Reduced-order model generation device and reduced-order model generation method

Abstract

A reduced-order model generation device (100) comprises: a model generation unit (112) for generating a reduced-order model which is obtained by reducing the order of a physical model which describes a physical phenomenon; and a model order reduction unit (113) for determining the order for the reduced-order model which allows an error between a result of a simulation using the reduced-order model under a prescribed simulation condition, and a reference value to stay within an allowable limit of error. The reduced-order model generation device (100) may be provided with a condition generation unit (114) for calculating a prescribed simulation condition on the basis of experimental design. The reference value represents a result of a simulation using the physical model under the prescribed simulation condition.

Description

REDUCED-DIMENSIONAL MODEL GENERATION DEVICE AND REDUCED-DIMENSIONAL MODEL GENERATION METHOD

[0001] The present invention relates to a low-dimensional model generation device and a low-dimensional model generation method for generating a low-dimensional physical model.

[0002] To build a digital twin, a physical model (simulation model) that reproduces real-world phenomena on a computer is used. It is desirable to use a low-dimensional model as the physical model, which allows for simulations that minimize computer resources and calculation time. For low-dimensional models, high-fidelity models are reduced in dimension using mathematical techniques, such as singular value decomposition. Patent Document 1 discloses a method for reducing the dimension of data by extracting features using singular value decomposition and compressing image data using singular value decomposition.

[0003] International Publication No. 2008 / 015799

[0004] In the method described in Patent Document 1, in order to extract and reduce the dimension of an image feature, singular value decomposition is used to determine the truncation order so that the difference between the i-th singular value and the (i+1)-th singular value is smaller than a specified value. However, in such a method using singular values, the difference before and after singular value decomposition may not necessarily fully represent the truncation error before and after data compression.

[0005] For example, in low-dimensional models generated to predict product characteristics (such as low-dimensional models for predicting temperature information), the accuracy of the low-dimensional model and the computational resources required for simulation change depending on factors such as the device's operating conditions and environmental conditions. For this reason, there is a demand for a method to provide an evaluation index that can absolutely and intuitively determine the order / dimension of a low-dimensional model and appropriately evaluate the accuracy of the low-dimensional model.

[0006] The present invention has been made in view of the above background, and aims to provide a reduced-dimensional model generation device and a reduced-dimensional model generation method that enable determination of dimensions that satisfy given conditions when reducing the dimension of a physical model.

[0007] In order to solve the above-mentioned problems, the reduced-dimensional model generation device according to the present invention includes a model generation unit that generates a reduced-dimensional model by reducing the dimensions of a physical model that describes a physical phenomenon, and a model reduction unit that determines the dimensions of the reduced-dimensional model such that the error between the results of a simulation using the reduced-dimensional model under specified simulation conditions and a reference value is within an allowable error.

[0008] According to the present invention, it is possible to provide a reduced-dimensional model generation device and a reduced-dimensional model generation method that enable determination of dimensions that satisfy given conditions when reducing the dimension of a physical model. Problems, configurations, and effects other than those described above will become clear from the description of the following embodiments.

[0009] 1 is a functional block diagram of a low-dimensional model generating device according to an embodiment; FIG. 2 is a flowchart of a model generation process according to an embodiment; FIG. 3 is a flowchart of a dimension reduction process according to an embodiment; FIG. 4 is a screen configuration diagram of a setting screen according to an embodiment; FIG. 5 is a screen configuration diagram of an evaluation screen according to an embodiment; and FIG. 6 is a hardware configuration diagram showing an example of a computer that realizes the functions of the low-dimensional model generating device according to an embodiment.

[0010] Overview of the Low-Dimensional Model Generation Device The following describes a low-dimensional model generation device in an embodiment for carrying out the present invention. The low-dimensional model generation device mathematically models physical phenomena and generates a low-dimensional model by reducing the dimension of a physical model described by a mathematical formula. For example, the low-dimensional model generation device generates a low-dimensional model by reducing the dimension (order) of a matrix included in the mathematical formula.

[0011] The reduced-dimensional model generation device generates a reduced-dimensional model of a dimension that satisfies given conditions. The given conditions may be, for example, a tolerance for error in the simulation results using the original physical model and the reduced-dimensional model. The simulation is performed under boundary conditions for comprehensive verification from possible values ​​determined using, for example, experimental design. Such a reduced-dimensional model generation device can generate a reduced-dimensional model that satisfies the given conditions and requires a short simulation time.

[0012] <Configuration of Low-Dimensional Model Generation Device> Fig. 1 is a functional block diagram of a low-dimensional model generation device 100 according to this embodiment. The low-dimensional model generation device 100 is a computer, and includes a control unit 110, a storage unit 120, and an input / output unit 180. User interface devices such as a display, keyboard, and mouse are connected to the input / output unit 180. The input / output unit 180 may include a communication device, enabling data transmission and reception with other devices. Furthermore, a media drive may be connected to the input / output unit 180, enabling data exchange using a recording medium.

[0013] <<Low-Dimensional Model Generation Device: Storage Unit>> The storage unit 120 is configured to include storage devices such as a ROM (Read Only Memory), a RAM (Random Access Memory), and an SSD (Solid State Drive). The storage unit 120 stores model data 121, evaluation conditions 122, simulation results 123, and a program 128. Note that the various storage contents of the storage unit 120 may be stored in an external storage device such as a cloud server and read as needed.

[0014] The model data 121 stores data related to the physical model, such as object data such as shape, size, and physical property values, boundary conditions for performing a simulation, and mathematical expressions, matrices, and parameters that describe the physical model. The evaluation conditions 122 store values ​​of boundary conditions for performing a simulation and conditions for calculating these values ​​(e.g., number of samples / number of designs in a design of experiments). The simulation results 123 store results of the simulation (e.g., values ​​of state quantities) and execution time. The program 128 includes a description of the dimensional reduction process (see FIG. 3), which will be described later.

[0015] <<Reduced-Order Model Generating Device: Control Unit>> The control unit 110 is configured to include a CPU (Central Processing Unit) and is equipped with a data receiving unit 111, a model generating unit 112, a model reduction unit 113, a condition generating unit 114, a simulation unit 115, an error evaluation unit 116, and a display control unit 117. The control unit 110 may be configured to include a GPU (Graphics Processing Unit), an FPGA (Field Programmable Gate Array), an ASIC (Application Specific Integrated Circuit), etc.

[0016] <<Control Unit: Data Receiving Unit>> The data receiving unit 111 receives input to the low-dimensional model generation device 100 and stores it in model data 121 and evaluation conditions 122. The input includes data related to the physical model, boundary conditions when performing a simulation, conditions for the low-dimensional model (see allowable error described later), and the like.

[0017] <<Control Unit: Model Generation Unit>> The model generation unit 112 generates a physical model that describes a physical phenomenon. For example, the model generation unit 112 generates a physical model described by an equation including a matrix based on object data. The model generation unit 112 also generates a physical model (low-dimensional model) by reducing the dimension of this physical model. For example, when the physical model includes a matrix, the model generation unit 112 calculates a matrix by reducing the dimension of the matrix to generate a low-dimensional model.

[0018] <<Control Unit: Model Reduction Unit>> The model reduction unit 113 calculates the dimension of a low-dimensional physical model that satisfies a given condition, by reducing the dimension of the physical model generated by the model generation unit 112. This low-dimensional physical model is also referred to as a low-dimensional model. The given condition is, for example, that the difference (error) between the result of a simulation using the low-dimensional model and the result (reference value) of a simulation using the physical model before being reduced by the model reduction unit 113 is within an allowable error.

[0019] <<Control Unit: Condition Generation Unit / Simulation Unit>> The condition generation unit 114 calculates the values ​​of boundary conditions when executing a simulation. The condition generation unit 114 calculates the values ​​of boundary conditions using, for example, experimental design. The simulation unit 115 executes a simulation using a physical model including a low-dimensional model. The simulation unit 115 stores the results of the execution of the simulation (values ​​of state quantities) and the execution time in the simulation result 123.

[0020] <<Controller: Error Evaluation Unit / Display Controller>> The error evaluation unit 116 calculates the error in the results of a simulation using the physical model and the low-dimensional model. The display controller 117 displays the evaluation results of the low-dimensional model (see evaluation screen 320 in FIG. 5 , which will be described later).

[0021] As described above, the reduced-order model generation device 100 includes a model generation unit 112 that generates a reduced-order model by reducing the dimensions of a physical model that describes a physical phenomenon. The reduced-order model generation device 100 also includes a model reduction unit 113 that determines the dimensions of the reduced-order model such that the error between the result of a simulation using the reduced-order model under specified simulation conditions and a reference value falls within an allowable error. The reference value is the result of a simulation using the physical model under the specified simulation conditions. The reduced-order model generation device 100 also includes a condition generation unit 114 that calculates specified simulation conditions (boundary conditions) based on experimental design.

[0022] <Physical Model> Before describing the method for reducing the order of a model in the reduced-order model generation device 100, we will explain a method for generating a physical model to be reduced in order by using a Parametric Model Order Reduction method that uses the Krylov subspace method. The following description focuses on a model of heat conduction problems in an object, but is not limited to this and other physical models may also be used.

[0023] First, the system matrix of the state equation is calculated based on the object data and boundary conditions, for example, by discretization using the finite element method. More specifically, the object data and boundary conditions are discretized into finite elements to generate a matrix-format discrete equation of the heat conduction equation. Equation (1) is the matrix-format discrete equation of the discretized heat conduction equation. The object data refers to the shape and size of the object, as well as physical properties such as thermal conductivity, specific heat, and density. Boundary conditions include fixed temperature conditions, heat flow rate, and heat transfer conditions.

[0024]

[0025] where E is the heat capacity matrix, K is the heat conduction matrix, p is a parameter (e.g., heat transfer coefficient), θ is a temperature vector, B is an input coefficient matrix, u is an input vector (e.g., heat generation amount), i is a parameter index (subscript), and N ｃ is the number of parameters. ｄ is the change in the thermal conduction matrix of K, and indicates the thermal conduction matrix of the nonlinear part that changes depending on the state. ｉ (K ｄ ) ｉ )) is the system matrix. Next, a method in which the model generation unit 112 generates a reduced-dimensional model from the matrix-form discrete equation shown in Equation (1) will be described. For ease of explanation, N ｃ is set to 1. Transforming equation (1) yields equation (2).

[0026]

[0027] Here, the system matrix is ​​converted into a transfer function, and the frequency expansion point s ０ Around, and parameter expansion point p ０ By performing a Taylor expansion around the

[0028]

[0029] In this case, if the influence of the cross term is assumed to be small, it is known that the transfer function can be approximated as shown in equation (4), where k is the order at which the Taylor expansion is truncated.

[0030]

[0031] Therefore, the transfer function H(s, p) is expressed in the Krylov subspace K ｓ (A ｓ , R ｓ ) and the Krylov subspace K shown in equation (8) ｐ (A ｐ , R ｐ ) are approximated as projective coordinates in

[0032]

[0033] Therefore, the frequency expansion point s ０ , parameter expansion point p ０ In this case, the projection matrix V obtained by fixing each of these and using an algorithm such as the Block Arnoldi method is expressed as equation (13). Here, span is the projection matrix V （ｓ，０） and V （ｐ，０） shows a linear combination of

[0034]

[0035] The number of parameters up to this point is N ｃ (see equation (1)) has been set to 1, but the same applies even if it is greater than 1. The frequency and the number of parameters to be expanded in the Taylor series are set to l and m, respectively, and the transfer function H(s, p) is expanded in the Taylor series to obtain the projection matrix V in the form of equation (14).

[0036]

[0037] Here, the temperature vector θ can be approximated as shown in equation (15) using an (n, l+m)-dimensional projection matrix V, where n is the degree of freedom of the model (the dimension of the matrix when discretized by the finite element method), and (l+m) is the column size of the projection matrix.

[0038]

[0039] Substituting equation (15) into the system matrix of equation (1), the projection matrix V Ｔ Multiplying by this yields equation (16).

[0040]

[0041] E.K.K. ｄis n×n degrees of freedom, and the degrees of freedom on the left side of equations (17) to (19) are (l+m)×(l+m). Therefore, if (l+m) is less than n, the system matrix is ​​reduced in dimension. Generally, in the state equation "dx(t) / dt=Ax(t)+Bu(t)", x(t) is called the state vector, A is the system matrix, B is the input coefficient matrix, and u(t) is called the input vector. In this embodiment, equation (16) is also called the state equation, and E ～ (On top of E), (K ～ +Σp ｉ (K ～ ｄ ) ｉ ) is also called a system matrix. The reduced-order physical model described by equation (16) is the physical model that is the target of order reduction according to the present invention. In other words, the reduced-order model generated by an existing method is further reduced in order according to the present invention.

[0042] <Model Generation Process> Fig. 2 is a flowchart of the model generation process according to this embodiment. The process of generating a physical model (see Equation (16)) that indicates the physical behavior of an object will be described using Fig. 2. In step S11, the data receiving unit 111 receives input of object data, boundary conditions, and expansion points of frequencies and parameters, and stores them in model data 121. In step S12, the model generation unit 112 calculates a system matrix (see Equations (1) and (2)) based on the object data and boundary conditions. Subsequently, the model generation unit 112 calculates a transfer function and performs a Taylor expansion (see Equation (3)).

[0043] In step S13, the model generation unit 112 calculates a Krylov subspace (see equations (7) and (8)) using the Krylov subspace method. In step S14, the model generation unit 112 calculates a projection matrix V (see equations (13) and (14)) and stores it in the model data 121. In step S15, the model generation unit 112 calculates a system matrix (see equation (16)) and stores it in the model data 121.

[0044] <<Dimension Reduction Method>> Below, a method for calculating a system matrix (see equation (24) described below) of a reduced-dimensional model by performing singular value decomposition on the projection matrix V (see equations (13) and (14)) to reduce its dimension will be described. When reducing the dimension of the projection matrix V, for example, a simulation is performed under boundary conditions determined by experimental design, and the dimension is determined by evaluating the error. In the following description, the boundary conditions, the range of the boundary conditions, the allowable error due to dimension reduction (tolerance error), the evaluation starting dimension, and the increment of the order are assumed to be given. First, the projection matrix V is subjected to singular value decomposition as shown in equation (21).

[0045]

[0046] where Σ is the singular value σ of the projection matrix V ｉ are diagonal matrices with diagonal elements, U and Q are left singular vectors u ｉ and the right singular vector q ｉ is a unitary matrix with a column vector Ｔ U=Q Ｔ Q = I). Singular values ​​σ ｉ The columns of V and Q are arranged in descending order of contribution (absolute value). ｉ , q ｉ Equation (22) is obtained.

[0047]

[0048] If equation (22) is truncated to degree r (r<l+m), the projection matrix V is contracted to degree r, and the contracted U ｒ (See equation (23)). The reduced-order physical model (reduced-order model) is written as in equation (24).

[0049]

[0050] Next, a method for determining the truncation order r will be described. One method involves calculating the cumulative contribution rate and the difference between the singular values ​​obtained by singular value decomposition, and using these to determine the truncation order. However, when the cumulative contribution rate is used to reduce the dimension of a model, it can be difficult to evaluate the truncation error as a clear index because the singular value is a relative index. For example, it is difficult to determine a truncation order that satisfies the allowable error. This can lead to problems such as an order that is too large, resulting in an increased computational load, or, conversely, a truncation order that is too small, resulting in insufficient accuracy.

[0051] Furthermore, in low-dimensional models, state quantities (such as temperature) can be calculated by numerically integrating discrete equations. However, because the state quantities change depending on the boundary conditions of the simulation (environmental factors, design specifications, or usage conditions), the cumulative contribution ratio cannot take into account the influence of the boundary conditions, making it extremely difficult to evaluate the error of low-dimensional models.

[0052] To solve these problems, the present invention uses boundary conditions that are randomly and comprehensively generated by, for example, experimental design, to evaluate the calculation accuracy and calculation time of the reduced-dimensional model, thereby generating a reduced-dimensional model with a suitable truncation order r. In the following, a simulation will be performed using the reduced-dimensional model under the evaluation conditions determined by experimental design. ｉ，ｊ is the value of the jth boundary condition at the i-th sample. For example, the maximum value u of the jth boundary condition ｍａｘ，ｊ , minimum value u ｍｉｎ，ｊ Let N be the number of samples, and x ｉ，ｊ is calculated as shown in equation (29).

[0053]

[0054] In formula (29), e ｉ，ｊ is a random number between 0 and 1, and L ｉ，ｊ is a vector of randomly permuted integers from 1 to N ({1, 2, ..., N}) for each j. The set of boundary condition values ​​(x ｉ，１ , x ｉ，２, ...) is the evaluation condition for the i-th sample. The sampling method shown here is based on Latin hypercube sampling, but other sampling methods such as random sampling or orthogonal arrays may also be used to generate the evaluation conditions. Using the evaluation conditions thus obtained, a simulation is performed using a system matrix reduced to r dimensions while changing r, and the r whose calculation results satisfy the desired conditions is determined.

[0055] 3 is a flowchart of the dimension reduction process according to this embodiment. The process of reducing the dimension of the system matrix (see Equation (16)), which is the physical model generated in the model generation process (see FIG. 2), will be described with reference to FIG.

[0056] In step S21, the data accepting unit 111 accepts evaluation conditions for the reduced-dimensional model and stores them in the evaluation conditions 122. The evaluation conditions include boundary conditions, the range of boundary conditions (e.g., maximum and minimum values), the allowable error after dimension reduction, the number of samples in the experimental design, the initial dimension which is the first dimension at which evaluation starts, and the step dimension which is the increment of dimension when evaluation is repeated. Fig. 4 is a diagram showing the screen configuration of a setting screen 310 according to this embodiment. Setting values ​​used in the dimension reduction process, such as the range of boundary conditions, the allowable error, and the number of samples, are input into the setting screen 310.

[0057] Returning to Fig. 3, the description of the dimension reduction process will be continued. In step S22, the condition generation unit 114 calculates the boundary condition values ​​(see equation (29)) as evaluation conditions based on the experimental design method, and stores them in the evaluation conditions 122. In step S23, the model generation unit 112 calculates a physical model (system matrix (see equation (16))) of maximum dimension. Note that the maximum dimension is (l + m), which is the dimension of the projection matrix V.

[0058] In step S24, the simulation unit 115 uses the maximum-dimensional physical model calculated in step S23 to execute a simulation under each evaluation condition (a set of boundary conditions) in the evaluation conditions 122. The simulation unit 115 stores the results of the simulation and the execution time in the simulation result 123.

[0059] In step S25, the model reduction unit 113 starts the process of repeating steps S26 to S29 while increasing the dimension by step, starting from the initial dimension. Hereinafter, the dimension of this repeated process will be referred to as the processing target dimension. In step S26, the model generation unit 112 calculates a reduced-dimensional model (see equation (24)), which is a physical model of the processing target dimension.

[0060] In step S27, the simulation unit 115 uses the reduced-dimensional model of the processing target dimension calculated in step S26 to execute a simulation under each evaluation condition in the evaluation condition 122. The simulation unit 115 stores the simulation result and execution time in the simulation result 123.

[0061] In step S28, the error evaluation unit 116 calculates the error of the simulation results in steps S24 and S27. The error is, for example, the maximum value of the errors of each state quantity under each evaluation condition. The error may also be the sum of the errors of each state quantity under multiple boundary conditions.

[0062] In step S29, if the error is equal to or less than the allowable error (step S29→YES), the model reduction unit 113 determines that the dimension to be processed is a reduced dimension, and proceeds to step S30. If the error exceeds the allowable error (step S29→NO), the model reduction unit 113 sets the value obtained by adding the step dimension to the dimension to be processed as the next dimension to be processed, and returns to step S26. In step S30, the display control unit 117 displays the evaluation screen 320 on a display connected to the input / output unit 180.

[0063] <Evaluation Screen> Fig. 5 is a screen configuration diagram of the evaluation screen 320 according to this embodiment. The evaluation screen 320 displays the simulation error and processing time for each dimension. The evaluation starts from 10 dimensions, and at 50 dimensions the error falls below the allowable error of 0.5. The result obtained by the dimension reduction process is 50 dimensions.

[0064] As described above, the low-dimensional model generating device 100 includes the display control unit 117 that outputs the evaluation screen 320 including the error for each dimension of the low-dimensional model.

[0065] Other Physical Models So far, we have described a method of reducing the dimension of a projection matrix generated by the Krylov subspace method for a system matrix of a state equation by singular value decomposition. The present invention is not limited to this, and a physical model may be generated directly from target data for generating the physical model, or a reduced-dimensional model of a physical model may be generated using, for example, dynamic mode decomposition or sparse modeling.

[0066] <Dynamic Mode Decomposition> In the dynamic mode decomposition, matrix X indicating a state is taken as matrix Y indicating a state one time step ahead, and the transformation from matrix X to matrix Y is approximated by a linear transformation matrix A as shown in equation (30). Here, linear transformation matrix A is || Ｆ is the matrix norm, and is the matrix A that minimizes equation (31).

[0067]

[0068] In the dynamic mode decomposition method, the data of the input matrix X and the output matrix Y may be sensor data or data acquired using a simulation model. A method for determining the linear transformation matrix A will be described below. The problem of determining A that minimizes Equation (31) is solved by solving the pseudo-inverse matrix X of X. † By using the above formula, the calculation can be reduced to the formula (32).

[0069]

[0070] When X is subjected to singular value decomposition as shown in equation (33), the pseudo-inverse matrix X † is expressed as equation (34), and equation (35) is obtained.

[0071]

[0072] Here, U is contracted in the same way as in equation (23) to obtain U as shown in equation (36). ｒ Here, x ｉ , v ｉ is a column vector of X and V.

[0073]

[0074] U from the left in equation (35) ｒＴ From the right, U ｒ and multiplying it by , the reduced-dimensional linear transformation matrix A shown in equation (37) ｒ The maximum value (maximum dimension) of r included in equation (36) is the number of data, for example, the number of measured values ​​(number of sensors).

[0075]

[0076] Reduced-dimensional linear transformation matrix A ｒ (system matrix describing a low-dimensional model), it is possible to predict state Y one time step ahead from state X. The process of finding a dimension below the tolerance is as shown in FIG. 3.

[0077] <Sparse Modeling Method> Following the dynamic mode decomposition method, the sparse modeling method may be used. The coefficients in the state equation may be identified using a method such as Lasso regression to construct a low-dimensional prediction model. The time derivative X of the state quantity X is ・ (· on X), the library matrix Θ(X) related to the state quantity X, and the coefficient matrix Ξ are used to express the state equation as shown in equation (38). Note that the maximum value (maximum dimension) of r included in equation (39) is the number of data, for example, the number of measured values ​​(for example, the number of sensors × the number of measurements).

[0078]

[0079] Here, the coefficient matrix Ξ is found by minimizing the norm of the coefficient matrix Ξ. Here, if an appropriate coefficient λ is used to avoid overfitting, the Lasso regression equation (41) is obtained, and by calculating this, the coefficient ξ ｋ can be obtained.

[0080]

[0081] Note that arg min(·) on the right side of equation (41) is the coefficient ξ ’ ｋis the minimum value among the above. Considering the order r of the library matrix Θ(X) (system matrix describing the reduced-dimensional model), the dimension of the reduced-dimensional model changes depending on the order r considered, and by considering a higher order, improvement in the accuracy of the reduced-dimensional model can be expected. However, while adopting a higher order improves accuracy, there is a risk of an increase in processing time. For this reason, a smaller order r is preferable, whereby the difference between the data to be subjected to the reduced-dimensional model and the identified state equation is within the allowable error.

[0082] <Features of the reduced-order model generation device> The reduced-order model generation device generates a reduced-order model whose error from the simulation result with the original physical model is within the tolerance. Such a reduced-order model generation device can generate a reduced-order model with a short simulation time and small error, which can shorten the time for product development, for example.

[0083] <<Modification: Other Physical Models>> The dimension reduction process (see FIG. 3) can be applied to a state equation including a system matrix as described above, and reduces the dimension of the system matrix. Note that a state equation is an equation that allows the time derivative of a state quantity or the state quantity of the next time step to be calculated based on the current state quantity. This is not limited to the above-described reduced-dimensional models, and can also be applied to physical models described by equations including matrices. The dimension reduction process can be used to determine the dimension of a reduced-dimensional model described by an equation including a matrix obtained by reducing the dimension of the matrix.

[0084] As described above, the physical model is described by a mathematical expression including a matrix, and the reduced-order model is described by a mathematical expression with a reduced order of the matrix. Also, the physical model is described by a state equation, and the reduced-order model is described by a state equation including a system matrix with a reduced order of the system matrix included in the state equation of the physical model.

[0085] <<Modification: Evaluation Method of Reduced-Dimensional Model>> In the above-described embodiment, the error of the reduced-dimensional model is the difference between the simulation results of the physical model before the reduction under boundary conditions determined by the experimental design. As another evaluation method, the error of the reduced-dimensional model may be the difference between the results (measured values) obtained in an experiment of a physical phenomenon using an object, rather than a numerical simulation. Note that the boundary conditions when conducting the experiment do not have to be the exact values ​​determined by the experimental design, but may be close values. The measured values ​​obtained in an experiment under boundary conditions of close values ​​can be used as reference values, and the dimensions can be determined so that the error in the results of a simulation using the reduced-dimensional model under boundary conditions of close values ​​falls within the allowable error.

[0086] As explained above, the reference value is a measurement value obtained in an experiment on a physical phenomenon using an object.

[0087] Although several embodiments of the present invention have been described above, these embodiments are merely examples and do not limit the technical scope of the present invention. In the above-described embodiments, the given condition is the allowable error, but it may also be the execution time of the simulation, and the maximum dimension within the allowable time may be found.

[0088] The present invention can take on various other embodiments, and various modifications such as omissions and substitutions can be made without departing from the spirit of the present invention. These embodiments and modifications are included in the scope and spirit of the invention described in this specification, etc., and are also included in the invention described in the claims and their equivalents.

[0089] <Hardware Configuration> The low-dimensional model generation device 100 according to the embodiment described above is realized by a computer 900 having a configuration as shown in Fig. 6, for example. Fig. 6 is a hardware configuration diagram showing an example of the computer 900 that realizes the functions of the low-dimensional model generation device 100 according to the embodiment. The computer 900 includes a CPU 901, a ROM 902, a RAM 903, an SSD 904, an input / output interface 905 (referred to as an input / output I / F (Interface) in Fig. 6), a communication interface 906 (referred to as a communication I / F in Fig. 6), and a media interface 907 (referred to as a media I / F in Fig. 6). The computer 900 may include a hard disk drive (HDD) instead of the SSD 904, or may include an HDD in addition to the SSD 904.

[0090] The CPU 901 operates based on programs stored in the ROM 902 or the SSD 904, and performs control by the control unit 110 in Fig. 1. The ROM 902 stores a boot program executed by the CPU 901 when the computer 900 starts up, programs related to the hardware of the computer 900, and the like. The CPU 901 controls an input device 910 such as a mouse or keyboard, and an output device 911 such as a display or printer, via an input / output interface 905. The CPU 901 acquires data from the input device 910 and outputs generated data to the output device 911 via the input / output interface 905.

[0091] The SSD 904 stores programs executed by the CPU 901 and data used by the programs. The communication interface 906 receives data from other devices (not shown) via a communication network and outputs the data to the CPU 901, and also transmits data generated by the CPU 901 to other devices via the communication network.

[0092] The media interface 907 reads a program or data stored in the recording medium 912 and outputs it to the CPU 901 via the RAM 903. The CPU 901 loads the program from the recording medium 912 onto the RAM 903 via the media interface 907 and executes the loaded program. The recording medium 912 is an optical recording medium such as a DVD (Digital Versatile Disk), a magneto-optical recording medium such as an MO (Magneto Optical Disk), a magnetic recording medium, a conductive memory tape medium, a semiconductor memory, or the like.

[0093] For example, when the computer 900 functions as the low-dimensional model generation device 100 according to the embodiment described above, the CPU 901 of the computer 900 executes a program 128 (see FIG. 6 ) loaded onto the RAM 903, thereby realizing the functions of the low-dimensional model generation device 100. The CPU 901 reads the program from a recording medium 912 and executes it. Alternatively, the CPU 901 may read the program from another device via a communication network, or may install the program 128 from the recording medium 912 onto the SSD 904 and execute it.

[0094] REFERENCE SIGNS LIST 100 Reduced-dimensional model generating device 111 Data receiving unit 112 Model generating unit 113 Model reduction unit 114 Condition generating unit 115 Simulation unit 116 Error evaluation unit 117 Display control unit 121 Model data 122 Evaluation conditions 123 Simulation results 128 Program 320 Evaluation screen

Claims

1. A reduced-dimensional model generation device comprising: a model generation unit that generates a reduced-dimensional model by reducing the dimensions of a physical model that describes a physical phenomenon; and a model reduction unit that determines the dimensions of the reduced-dimensional model such that the error between the results of a simulation using the reduced-dimensional model under specified simulation conditions and a reference value is within an allowable error.

2. The low-dimensional model generating device according to claim 1, wherein the reference value is a result of a simulation using the physical model under predetermined simulation conditions.

3. The low-dimensional model generating device according to claim 1, wherein the reference value is a measurement value obtained in an experiment on the physical phenomenon using an object.

4. The reduced-dimensional model generating device according to claim 1, further comprising a condition generating unit that calculates the predetermined simulation conditions based on an experimental design method.

5. The low-dimensional model generating device according to claim 1, wherein the physical model is described by a mathematical expression including a matrix, and the low-dimensional model is described by a mathematical expression in which the order of the matrix is ​​reduced.

6. The reduced-order model generating device according to claim 5, wherein the physical model is described by a state equation, and the reduced-order model is described by a state equation including a system matrix obtained by reducing the order of a system matrix included in the state equation of the physical model.

7. The low-dimensional model generating device according to claim 1, further comprising a display control unit that outputs an evaluation screen including the error for each dimension of the low-dimensional model.

8. A low-dimensional model generation method, in which a low-dimensional model generation device executes the steps of: generating a low-dimensional model by reducing the dimensions of a physical model that describes a physical phenomenon; and determining the dimensions of the low-dimensional model such that the error between the results of a simulation using the low-dimensional model under specified simulation conditions and a reference value is within an allowable error.

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