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 time derivative value calculation unit, a fluctuation difference calculation unit, an estimation unit, a calculation unit, a correction unit, and an output control unit. The storage unit stores time-series data including one or more variables. The time derivative value calculation unit calculates a time derivative value of each of the variables. The fluctuation difference calculation unit calculates a difference indicating fluctuation of a long-term component of the variable based on a designated time sample interval. The estimation unit estimates a coefficient of a linear regression equation by machine learning using the time derivative value and the difference as learning data. The output control unit outputs the linear regression equation.SELECTED DRAWING: Figure 6

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 [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] The information processing apparatus according to the embodiment ,time Interval differential value calculation unit, fluctuation difference calculation unit, estimation unit, calculation unit, and correction unit and Prepare. Included in time series data The time differential value of a variable is calculated. The fluctuation difference calculation unit calculates a difference indicating a fluctuation of a long-term component of the variable based on a specified time sample interval. The estimation unit estimates coefficients of a linear regression equation by machine learning using the time differential value and the difference as learning data. 。 [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 for explaining an example in which errors accumulate during long-term future prediction. [Figure 3] FIG. 10 is a diagram for explaining an example in which errors accumulate during long-term future prediction. [Figure 4A] An example of CFD results for natural air-cooled power electronics equipment. [Figure 4B]A graph in which the vertical axis of the graph in Figure 4A is expressed as a logarithmic scale. [Figure 5] FIG. 10 is a diagram showing an example of physically plausible coefficient estimation. [Figure 6] FIG. 2 is a diagram showing an example of the functional configuration of the information processing apparatus according to the embodiment. [Figure 7] FIG. 10 is a diagram showing an example of the variance-covariance matrix of the error of Equation (11) and the variance-covariance matrix of the error of Equation (15). [Figure 8] This diagram explains an example of mixing two long-term components. [Figure 9] A diagram showing an example of how to mix two long-term components. [Figure 10] A diagram showing an example of the variance-covariance matrix of the error when two long-term components are mixed. [Figure 11] Figure showing Example 1 of the effect of mixing two long-term components. [Figure 12] Figure showing Example 2 of the effect of mixing two long-term components. [Figure 13] 1 is a flowchart illustrating an example of a model generation method according to an embodiment. [Figure 14] 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 simple method for simulating phenomena by dividing complex products and systems 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]

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[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]

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[0013] When constructing the above formula (2) deductively, the actual phenomenon and structure are 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 the temperature and speed of the material itself. 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] In sparse identification of nonlinear dynamics (SINDy), which is an extension of the function identification problem, the time derivative of the variable vector X is given in the form of the following equation (3) under the assumption that the true model can be expressed as a linear combination of nonlinear functions.

[0015]

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[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]

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[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. B The 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 reason for this is that when the time series data is converted into the form of the ordinary differential equation of the above equation (4), each piece of data is treated independently, and this will be explained in more detail using FIG.

[0022] 2 and 3 are diagrams for explaining examples of error accumulation during long-term future prediction. FIG. 2 shows an example of calculating a least-squares solution using learning data created by forward differencing using discrete value data. In this case, it is difficult to consider whether the error is positive or negative, and there is a possibility that the positive and negative of the error will be biased. Therefore, when performing long-term future prediction using the generated prediction formula, errors accumulate, for example, as shown in FIG. 3 (problem 1).

[0023] For example, if A: Error 1 = 50, Error 2 = 15, and B: Error 1 = 60, Error 2 = -20, then the sum of squared errors for each are 2725 for A and 4000 for B, giving A a better estimation result than B. However, the cumulative error is 65 for A and 40 for B, giving B the advantage. One possible method is to devise an error function, but this would require taking the order of the data into account, resulting in very complicated processing and posing issues such as increased learning time.

[0024] Furthermore, in engineering problems, it is easy to encounter problems where the influence of some data is very strong. This problem will be explained using Figures 4A and 4B.

[0025] Figure 4A shows an example of the results of computational fluid dynamics (CFD) for a power electronics device that is naturally cooled. Figure 4B shows the same graph as Figure 4A, but with a logarithmic vertical axis. Generally, the larger the temperature change, the smaller the time sample Δt is taken. As shown in Figures 4A and 4B, the shorter the Δt, the more drastic the temperature change, and therefore the greater the influence of some data (Problem 2). Appropriate weighting of the data is required, but this problem is difficult to solve by data normalization (including logarithmic conversion) or by devising error functions (relative error, etc.).

[0026] To solve problem 2, it is necessary to consider the correlation between error terms, which requires the introduction of a concept such as generalized least squares (GLS).GLS assumes a variance-covariance matrix Ω (equation (5) below) for the error terms.

[0027]

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[0028] y=Xβ+ε,ε~N(0,σ 2 Ω), the estimated quantity is given by the following equation (6).

[0029]

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[0030]

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[0031] The state update amount is the product of the time derivative of T1 and Δt, and Δt is not constant, so considering the error using the following equation (8) is insufficient when considering the accumulation of errors in long-term future forecasts.

[0032]

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[0033] Therefore, Patent Document 1 proposes a method for performing learning that takes into account the arrangement of data by devising a method for preprocessing data.

[0034] Consider discretizing the right-hand side of the following equation (9) for the temperature node 1 using the following equation (10) with first-order accuracy forward difference.

[0035]

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[0036]

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[0037] The above formula (10) can be transformed into the following formula (11).

[0038]

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[0039] Patent Document 1 focuses on the fact that the coefficient vector Ξ (Ξ1 in equation (11) is the component of temperature node 1 of Ξ) in the above equations (4) and (11) is common, and proposes a machine learning method using data in which the above equations (4) and (11) are mixed and calculated from time-series data.

[0040] Considering the least squares solution of the above equation (11), the following equation (12) can be derived. It can be seen that the following equation (12) has an interaction term.

[0041]

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[0042] The interaction term in equation (12) above indicates that the variance-covariance matrix of the error term can be incorporated by ingenious preprocessing, as in the generalized least squares method. Furthermore, this method can select the error terms that affect the interaction to a certain extent (such as not crossing data sets). Therefore, physically valid coefficient estimates can be achieved.

[0043] Figure 5 shows an example of physically reasonable coefficient estimation. The short-term component improves the accuracy of one-move-ahead forecasts based on the idea of ​​least squares. The long-term component improves the accuracy of long-term-ahead forecasts based on the idea of ​​generalized least squares.

[0044] Efficient learning is possible by normalizing the short-term component of the above formula (4) and the long-term component of the above formula (11) as shown in formula (13) below and then mixing them for learning. Here, α1 is a vector indicating a different value for each node n. For example, the first component of α1 indicates the value of node 1, and the second component of α1 indicates the value of node 2.

[0045]

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[0046] However, Patent Document 2, which uses the above-mentioned equation (12), has the following two problems 3 and 4.

[0047] Task 3 is (M l -i+1). This weighting gives a larger weight to the error in the earlier time period (earlier sample time). l -i+1) is added. Here, M l indicates the number of data in dataset l.

[0048] Problem 4 is that the errors between sample times that are far apart are also multiplied.

[0049] For example, the variance-covariance matrix Ω -1 is the following equation (14), and the fact that the larger the row and column numbers (the later the sample time), the smaller the weighting corresponds to issue 3. Also, the fact that elements with a large difference between row and column numbers n are also weighted (≠0) corresponds to issue 4.

[0050]

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[0051] 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.

[0052] [Example of functional configuration] 6 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 time derivative calculation unit 12, a fluctuation difference calculation unit 13, a nonlinear function generation unit 14, a regression equation generation unit 15, an estimation unit 16, an output control unit 17, and a display control unit 18.

[0053] The memory unit 11 stores time-series data including at least one of a dependent variable and an independent variable. The dependent variable (objective variable) is a variable that is determined depending on the independent variable (explanatory variable). The independent variable is a variable that indicates the cause of a change in the dependent variable. The dependent variable is, for example, the temperature of an electronic component and a heat sink. The independent variable is, for example, the wind speed indicating 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.

[0054] 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.

[0055] 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.

[0056] The time differential value calculation unit 12 calculates the time differential value of a variable (dependent variable or independent variable) included in the time series data. The time differential value of the variable included in the time series data is used as learning data expressed in the form of the above formula (4).

[0057] The fluctuation difference calculation unit 13 calculates a difference indicating the fluctuation of the long-term component of the variable included in the time series data. Specifically, the fluctuation difference calculation unit 13 discretizes the left side of the above formula (4) with first-order accuracy, for example, by forward differentiation, to calculate the above formula (10).

[0058] Here, the fluctuation difference calculation unit 13 calculates the difference indicating the fluctuation of the long-term component by transforming the above formula (10) into the following formula (15): In Patent Document 1, the above formula (10) is transformed into the above formula (11) to calculate the difference indicating the fluctuation from the initial value of the variable.

[0059]

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[0060] Considering the least squares solution of the above equation (15), the following equation (16) can be derived. It can be seen that equation (16) also has an interaction term.

[0061]

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[0062] It can be seen that the earlier the time period (the earlier the sample time), the less weight is given to the error (solution of problem 3). Furthermore, t in the above equations (15) and (16) m This allows us to control the range of influence of the interaction term (solution of problem 4).

[0063] FIG. 7 is a diagram showing an example of the variance-covariance matrix of the error in equation (11) and the variance-covariance matrix of the error in equation (15).

[0064] However, the method using equation (15) alone does not include t m The smaller the value, the more the following two points become true, creating a contradictory issue. The proportion (number) of interaction terms is reduced (1:(t m -1) / 2). -The error between sample points close in time can be evaluated.

[0065] t m =M l in the case of, t m = 2; main effect terms: 2, interaction terms: tm C2=t m (t m -1) / 2=1 t m = 4; main effect terms: 4, interaction terms: 6 t m =10; main effect term: 10, interaction term: 45 t m =20; main effect term: 20, interaction term: 190 t m=50; Main effect term: 50, Interaction term: 1125

[0066] Therefore, the information processing device 1 of the embodiment performs learning by mixing two or more types of differences indicating the fluctuations of the long-term component in the above-mentioned equation (15). That is, the fluctuation difference calculation unit 13 calculates the differences indicating the fluctuations of the long-term component based on two or more types of time sample intervals.

[0067] 8 and 9 are diagrams for explaining an example in which two long-term components are mixed. When two long-term components are mixed, the variance-covariance matrix Ω -1 In this case, the weighting of errors between sample points close in time is increased. Also, the number of interaction terms increases, improving the ratio between the number of main effect terms and the number of interaction terms.

[0068] The two long-term components are normalized and combined using coefficients α1 and α2, as shown in Fig. 9. The coefficients α1 and α2 ensure that the sum of the time derivatives included in the training data is greater than the sum of the differences that indicate the fluctuations of the long-term components.

[0069] Figure 10 shows the error variance-covariance matrix Ω when two long-term components are mixed. -1 1 is a diagram illustrating an example of the variance-covariance matrix Ω. -1 The regions N1 to N3 in the column are data corresponding to each condition of the detailed numerical analysis or experiment. As shown in Figure 10, the variance-covariance matrix Ω of the error -1 has non-zero values ​​near the diagonal elements.

[0070] Figure 11 shows Example 1 of the effect of mixing two long-term components. Figure 11 shows an example of application to forced-air-cooled power electronics equipment with variable contact thermal resistance. The vertical axis shows the average prediction error for seven types of evaluation data simulated by changing boundary conditions, heat generation conditions, etc.

[0071] Data 1 on the horizontal axis represents the case where training data without long-term components was used. Data 2 on the horizontal axis represents the case where the training method of Patent Document 1 (a method using differences indicating fluctuations from the initial values ​​of variables) was used. Data 3 on the horizontal axis represents the case where training data including one long-term component was used. Data 4 on the horizontal axis represents the case where training data including two long-term components was used.

[0072] As shown in FIG. 11, the average prediction error can be minimized most effectively when training data containing two long-term components is used.

[0073] Figure 12 shows Example 2 of the effect of mixing two long-term components. Figure 12 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 boundary conditions, heat generation conditions, etc.

[0074] Data 1 on the horizontal axis represents the case where the learning method of Patent Document 1 (a method using differences indicating the fluctuations from the initial values ​​of variables) was used. Data 2 on the horizontal axis represents the case where learning data including one long-term component was used. Data 3 on the horizontal axis represents the case where learning data including two long-term components was used.

[0075] As shown in FIG. 12, the average prediction error can be minimized most effectively when training data containing two long-term components is used.

[0076] 6, the nonlinear function generator 14 generates a nonlinear function based on at least one of the dependent variable and the independent variable. For example, the nonlinear function generator 14 generates a nonlinear function based on the temperature T i and the temperature T at position j j and generate a nonlinear function based on the

[0077] The regression equation generating unit 15 generates a linear regression equation using the nonlinear function generated by the nonlinear function generating unit 14 as a basis function.

[0078] The estimation unit 16 estimates the coefficients of the linear regression equation generated by the regression equation generation unit 15 by machine learning using, as learning data, time differential values ​​and differences indicating fluctuations of two or more types of long-term components. Specifically, the estimation unit 16 estimates the coefficients of the linear regression equation by machine learning using both the learning data expressed in the form of the above formula (4) and the learning data in which two or more types of differences indicating fluctuations of the long-term components of the above formula (15) are mixed.

[0079] If only the short-term component is taken into account, the long-term forecast accuracy of the model will deteriorate. Conversely, if only the long-term component is taken into account, the short-term forecast accuracy of the model will deteriorate, and the short-term forecast will not match, so the long-term forecast accuracy of the model will also deteriorate.

[0080] The least squares method used in machine learning is a weighted sum method that ignores weight adjustment, so preprocessing the training data, as shown in Figure 9 above, is important in order to further improve the accuracy of the model.

[0081] Furthermore, in the example embodiment, the candidate basis functions include, for example, addition and subtraction between variables, and the results of these calculations have physical meanings, so normalizing the variables (dependent variables and independent variables) can cause problems. Therefore, the estimation unit 16 estimates the coefficients of the linear regression equation using a machine learning method that does not require normalization of variables. Note that a method of normalizing the basis functions themselves is also possible. In this case, it is necessary to take into account that the training data is a mixture of short-term and long-term components with large variances.

[0082] 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.

[0083] The display control unit 18 displays display information on the display device. For example, the display control unit 18 displays the linear regression equation output by the output control unit 17. For another example, the display control unit 18 displays basis function candidates on the display device and accepts, from the basis function candidates, a designation of a basis function (for example, a column vector included in the library θ(X) of the above-mentioned equation (3)) used to generate the linear regression equation. For another example, the display control unit 18 displays, on the display device, display information that accepts a designation of a time sample interval used to calculate a difference indicating a fluctuation in the long-term component of a variable.

[0084] [Example of how to generate a model] 13 is a flowchart showing an example of a model generation method according to an embodiment. First, the time differential value calculation unit 12 calculates time differential values ​​of variables (dependent variables or independent variables) included in the time-series data and candidate basis functions (step S1). Next, the fluctuation difference calculation unit 13 calculates two or more types of differences indicating fluctuations in the long-term components (step S2).

[0085] Next, the information processing device 1 initializes data (for example, hyperparameters) used when machine learning the model (step S3).

[0086] Next, the estimation unit 16 estimates the coefficients of the linear regression equation generated by the regression equation generation unit 15 by machine learning using the time differential values ​​calculated in step S1 and the two or more types of differences calculated in step S2 as learning data (step S4). Specifically, the time differential values ​​of the variables included in the time series data are used as learning data in the form of the above-mentioned equation (4), and the differences indicating fluctuations in the long-term components of the variables included in the time series data are used as learning data in the form of the above-mentioned Figure 9.

[0087] The learning data used in the estimation process of step S4 may be, for example, a portion of data selected randomly from the entire learning data, or may be, for example, selected in order from unused data included in the learning data.

[0088] Next, the estimation unit 16 determines whether the result of the coefficient estimation process satisfies a convergence condition (step S5). The convergence condition is, for example, the number of times the coefficient estimation process is executed. Note that the process of step S5 is not essential, and the process of step S5 may be skipped.

[0089] If the convergence condition is not satisfied (step S5, No), the process returns to step S4. If the convergence condition is satisfied (step S5, Yes), the output control unit 17 calculates a performance evaluation index of the model (step S6). For example, the performance evaluation index is an index for selecting a model such as an information criterion. In general, the performance evaluation index is an index that balances the degree of fit to the model with the simplicity of the model.

[0090] Next, the output control unit 17 determines whether the trained model satisfies a convergence condition (step S7). The convergence condition is, for example, the number of times the model training process (steps S4 to S6) has been executed. Another example of the convergence condition is that the performance evaluation index calculated by the process of step S6 is greater than a predetermined evaluation threshold. If the convergence condition is not satisfied (step S7, No), the hyperparameters are updated (step S8), and the process returns to step S4.

[0091] If the convergence condition is satisfied (Yes at step S7), the output control unit 17 outputs the model (step S9).

[0092] As described above, in the information processing device 1 of the embodiment, the storage unit 11 stores time-series data including one or more variables. The time derivative calculation unit 12 calculates a time derivative of the variable. The fluctuation difference calculation unit 13 calculates a difference indicating a fluctuation of a long-term component of the variable based on a specified time sample interval. The estimation unit 16 estimates coefficients of a linear regression equation by machine learning using the time derivative and the difference as learning data. Then, the output control unit 17 outputs the linear regression equation.

[0093] 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.

[0094] 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).

[0095] Finally, an example of the hardware configuration of the information processing device 1 according to the embodiment will be described.

[0096] [Example of hardware configuration] FIG. 14 is a diagram illustrating an example of a hardware configuration of the information processing apparatus 1 according to the embodiment.

[0097] 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.

[0098] 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.

[0099] 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.

[0100] The communication device 206 is an interface for communicating with other devices.

[0101] 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.

[0102] 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.

[0103] 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.

[0104] The program executed by the information processing device 1 of the embodiment has a modular configuration including functional blocks that can also be realized by the program, among the functional blocks described above (FIG. 3). 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.

[0105] 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.

[0106] 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.

[0107] The information processing device 1 of the embodiment may operate in any manner, for example, as a cloud system on a network.

[0108] 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]

[0109] 1. Information processing equipment 11 Storage section 12 Time derivative calculation section 13 Fluctuation difference calculation section 14 Nonlinear function generator 15 Regression equation generation section 16 Estimation part 17 Output control section 201 Control device 202 Main storage 203 Auxiliary storage device 204 Display device 205 Input Device 206 Communication Equipment

Claims

1. A time derivative calculation unit that calculates a time derivative of a variable included in time series data; a fluctuation difference calculation unit that calculates a difference indicating a fluctuation of a long-term component of the variable based on a specified time sample interval; an estimation unit that estimates coefficients of a linear regression equation by machine learning using the time differential value and the difference as learning data; An information processing device comprising:

2. the fluctuation difference calculation unit calculates a difference indicating a fluctuation of the long-term component based on two or more types of time sample intervals; the estimation unit estimates coefficients of a linear regression equation by machine learning using the time differential value and a difference indicating fluctuations of two or more types of the long-term components as learning data. The information processing device according to claim 1 .

3. the sum of the time differential values ​​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. a nonlinear function generator that generates a nonlinear function based on the variables; a regression equation generation unit that generates the linear regression equation using the nonlinear function as a basis function; The information processing device according to claim 1 or 2, further comprising:

5. 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 4 , further comprising:

6. The values ​​of the variables are expressed in units that are standardized for each physical quantity represented by the variables.

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

7. An information processing device comprising: a step of calculating a time derivative value of a variable included in time series data; a step in which the information processing device calculates a difference indicating a fluctuation of a long-term component of the variable based on a specified time sample interval; a step of estimating coefficients of a linear regression equation by machine learning using the time differential value and the difference as learning data by the information processing device; An information processing method including:

8. Computer, a time derivative calculation unit that calculates a time derivative of a variable included in the time series data; a fluctuation difference calculation unit that calculates a difference indicating a fluctuation of a long-term component of the variable based on a specified time sample interval; an estimation unit that estimates coefficients of a linear regression equation by machine learning using the time differential value and the difference as learning data; A program to function as a

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