Information processing apparatus, information processing method, and program

Abstract

To further improve generation accuracy of a model of a physical phenomenon.SOLUTION: The information processing device includes a regression equation generation unit and an estimation unit. The regression equation generator generates a regression equation for obtaining one or more output variables, the regression equation including a plurality of input variables and a plurality of coefficients respectively corresponding to the plurality of input variables. The processor is configured to estimate the plurality of coefficients by using one or more correction values for correcting one or more target coefficients included in the plurality of coefficients, the one or more correction values being determined based on knowledge about a relationship between an input variable corresponding to the target coefficient and the output variable.SELECTED DRAWING: Figure 3

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 Application Publication No. 2024-098397 [Non-patent literature]

[0004] [Non-Patent Document 1] SL Brunton, JL Proctor, JN Kutz, “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. et al. “Physics-Informed Machine Learning for Surrogate Modeling of Heat Transfer Phenomena.”, Journal of Computational and Nonlinear Dynamics. 2023, 18(11), 111001. Summary of the Invention [Problem to be solved by the invention]

[0005] An object of the present invention is to provide an information processing device, an information processing method, and a program that can further improve the accuracy of generating a model of a physical phenomenon. [Means for solving the problem]

[0006] According to an embodiment, an information processing apparatus includes a regression equation generation unit and an estimation unit. The regression equation generation unit generates a regression equation that includes a plurality of input variables and a plurality of coefficients corresponding to the plurality of input variables and that determines one or more output variables. The estimation unit estimates the plurality of coefficients using one or more correction values ​​that correct one or more target coefficients included in the plurality of coefficients, the correction values ​​being determined based on knowledge of the relationship between the input variable corresponding to the target coefficient and the output variable. [Brief explanation of the drawings]

[0007] [Figure 1] FIG. 2 is a diagram showing an example of the configuration of a battery module. [Figure 2] FIG. 10 is a diagram showing an example of time-series data. [Figure 3] FIG. 1 is a diagram showing an example of the functional configuration of an information processing apparatus. [Figure 4] A diagram showing an example of knowledge. [Figure 5] 1 is a flowchart of a method for generating a model. [Figure 6] FIG. 10 is a diagram showing how the coefficients of a regression equation are estimated. [Figure 7] FIG. 10 is a diagram showing an example of knowledge given between some variables. [Figure 8] FIG. 1 is a hardware configuration diagram of an information processing device. DETAILED DESCRIPTION OF THE INVENTION

[0008] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of an information processing apparatus according to the present invention will be described in detail below with reference to the accompanying drawings.

[0009] An example of a method for generating a model of a physical phenomenon will be described below. For example, assuming that a differential equation representing the model is expressed in the form of the following equation (1), the model is generated by estimating coefficients ξ1 to ξ8.

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[0010] As a method for estimating the coefficients, for example, a sparse estimation technique is used, which estimates each coefficient so that the value of most of the coefficients is zero. For example, in equation (1), the values ​​of coefficients ξ1 to ξ3 are estimated to be zero, and the value of coefficient ξ4 is estimated to be a value other than zero. This example means that the value of the variable on the left side (the differential value of x1) is estimated from the value of variable z2. This estimation technique can be interpreted as a method for estimating coefficients and selecting a variable effective for estimation (z2 in the above example).

[0011] The variables x and z used to generate a model are, for example, variables contained in time-series data obtained by measuring the object to be modeled. x is a dependent variable and z is an independent variable. A dependent variable is a variable that is determined depending on the independent variable. An independent variable is a variable that indicates the cause of change in the dependent variable. An example of a dependent variable is the temperature of an electronic component or heat sink. An example of an independent variable is the wind speed indicating the wind strength of a fan that cools an electronic component, the pressure difference between the inlet and outlet of a cooling flow path, the current flowing through an electronic component, and the voltage input to an electronic component.

[0012] Hereinafter, the variables that are input to the equation representing the model (variables included on the right side) will be referred to as input variables, and the variables that are output from the equation (variables included on the left side) will be referred to as output variables. For example, in equation (1), the variables x and z correspond to input variables, and the differential value of the variable x corresponds to the output variable. In this way, the input variables may include not only independent variables, but also dependent variables (variable x) or terms calculated from the dependent variables.

[0013] FIG. 2 is a diagram showing an example of time-series data. The data number is information for identifying data acquired at different times. The data number may be expressed as the time at which the data is acquired. FIG. 2 shows an example in which almost the same values ​​are acquired as variables z1 and z2 at each time. In such a case, as in the case where there is a relationship between multiple variables that can be expressed by a linear combination (multicollinearity), the variable z 1、 It is difficult to estimate the coefficient of z2 with high accuracy.

[0014] This will be explained further using an example in which the thermal network method is used to model a physical phenomenon. Note that the physical quantities and physical phenomena to be modeled are not limited to heat transfer handled by thermal networks, but may be any other physical quantities. In the thermal network method, the conservation of energy at each node is expressed by the following equation (2).

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[0015] C is the heat capacity, R is the thermal resistance, Q is the amount of heat generated, T is the temperature, and N is the number of nodes. In equation (2), for example, the amount of heat generated Q corresponds to the independent variable z in equation (1). Also, the temperature difference (T j -T n ) corresponds to the dependent variable x in equation (1). n is an integer that satisfies 1≦n≦N. j is an integer that satisfies 1≦j≦N, j≠n.

[0016] Thermal fluid analysis can be performed on, for example, a battery module. Fig. 1 is a diagram showing an example of the configuration of a battery module 50. The battery module 50 has a configuration in which 12 battery cells are connected in series, with each battery cell being connected in parallel with two other battery cells. For example, battery cells c-1 and c-2 (c is 1 to 12) are two battery cells connected in parallel.

[0017] According to a conventional method, a thermal fluid analysis is performed on the battery module 50 using time series data such as that shown in FIG. 2, and an approximate equation (such as a Reduced Order Model: ROM) for temperature prediction generated using the results of the thermal fluid analysis is expressed, for example, as the following equation (3):

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[0018] For example, the first line of equation (3) is the temperature T 1-1 The differential value of is the heat generation amount Q of battery cell 1-2. 1-2 is related to the calorific value Q 1-2 However, the correct expression is that the temperature T of battery cell 1-1 is 1-1 The differential value of is the heat generation amount Q of the same battery cell 1-1. 1-1 is related to the calorific value Q 1-1 One of the reasons for this battery cell discrepancy is that data with nearly identical values ​​is obtained, as shown in Figure 2. The equation (3) generated in this way may not be able to accurately estimate the temperature for unknown input data.

[0019] Therefore, the information processing device of the embodiment estimates the coefficients of the equation using correction values ​​that are determined based on prior knowledge about the relationship between the input variable (heat generation amount Q in the above example) and the output variable (temperature T in the above example) of the modeled equation (regression equation).

[0020] In this embodiment, coefficients are estimated using a sparse estimation technique. Estimation techniques using the sparse estimation technique include a technique called TA, which performs coefficient estimation and variable selection separately, and a technique called TB, which performs coefficient estimation and variable selection together. Technique TA includes the following techniques: Recursive Feature Elimination (RFE) is a method to sequentially remove unimportant features from a given feature set. ·STLS(Sequential Threshold Least-Squares) Methods shown in Patent Documents 1 to 3

[0021] In the following, we will mainly explain an example in which coefficient estimation and variable selection are performed separately, as in method TA. An example in which coefficient estimation and variable selection are performed together, as in method TB, will be explained in a modified example.

[0022] 3 is a diagram illustrating an example of the functional configuration of the information processing device 100 according to the embodiment. The information processing device 100 according to the embodiment includes a storage unit 121, a nonlinear function generation unit 101, a regression equation generation unit 102, an estimation unit 110, and an output control unit 103.

[0023] At least a part of each of the above units (nonlinear function generating unit 101, regression equation generating unit 102, estimation unit 110, and output control unit 103) may be realized by one or more processing units. Each of the above units is realized, for example, by one or more processors. For example, each of the above units may be realized by having a processor such as a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit) execute a program, i.e., by software. Each of the above units may be realized by a processor such as a dedicated IC (Integrated Circuit), i.e., by hardware. Each of the above units may be realized by a combination of software and hardware. When multiple processors are used, each processor may realize one of the units, or may realize two or more of the units.

[0024] Furthermore, the information processing device 100 may be physically configured as one device or may be physically configured as multiple devices. For example, the information processing device 100 may be constructed in a cloud environment. Furthermore, each unit within the information processing device 100 may be distributed across multiple devices.

[0025] The storage unit 121 stores various information used in the information processing device 100. For example, the storage unit 121 stores time-series data including at least one of a dependent variable and an independent variable. In the information processing device 100 according to the embodiment, the value of the 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 is unified to either kg or g, rather than mixing a dependent variable expressed in kg and a dependent variable expressed in g. Similarly, the value of the independent variable is expressed in a unit that is unified for each physical quantity indicated by the independent variable.

[0026] Note that multiple types of time series data may be stored in the storage unit 121. The multiple types of time series data may differ in at least one of the initial condition and the boundary condition.

[0027] The storage unit 121 can be configured from any commonly used storage medium such as a flash memory, a memory card, a RAM (Random Access Memory), an HDD (Hard Disk Drive), and an optical disk.

[0028] The nonlinear function generator 101 generates a nonlinear function based on at least one of a dependent variable and an independent variable. For example, the nonlinear function generator 101 generates a nonlinear function based on a temperature T n and the temperature T at position j j The nonlinear function generating unit 101 generates a nonlinear function based on the above. Position n and position j are positions corresponding to, for example, any of N nodes. The nonlinear function generating unit 101 may generate a plurality of nonlinear functions using a plurality of methods (for example, Patent Document 3).

[0029] The regression equation generation unit 102 generates a regression equation that includes a plurality of input variables and a plurality of coefficients corresponding to each of the plurality of input variables and that determines one or more output variables. For example, the regression equation generation unit 102 mixes the nonlinear functions generated by the nonlinear function generation unit 101 and generates a linear regression equation that uses the nonlinear functions as basis functions.

[0030] The following equation (4) shows an example of the generated linear regression equation: Equation (4) is an example of an equation generated as an equation corresponding to the above equation (2).

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[0031] In equation (4), the input variables are the heat generation amount Q and h p (T j -T n ) The output variable is the variable T n is the differential value of h p represents a nonlinear function. P represents the number of basis function candidates. h p (T j -T n ) corresponds to the basis function candidates. In the following, the basis function candidates are defined as θ n,p ^(t l,m ) where "n,p" is a subscript to indicate the candidate of the pth basis function at node n. l,m represents time. l represents the type of time series data. For example, when multiple types of time series data are used, the multiple types of time series data are distinguished by l. m corresponds to the data number within the time series data. For example, if the time series data in Figure 2 is time series data of type l, then t l,D01 represents the time corresponding to data number "D01". n,p represents the coefficient corresponding to the p-th basis function candidate at node n.

[0032] The estimation unit 110 estimates multiple coefficients using correction values ​​determined based on knowledge of the relationship between input variables corresponding to one or more coefficients to be corrected (hereinafter referred to as target coefficients) and output variables. The correction values ​​are values ​​used to correct the corresponding target coefficients. The estimation unit 110 includes a coefficient estimation unit 111, a calculation unit 112, and a correction unit 113.

[0033] The coefficient estimation unit 111 estimates the coefficients of the linear regression equation generated by the regression equation generation unit 102 by machine learning using time differential values ​​and differences as learning data. The coefficient estimation unit 111 may estimate 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 (e.g., Patent Document 3).

[0034] The calculation unit 112 calculates the influence based on the magnitude of the term (coefficient × basis function). n -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 n,p × a representative value of the basis function. That is, the calculation unit 112 calculates the product of the coefficient estimated by the coefficient estimation unit 111 and the maximum value of the basis function corresponding to the coefficient as the influence. The calculation unit 112 may calculate the influence for a nonlinear function generated by any one of a plurality of methods (for example, Patent Document 3).

[0035] The following formula (5) is a formula showing an example of calculating the representative value (maximum value) of the basis function.

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[0036] The representative value is not limited to the maximum value shown in Equation (5) and may be any other value. For example, the representative value may be the root mean square (RMS) or the standard deviation such as the Z-score.

[0037] Furthermore, in this embodiment, the calculation unit 112 calculates the influence of a target coefficient among the multiple coefficients of the linear regression equation, corrected by a correction value α. The correction value α is determined based on knowledge (prior knowledge, prior information) about the relationship between the input variable corresponding to the target coefficient and the output variable.

[0038] Fig. 4 is a diagram showing an example of knowledge. Fig. 4 shows an example in which a value indicating the degree of relationship between each temperature T (T1 to T8, etc.) corresponding to an output variable and the temperature T and heat generation amount Q corresponding to an input variable is set as knowledge. The larger the value, the greater the degree of relationship.

[0039] For example, temperature T1 represents the temperature at the node corresponding to number "1." Heat generation amount Q1 represents the amount of heat generation at the node corresponding to number "1." For example, FIG. 4 shows that temperature T1 has a strong correlation with temperatures T2, T3, and heat generation amount Q1. Note that between the same variables (for example, temperature T1 and temperature T1), a value of zero is set.

[0040] In the following, the coefficient ξ n、p The correction value α for n、p The correction value α n、p is the corresponding coefficient ξ n、p The same value may be set for each group to which the group belongs. An example will be explained using row 2 (T2) and column 3 (T3) in FIG. 4. The value " in row 2, column 3 in FIG. 4 is 0.1. For example, in row 2, column 3, [ξ 2、p h p +ξ 2、p+1 h p+1 +···](T3-T2). A group is a group of coefficients contained in the symbol []. In this example, the coefficient ξ 2、p , ξ 2、p+1 Correction value α corresponding to 2、p , α 2、p+1 The value of ··· is the common value 0.1.

[0041] The correction value α is set to a larger value as the degree of relationship between the input variable and output variable corresponding to the target coefficient becomes greater. For example, the correction value α may be a real number between 0 and 1. The maximum value of the correction value α is not limited to 1, and may be, for example, a value greater than 1. Note that a fixed value (for example, 1) may be set as the correction value for a coefficient corresponding to a variable for which knowledge cannot be obtained. In this case, correction values ​​(fixed values) are also set for coefficients other than the target coefficient.

[0042] The way of expressing the knowledge is not limited to that shown in FIG. 4, and the method of setting the correction values ​​based on the knowledge is not limited to that described above. Any method of setting the correction values ​​based on knowledge obtained in advance about the relationship between the input variables and the output variables may be used. The correction values ​​for each coefficient may themselves be given as knowledge.

[0043] Returning to the description of Fig. 3, the modifying unit 113 modifies the coefficients based on the influence calculated by the calculating unit 112. For example, the modifying unit 113 modifies the coefficients of basis functions whose influence is equal to or less than a threshold to 0 (zero). At this time, when learning is performed using data in which data that has been subjected to different preprocessing is mixed (when multiple nonlinear functions are generated by multiple methods), the modifying unit 113 may target one (either) of the data before mixing as the representative value of the basis function candidate in terms of the magnitude of the term (for example, Patent Document 3).

[0044] For example, the correction unit 113 may correct the coefficient ξ when the following formula (6) or formula (7) is satisfied: n,p Correct λ to zero. n is a hyperparameter determined for each node n, and λ n <1. The right side of equation (6) or equation (7) corresponds to the threshold value.

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[0045] As described above, the correction value α is set to a larger value as the degree of relationship between the input variable and output variable corresponding to the target coefficient increases. Also, as shown in equations (6) and (7), the threshold value used to determine whether the coefficient value is set to zero increases as the correction value α increases. Therefore, the greater the degree of relationship, the more likely it is that the coefficient will not become zero, i.e., the more likely it is that the corresponding variable will be selected.

[0046] Therefore, even in a situation like that described in Figure 2, where almost identical values ​​are obtained for different variables, if the correction values ​​are set appropriately based on knowledge, it becomes possible to select more appropriate variables and estimate coefficients with higher accuracy.

[0047] The method using equation (6) or equation (7) can be interpreted as a method of controlling the selection of variables (basis functions) by correcting the threshold with the correction value α. The selection of variables may be controlled by correcting the coefficient with the correction value α. For example, the modifying unit 113 may correct the coefficient ξ when the following equation (8) is satisfied: n,p may be modified to zero. λ is a hyperparameter commonly defined for multiple nodes, and λ<1.

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[0048] When the convergence condition is satisfied, the output control unit 103 outputs the linear regression formula expressed by the modified coefficients. The convergence condition is, for example, the number of iterations of the machine learning process. The output control unit 103 may display the linear regression formula on a display device.

[0049] Next, a description will be given of a model generation process performed by the information processing device 100. Fig. 5 is a flowchart showing an example of a model generation method according to an embodiment.

[0050] The regression equation generating unit 102 mixes the nonlinear functions generated by the nonlinear function generating unit 101 and generates a linear regression equation using the nonlinear functions as basis functions (step S101).

[0051] The estimation unit 110 acquires knowledge about the relationship between the input variables and the output variables in advance (step S102). The estimation unit 110 may then use the acquired knowledge to calculate a correction value for each coefficient.

[0052] The estimation unit 110 initializes data (for example, hyperparameters) used when machine learning the model (step S103).

[0053] Next, the coefficient estimation unit 111 estimates the coefficients of the linear regression equation generated by the regression equation generation unit 102 (step S104). Any method may be used to estimate the coefficients, and for example, a method of estimation using the non-negative least squares method may be applied.

[0054] Next, the calculation unit 112 calculates the above-mentioned influence (the magnitude of the term) using a correction value based on knowledge, and the modification unit 113 deletes the basis functions whose influence is equal to or less than the threshold by modifying the coefficients of the basis functions whose influence is equal to or less than the threshold to zero (step S105). For example, the modification unit 113 modifies the coefficients of the basis functions whose influence is equal to or less than the threshold to zero, as shown in the above equation (6) or (7).

[0055] Next, the modification unit 113 determines whether the results of the coefficient estimation and modification process satisfy a convergence condition (step S106). The convergence condition is, for example, the number of times the coefficient estimation and modification process is executed.

[0056] If the convergence condition is not satisfied (step S106: No), the process returns to step S104. Thereafter, the coefficient estimation unit 111 updates the linear regression equation using the coefficients corrected by the correction unit 113, and then re-estimates the coefficients of the updated linear regression equation (step S104). Next, the calculation unit 112 updates the influence using the product of the correction value, the coefficients of the updated 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 113 re-corrects the coefficients of the updated linear regression equation based on the updated influence (step S105). The information processing device 100 repeats the estimation of the coefficients, the calculation of the influence, and the correction of the coefficients a predetermined number of times.

[0057] If the convergence condition is satisfied (step S106: Yes), the output control unit 103 calculates a performance evaluation index of the model (step S107). The performance evaluation index may be any index, and may be, for example, an index using one or more of the following indexes: ·Root Mean Square Error (RMSE) L0 norm L1 norm L2 norm

[0058] Next, the output control unit 103 determines whether the trained model satisfies a convergence condition (step S108). In this case, the convergence condition is, for example, the number of times the model training process is executed. Alternatively, for example, the convergence condition is when the calculated performance evaluation index is greater than a predetermined evaluation threshold. If the convergence condition is not satisfied (step S108: No), the hyperparameters are updated (step S109), and the process returns to step S104. The hyperparameters are, for example, λ , which is used to calculate the thresholds in equations (6) and (7). n is.

[0059] If the convergence condition is satisfied (step S108: Yes), the output control unit 103 outputs the model (step S110) and ends the generation process.

[0060] The knowledge may be updatable. In this case, the estimation unit 110 may obtain updated knowledge in step S102 and update the correction value using the updated knowledge.

[0061] A specific example of the process according to the embodiment will be described. n This figure shows how the coefficients of the regression equation for determining are estimated. The dashed lines in the upper part of Figure 6 correspond to given knowledge. For example, two variables connected by a dashed line indicate variables that have a strong degree of relationship.

[0062] The bottom diagram of Figure 6 shows an example of coefficients that can be estimated using the above knowledge. For example, the temperature T n For the temperature T(T1, T2, T3, T4, . . . T a ), and out of the heat generation amount Q (Q1, Q2, Q3, Q4, ...), temperature T2, temperature T3 and heat generation amount Q2 were selected as variables, and the corresponding coefficients were estimated.

[0063] Next, we will explain an example of how to provide knowledge. The example in Figure 4 includes knowledge that indicates the relationship between the temperatures of different nodes. However, the criteria for determining the relationship between temperatures may differ depending on the person, and it may not be possible to properly set whether or not there is a relationship. In contrast, it may be relatively easy to set the relationship between the node temperature and a variable other than the node temperature. Variables other than the node temperature include, for example, the heat generation amount of the node and the environmental temperature measured independently of the node.

[0064] Therefore, knowledge may be given only about the relationships between some variables that are judged to be able to be appropriately set. For coefficients corresponding to variables for which knowledge is given, a correction value α between 0 and 1 is set. For coefficients corresponding to variables for which knowledge is not given, the correction value α is set to 1, for example.

[0065] FIG. 7 shows an example of knowledge given between some variables. In FIG. 7, the temperature T nFor Q, only knowledge of the relationship with the calorific value Q2 is given. For example, an example of an approximate formula generated by this embodiment using knowledge such as that shown in FIG. 7 and time-series data such as that shown in FIG. 2 is shown in the following formula (9). Unlike formula (3) generated by the conventional method, the correct variables are selected in formula (9).

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[0066] (Variation) Next, an example in which coefficient estimation and variable selection are performed together as in method TB will be described.

[0067] In a modified example, the estimation unit 110 estimates the coefficients by optimizing a loss function including a regression equation and a regularization term. The estimation unit 110 may use any conventionally used regularization term. Examples of regularization terms are shown below. L1 norm of Lasso (Least absolute shrinkage and selection operator): ||β||1 Ridge's L2 norm: ||β||2 2 Elastic net L1+L2 norm Trace norm of Trace Lasso: ||Xdiag(β)|| * Adaptive Lasso norm: ||β / β γ ~||1 ·Hypothesis Transfer Norms: λ||β||2 2 +(1-λ)||β-β~||2 2 Fused lasso norms: λ||β||1+(1-λ)Σ||β j -β j-1 ||1

[0068] The estimation unit 110 of the modified example estimates the coefficients of the regression equation by correcting the regularization term with a correction value α and optimizing a loss function including the corrected regularization term. The following equation (10) shows an example of an equation representing the optimization of a loss function including a regularization term. Equation (10) is an example including the L1 norm as the regularization term.

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[0069] The equation in argmin in equation (10) corresponds to the loss function. Of the loss functions, y-Xβ corresponds to the regression equation. In this regression equation, X corresponds to the input variable, y corresponds to the output variable, and β(β n ) corresponds to the coefficient, and α n corresponds to the correction value. λ is a hyperparameter.

[0070] α n For example, α can take a value between 0 and 1. n can be a continuous value or a discrete value such as [0, 0.3, 0.6, 1.0]. n The value of can be different for each node n or can be common to all nodes. n The coefficient β corresponding to n But, α n This is corrected by α n Large variable x n is likely to be selected. n The value itself is the correction value α n is not corrected by

[0071] In this way, the information processing apparatus according to the embodiment estimates the coefficients of the regression equation using correction values ​​determined based on prior knowledge, thereby further improving the accuracy of generating a model of a physical phenomenon.

[0072] Finally, an example of the hardware configuration of the information processing apparatus 100 according to the embodiment will be described below with reference to Fig. 8, which is a diagram showing an example of the hardware configuration of the information processing apparatus 100 according to the embodiment.

[0073] The information processing device 100 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.

[0074] 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.

[0075] 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 100. The input device 205 is, for example, a keyboard or a mouse. When the information processing device 100 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.

[0076] The communication device 206 is an interface for communicating with other devices.

[0077] The program executed by the information processing device 100 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.

[0078] The program executed by the information processing device 100 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. The program executed by the information processing device 100 of the embodiment may also be provided via a network such as the Internet without being downloaded.

[0079] The program for the information processing apparatus 100 according to the embodiment may be provided in a state where it is pre-installed in a ROM or the like.

[0080] The program executed by the information processing device 100 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.

[0081] 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.

[0082] 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.

[0083] The information processing apparatus 100 of the embodiment may operate in any manner, for example, as a cloud system on a network.

[0084] 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]

[0085] 100 Information processing device 101 Nonlinear function generator 102 Regression equation generation unit 103 Output control section 110 Estimation part 111 Coefficient Estimation Unit 112 Calculation Unit 113 Correction section 121 Storage section

Claims

1. a regression equation generation unit that generates a regression equation for determining one or more output variables, the regression equation including a plurality of input variables and a plurality of coefficients corresponding to the plurality of input variables; an estimation unit that estimates the plurality of coefficients using one or more correction values ​​that correct one or more target coefficients included in the plurality of coefficients, the correction values ​​being determined based on knowledge of the relationship between the input variables corresponding to the target coefficients and the output variables; An information processing device comprising:

2. the estimation unit estimates the plurality of coefficients by optimizing a loss function including a regularization term corrected by the correction value. The information processing device according to claim 1 .

3. the correction value is determined for the target coefficients, which are some of the coefficients among the plurality of coefficients; The information processing device according to claim 1 .

4. The correction value is set to a larger value as the degree of relationship between the input variable corresponding to the target coefficient and the output variable increases. The information processing device according to claim 1 .

5. the input variables include basis functions represented by a plurality of nonlinear functions; The estimation unit a coefficient estimation unit that estimates the coefficients; a calculation unit that calculates an influence level of the target coefficient and the basis function corresponding to the target coefficient based on a representative value in data used to estimate the plurality of coefficients and the correction value; a correction unit that corrects the coefficients using the influence; Equipped with The information processing device according to claim 1 .

6. the coefficient estimation unit updates the regression equation using the coefficients corrected by the correction unit, and further estimates the coefficients of the updated regression equation; the calculation unit further calculates the influence degree based on the target coefficient included in the updated regression equation, the representative value of the basis function corresponding to the target coefficient, and the correction value; the correction unit further corrects the coefficients of the updated linear regression equation based on the updated influence degree; the estimation unit repeats 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 5 .

7. the modification unit modifies the coefficients corresponding to the basis functions whose influence levels are equal to or less than a threshold value to zero. The information processing device according to claim 5 .

8. an output control unit that outputs the regression equation represented by the estimated coefficients; The information processing device according to claim 1 .

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

10. The regression equation represents a model of a thermal network. The information processing device according to claim 1 .

11. An information processing method executed by an information processing device, a regression equation generating step of generating a regression equation for determining one or more output variables, the regression equation including a plurality of input variables and a plurality of coefficients corresponding to the plurality of input variables; an estimation step of estimating the plurality of coefficients using one or more correction values ​​for correcting one or more target coefficients included in the plurality of coefficients, the correction values ​​being determined based on knowledge of the relationship between the input variables corresponding to the target coefficients and the output variables; An information processing method including:

12. On the computer, a regression equation generating step of generating a regression equation for determining one or more output variables, the regression equation including a plurality of input variables and a plurality of coefficients corresponding to the plurality of input variables; an estimation step of estimating the plurality of coefficients using one or more correction values ​​for correcting one or more target coefficients included in the plurality of coefficients, the correction values ​​being determined based on knowledge of the relationship between the input variables corresponding to the target coefficients and the output variables; A program to execute.

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