is classified by detailed analysis case, and the time is arranged in ascending order. The vertical axis shows the time-differential component of temperature (short-term component) and the fixed-interval fluctuation component of temperature (long-term component) calculated based on Patent Document 1. The detailed analysis case switches where the value on the vertical axis changes stepwise.

[0025] When different types of data are normalized as shown in the following formula (5) and then mixed (Patent Document 1), the difference becomes large. This shows that it is difficult to solve the above-mentioned cause 3 by applying hypothesis testing.

[0026]

number

[0027] Here, i is the number of data, α is a weight, and α > 1. According to the above formula (5), the sum of the time derivative values ​​of the variables included in the training data becomes larger than the sum of the differences indicating the fluctuations from the initial values ​​of the variables.

[0028] Consider the following t-test. If the null hypothesis is a coefficient of 0, the t-value in multiple regression analysis is expressed by the following formula (6). A value of approximately 2 (95% confidence interval) or higher is often considered significant.

[0029]

number

[0030] where V e is the error variance SS e / (np), where p is the number of basis functions. np is the degree of freedom for error. SS e is the residual sum of squares expressed by the following formula (7).

[0031]

number

[0032] SS ii is the matrix SS in the following equation (8) ij The diagonal elements of the inverse matrix of the matrix SS ij =Σx ik x jk is a p-th order square matrix of sums of squared deviations and sums of products of deviations.

[0033]

number

[0034] Since the error variance is common to all basis functions, a method can be considered in which a value proportional to the standard error in the following equation (9) is used to obtain the following equation (10), thereby selecting basis functions for each equation using a common tol.

[0035]

number

[0036]

number

[0037] However, because the range of values ​​of the basis functions for short-term components (e.g., the time derivative of temperature) and long-term components (e.g., the amount of change from the initial temperature) is significantly different, the matrix of sums of squared deviations and sums of products of deviations becomes almost meaningless. Therefore, selecting basis function candidates by hypothesis testing is not effective.

[0038] Therefore, in Patent Document 2, the maximum value in the time series data is considered to be the representative value of the basis function, and specifically, the influence is calculated as the magnitude of the term = coefficient ξ kj × Maximum representative value of basis function i |θ ik The basis functions are selected by correcting the coefficients of the basis functions whose influence is equal to or less than the threshold value expressed on the right side of the following equation (11) to 0.

[0039]

number

[0040] However, when data from different preprocessing methods are mixed, the value of the long-term component may be selected as the representative value of the basis function candidate (Equation (12) below). This can be understood from the fact that the value of the long-term component is several orders of magnitude larger than the value of the short-term component in Figure 3.

[0041]

number

[0042] The influence (≒ square sum error) on the coefficient estimation of the left-hand side (in this embodiment, the time derivative of temperature) is dominated by the short-term component due to the influence of normalization. Therefore, selecting the normalized (value-corrected) long-term component value as the representative value of the basis function candidate is not suitable (physically incorrect) as the "representative value of the magnitude of the term" that represents the influence on the left-hand side (in this embodiment, the time derivative of temperature).

[0043] An example of the operation of the information processing apparatus according to the embodiment, which can further improve the accuracy of generating a model of a physical phenomenon, will be described below in detail.

[0044] [Example of functional configuration] 4 is a diagram illustrating an example of the functional configuration of the information processing device 1 according to the embodiment. The information processing device 1 according to the embodiment includes a storage unit 11, a nonlinear function generation unit 12, a regression equation generation unit 13, an estimation unit 14, a calculation unit 15, a correction unit 16, an output control unit 17, and a display control unit 18.

[0045] The memory unit 11 stores time-series data including at least one of a dependent variable and an independent variable. A dependent variable (objective variable) is a variable that is determined depending on an independent variable (explanatory variable). An independent variable is a variable that indicates the cause of a change in the dependent variable. An example of a dependent variable is the temperature of an electronic component or a heat sink. An example of an independent variable is the wind speed or pressure difference that indicates the wind strength of a fan that cools the electronic component, the current flowing through the electronic component, and the voltage input to the electronic component.

[0046] In the information processing device 1 according to the embodiment, the value of a dependent variable is expressed in a unit that is unified for each physical quantity indicated by the dependent variable. For example, if the physical quantity is weight, the dependent variable expressed in kg and the dependent variable expressed in g are not mixed, but are unified to kg or g. Similarly, the value of an independent variable is expressed in a unit that is unified for each physical quantity indicated by the independent variable.

[0047] It should be noted that multiple types of time series data may be stored in the storage unit 11. The multiple types of time series data may differ in at least one of the initial condition and the boundary condition.

[0048] The nonlinear function generator 12 generates a plurality of nonlinear functions by a plurality of methods based on at least one of the dependent variable and the independent variable. For example, the nonlinear function generator 12 generates a plurality of nonlinear functions by a plurality of methods based on the temperature T i and the temperature T at position j j The nonlinear function is generated based on the above. The plurality of methods also includes, for example, a method using time differentiation that indicates the short-term component and a method using difference that indicates the fluctuation of the long-term component.

[0049] The regression equation generating unit 13 mixes the plurality of nonlinear functions generated by the nonlinear function generating unit 12 and generates a linear regression equation using the functions as basis functions.

[0050] The estimation unit 14 estimates the coefficients of the linear regression equation generated by the regression equation generation unit 13. For example, the estimation unit 14 estimates the coefficients of the linear regression equation by machine learning using values ​​indicating short-term components (e.g., time differential values) and differences indicating long-term components (e.g., differences indicating fluctuations from the initial values ​​of variables) as learning data. At this time, the sum of the time differential values ​​included in the learning data is made larger than the sum of the differences indicating the long-term components (the above-mentioned equation (5)).

[0051] The calculation unit 15 calculates the influence based on the magnitude of the term (coefficient × basis function) for the nonlinear function generated by any one of the above-mentioned methods. i -T j ) changes over time. Therefore, the maximum value in the time series data is considered to be the representative value of the basis function, and the influence is calculated as the magnitude of the term = coefficient ξ kj × Maximum representative value of basis function i |θ ik That is, the calculation unit 15 calculates the product of the coefficient estimated by the estimation unit 14 and the maximum value of the basis function corresponding to the coefficient as the influence.

[0052] The modification unit 16 modifies the coefficients based on the influence calculated by the calculation unit 15. For example, the modification unit 16 modifies the coefficients of basis functions whose influence is equal to or less than a threshold to 0. At this time, when learning is performed using data in which data that has been pre-processed in different ways is mixed (when multiple nonlinear functions are generated by multiple methods), the modification unit 16 targets one (either) of the data before mixing as the representative value of the basis function candidate in the magnitude of the term (Equation (13) below).

[0053]

number

[0054] where S Shortindicates the region of the short-term component. In the example of thermal fluid analysis of the embodiment, it is desirable that the representative values ​​of the basis function candidates are targeted at the data of the short-term component (see FIGS. 2 and 3). Here, the threshold value in the case of simultaneous equations is, for example, the following equation (14) or (15).

[0055]

number

[0056]

number

[0057] Here, tol n is a hyperparameter, and tol n <1. m indicates time, and n indicates the space (temperature node) number (equation number). p is a number that identifies the basis function. In Patent Document 2, the same hyperparameter tol was used at all temperature nodes.

[0058] When a predetermined convergence condition is satisfied, the output control unit 17 outputs the linear regression equation expressed by the corrected coefficients. The predetermined convergence condition is, for example, the number of iterations of the machine learning process.

[0059] The display control unit 18 displays the display information on the display device. For example, the display control unit 18 displays the linear regression formula output by the output control unit 17. Furthermore, for example, the display control unit 18 displays basis function candidates on the display device and accepts designation of a basis function (for example, a column vector included in the library θ(X) of the above-mentioned formula (3)) used to generate the linear regression formula from the basis function candidates.

[0060] [Example of how to generate a model] 5 is a flowchart showing an example of a method for generating a model according to an embodiment. First, the information processing device 1 initializes data (for example, hyperparameters) used in machine learning of a model (step S1).

[0061] Next, the estimation unit 14 estimates the coefficients of the linear regression equation generated by the regression equation generation unit 13 by the non-negative least squares method using the following equation (16) (step S2).

[0062]

number

[0063] Here, we will explain the reason why the non-negative least squares method is used in step S2. In the conventional recursive threshold least squares method, coefficient estimation is performed using the least squares method. However, when the correlation between basis functions (≒ variables) is very high and the number of training data is small, coefficient estimation does not work well and the estimated values ​​of the coefficients may become very large.

[0064] Next, the calculation unit 15 calculates the above-mentioned influence (magnitude of the term), and the modification unit 16 deletes the basis functions whose influence is equal to or less than the threshold by modifying the coefficient of the basis function whose influence is equal to or less than the threshold to 0 (step S3). Specifically, the calculation unit 15 first determines the target for which the above-mentioned influence (magnitude of the term) is to be calculated. In the embodiment, the data of the short-term component (see FIGS. 2 and 3) is selected as the processing target. Then, the modification unit 16 modifies the coefficient of the basis function whose influence is equal to or less than the threshold according to the above-mentioned formula (14) or (15) to 0 for the data of the short-term component.

[0065] Next, the modification unit 16 determines whether or not the results of the coefficient estimation and modification process satisfy the convergence condition (step S4).

[0066] The convergence condition is, for example, the number of times the coefficient estimation and correction processes are executed. In this case, the estimation unit 14 updates the linear regression equation using the coefficients corrected by the correction unit 16, and then re-estimates the coefficients of the updated linear regression equation. Next, the calculation unit 15 updates the influence by the product of the updated coefficients of the linear regression equation and the maximum value of the basis function corresponding to the coefficients of the updated linear regression equation. Then, the correction unit 16 re-corrects the coefficients of the updated linear regression equation based on the updated influence. The information processing device 1 repeats the estimation of the coefficients, the calculation of the influence, and the correction of the coefficients a predetermined number of times.

[0067] If the convergence condition is not satisfied (step S4, No), the process returns to step S2. If the convergence condition is satisfied (step S4, Yes), the output control unit 17 calculates a performance evaluation index of the model (step S5). Next, the output control unit 17 determines whether the trained model satisfies the convergence condition (step S6). The convergence condition is, for example, the number of times the model learning process is executed. Another example of the convergence condition is that the performance evaluation index calculated by the process of step S5 is greater than a predetermined evaluation threshold. If the convergence condition is not satisfied (step S6, No), the hyperparameters are updated (step S7), and the process returns to step S2.

[0068] If the convergence condition is satisfied (Yes at step S6), the output control unit 17 outputs the model (step S8).

[0069] [Effect description] Next, the accuracy of the model generated by the information processing device 1 of the embodiment will be described.

[0070] FIG. 6 is a diagram showing Example 1 of the effect of the embodiment. The example in FIG. 6 shows a case where the method is applied to a forced-air-cooled power electronics device in which contact thermal resistance varies. The vertical axis shows the average prediction error for seven types of evaluation data simulated by changing the values ​​of boundary conditions, heat generation conditions, etc. Data 1 on the horizontal axis shows the case where the learning method of Patent Document 2 was used. Data 2 on the horizontal axis shows the case where the learning method of the embodiment was used. As shown in FIG. 6, the learning method of the embodiment can reduce the average prediction error more than conventional methods.

[0071] FIG. 7 is a diagram showing Example 2 of the effect of the embodiment. The example in FIG. 7 shows an example when applied to natural air-cooled power electronics equipment. The vertical axis shows the average prediction error for seven types of evaluation data simulated by changing the numerical values ​​of boundary conditions, heat generation conditions, etc. Data 1 on the horizontal axis shows the case where the learning method of Patent Document 2 was used. Data 2 on the horizontal axis shows the case where the learning method of the embodiment was used. As shown in FIG. 7, according to the learning method of the embodiment, the average prediction error can be reduced more than conventional methods.

[0072] As described above, in the information processing device 1 according to the embodiment, the storage unit 11 stores time-series data including at least one of a dependent variable and an independent variable. The nonlinear function generation unit 12 generates multiple nonlinear functions using multiple methods based on at least one of the dependent variable and the independent variable. The regression formula generation unit 13 combines multiple nonlinear functions to generate a linear regression formula using the combined nonlinear functions as a basis function. The estimation unit 14 estimates coefficients of the linear regression formula. The calculation unit 15 calculates, as an influence, the product of the coefficient and the maximum value of the basis function corresponding to the coefficient for a nonlinear function generated using one of the multiple methods. The correction unit 16 corrects the coefficient based on the influence. The output control unit 17 then outputs the linear regression formula represented by the corrected coefficients.

[0073] As a result, the information processing device 1 according to the embodiment can further improve the accuracy of generating a model of a physical phenomenon.

[0074] In the above embodiment, the information processing device 1 generates a linear regression equation for a thermal model, but it may also generate a linear regression equation for a model of other physical phenomena (e.g., electrical resistance, physical deformation amount).

[0075] Finally, an example of the hardware configuration of the information processing device 1 according to the embodiment will be described.

[0076] [Example of hardware configuration] FIG. 8 is a diagram illustrating an example of a hardware configuration of the information processing apparatus 1 according to the embodiment.

[0077] The information processing device 1 of the embodiment includes a control device 201, a main memory device 202, an auxiliary memory device 203, a display device 204, an input device 205, and a communication device 206. The control device 201, the main memory device 202, the auxiliary memory device 203, the display device 204, the input device 205, and the communication device 206 are connected via a bus 210.

[0078] The control device 201 executes a program read from the auxiliary storage device 203 to the main storage device 202. The main storage device 202 is a memory such as a ROM and a RAM. The auxiliary storage device 203 is a hard disk drive (HDD), a memory card, or the like.

[0079] The display device 204 displays display information. The display device 204 is, for example, a liquid crystal display. The input device 205 is an interface for operating the information processing device 1. The input device 205 is, for example, a keyboard or a mouse. When the information processing device 1 is a smart device such as a smartphone or a tablet terminal, the display device 204 and the input device 205 are, for example, a touch panel.

[0080] The communication device 206 is an interface for communicating with other devices.

[0081] The program executed by the information processing device 1 of the embodiment is provided as a computer program product, recorded in an installable or executable format on a computer-readable storage medium such as a CD-ROM, memory card, CD-R, or DVD.

[0082] The program executed by the information processing device 1 of the embodiment may be stored on a computer connected to a network such as the Internet and provided by being downloaded via the network. Alternatively, the program executed by the information processing device 1 of the embodiment may be provided via a network such as the Internet without being downloaded.

[0083] The program for the information processing device 1 of the embodiment may be provided in a state where it is pre-installed in a ROM or the like.

[0084] The program executed by the information processing device 1 of the embodiment has a modular configuration including functional blocks that can be realized by the program among the functional blocks described above (FIG. 4). As actual hardware, the control device 201 reads and executes the program from a storage medium, and the functional blocks are loaded onto the main storage device 202. In other words, the functional blocks are generated on the main storage device 202.

[0085] Note that some or all of the above-described functional blocks may be realized by hardware such as an integrated circuit (IC) instead of by software.

[0086] Furthermore, when each function is realized using a plurality of processors, each processor may realize one of the functions, or may realize two or more of the functions.

[0087] The information processing device 1 of the embodiment may operate in any manner, for example, as a cloud system on a network.

[0088] Although several embodiments of the present invention have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be embodied in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included within the scope and spirit of the invention, and are also included in the scope of the invention and its equivalents as defined in the claims. [Explanation of symbols]

[0089] 1. Information processing equipment 11 Nonlinear function generator 13 Regression equation generation section 14 Estimation part 15 Calculation section 16 Correction section 17 Output control section 18 Display control unit 201 Control device 202 Main storage 203 Auxiliary storage device 204 Display device 205 Input Device 206 Communication Equipment

Claims

1. a storage unit that stores time series data including at least one of a dependent variable and an independent variable; a nonlinear function generator that generates a plurality of nonlinear functions by a plurality of methods based on at least one of the dependent variable and the independent variable; a regression equation generation unit that mixes the plurality of nonlinear functions and generates a linear regression equation using the mixed nonlinear functions as a basis function; an estimation unit that estimates coefficients of the linear regression equation; a calculation unit that calculates, as an influence, a product of the coefficient and a maximum value of a basis function corresponding to the coefficient, for a nonlinear function generated by any one of the plurality of methods; a correction unit that corrects the coefficient based on the degree of influence; an output control unit that outputs the linear regression equation expressed by the corrected coefficients; The plurality of methods include a method using time differentiation that indicates a short-term component and a method using a difference that indicates a fluctuation in a long-term component. Information processing device.

2. the estimation unit updates the linear regression equation using the coefficients corrected by the correction unit, and then re-estimates the coefficients of the updated linear regression equation; the calculation unit updates the influence degree by a product of the updated coefficient of the linear regression equation and a maximum value of a basis function corresponding to the updated coefficient of the linear regression equation; the correction unit corrects the coefficients of the updated linear regression equation again based on the updated influence degree; repeating the estimation of the coefficient, the calculation of the influence degree, and the correction of the coefficient a predetermined number of times; The information processing device according to claim 1 .

3. The estimation unit estimates coefficients of a linear regression equation by machine learning using the time derivative and the difference as learning data; the sum of the time derivatives included in the learning data is greater than the sum of the differences; 3. The information processing device according to claim 1 or 2.

4. the calculation unit calculates, as an influence, a product of the coefficient and a maximum value of a basis function corresponding to the coefficient, for a nonlinear function generated by a method using time differentiation that indicates the short-term component. The information processing device according to claim 3 .

5. the modification unit modifies the coefficients of the basis functions whose influence levels are equal to or less than a threshold value to 0.

3. The information processing device according to claim 1 or 2.

6. the estimation unit estimates the coefficients by a non-negative least squares method; 3. The information processing device according to claim 1 or 2.

7. The value of the dependent variable is expressed in a unit that is standardized for each physical quantity indicated by the dependent variable, The value of the independent variable is expressed in a unit that is standardized for each physical quantity represented by the independent variable.

3. The information processing device according to claim 1 or 2.

8. a display control unit that displays the basis function candidates on a display device and receives, from the basis function candidates, a designation of a basis function to be used in generating the linear regression equation; The information processing device according to claim 1 or 2, further comprising:

9. A method of calculating a time series of a variable, the time series including at least one of a dependent variable and an independent variable, by an information processing device; generating a plurality of nonlinear functions by a plurality of methods based on at least one of the dependent variable and the independent variable by the information processing device; a step in which the information processing device mixes the plurality of nonlinear functions and generates a linear regression equation using the nonlinear functions as a basis function; a step of estimating coefficients of the linear regression equation by the information processing device; a step in which the information processing device calculates, as an influence, a product of the coefficient and a maximum value of a basis function corresponding to the coefficient, for a nonlinear function generated by any one of the plurality of methods; a step of correcting the coefficient based on the influence degree by the information processing device; a step of outputting the linear regression equation expressed by the corrected coefficients by the information processing device; The plurality of methods include a method using time differentiation that indicates a short-term component and a method using a difference that indicates a fluctuation in a long-term component. Information processing methods.

10. Computer, a storage unit that stores time series data including at least one of a dependent variable and an independent variable; a nonlinear function generator that generates a plurality of nonlinear functions by a plurality of methods based on at least one of the dependent variable and the independent variable; a regression equation generation unit that mixes the plurality of nonlinear functions and generates a linear regression equation using the mixed nonlinear functions as a basis function; an estimation unit that estimates coefficients of the linear regression equation; a calculation unit that calculates, as an influence, a product of the coefficient and a maximum value of a basis function corresponding to the coefficient, for a nonlinear function generated by any one of the plurality of methods; a correction unit that corrects the coefficient based on the degree of influence; functioning as an output control unit that outputs the linear regression equation expressed by the modified coefficients; The plurality of methods include a method using time differentiation that indicates a short-term component and a method using a difference that indicates a fluctuation in a long-term component. program.

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