Estimation device, learning device, estimation method, learning method, and program

Abstract

To reduce a computational load during learning that is required to calculate an analytical value distribution in an object to be analyzed.SOLUTION: An estimation device 220 calculates n-dimensional dimension-reduced input information, which is reduced-dimensional information corresponding to at least one parameter that affects an analytical value distribution in an object to be analyzed, based on a relationship between the parameter and n-dimensional reduced-dimensional information obtained by performing dimensional reduction of an N-dimensional analytical value distribution for the object to be analyzed. Then, based on the n-dimensional dimension-reduced input information, the estimation device 220 calculates an estimation result of the N-dimensional analytical value distribution corresponding to the parameter using a trained conversion model T capable of estimating the N-dimensional analytical value distribution from the dimension-reduced input information. Here, the conversion model T uses a first conversion model T1 that estimates an m-dimensional intermediate vector based on the dimension-reduced input information and a second conversion model T2 that calculates the estimation result of the analytical value distribution based on the intermediate vector.SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present invention relates to an estimation device, a learning device, an estimation method, a learning method, and a program, and is particularly suitable for use in calculating an analysis value distribution.

Background Art

[0002] In order to quantitatively grasp various physical phenomena, the governing equations (basic equations) that describe the physical phenomena are solved. When solving the governing equations, generally, numerical analysis using the finite element method or the like is performed. In this case, it is necessary to perform numerical analysis for each analysis condition. Therefore, for example, when calculating the distribution of analysis values (hereinafter referred to as analysis value distribution) in the analysis target, such as the distribution of magnetic flux density in a motor core, the calculation load is high. Therefore, it is conceivable to calculate the variables included in the governing equations using a learning model such as machine learning without performing numerical analysis (see Patent Document 1).

[0003] Patent Document 1 discloses creating a prediction model that learns the relationship between the d-axis current, q-axis current, and mechanical angle and the distribution of vector potential at each node of the motor by performing supervised learning. According to Patent Document 1, it is said that the distribution of vector potential can be predicted quickly without going through simulations. Furthermore, in Patent Document 1, a neural network that learns the relationship between a vector obtained by reducing the dimension of the distribution of vector potential by an autoencoder and the d-axis current, q-axis current, and mechanical angle is used to predict the distribution of vector potential, aiming to reduce the computational load required for learning. Note that there is Non-Patent Document 1, which obtains the characteristics of the motor itself to be analyzed by supervised learning. Non-Patent Document 1 discloses using an image showing the absolute value of the magnetic flux density on the rotor at a fixed mechanical angle as the input to a CNN (Convolutional Neural Network) to estimate the average torque and torque ripple of the motor. Also, in the dataset, there is a technique described in Non-Patent Document 2 as a technique for obtaining the Intrinsic Dimension, which is the minimum degree capable of explaining the dataset. Non-Patent Document 2 proposes a mathematical formula for deriving the Intrinsic Dimension from the geometric structure of the dataset.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Non-Patent Documents

[0005]

Non-Patent Document 1

[0006] However, Patent Document 1 does not describe the number of dimensions of the low-dimensionalized vector in the low-dimensionalization of the distribution of the vector potential by the autoencoder. For example, if the number of dimensions of the vector is too small, there is a risk that the distribution of the vector potential cannot be restored. Therefore, it is necessary to select a sufficiently large number of dimensions as the number of dimensions of the vector to be low-dimensionalized. In this case, however, the effect of reducing the computational load is limited. Also, although the technique described in Non-Patent Document 2 can derive the Intrinsic Dimension, it obtains the number of dimensions only for a dataset that is independently and identically distributed. Analytic value distributions such as the distribution of the vector potential almost always have a correlation between neighboring points. Therefore, the technique described in Non-Patent Document 2 cannot be applied to the technique described in Patent Document 1. Thus, if the number of dimensions of the vector to be low-dimensionalized is determined by trial and error, the computational load for determining the number of dimensions of the vector to be low-dimensionalized increases.

[0007] The present invention has been made in view of the above problems, and an object thereof is to reduce the computational load during learning required to calculate the analysis value distribution in the object to be analyzed.

Means for Solving the Problem

[0008] A first example of the estimation device of the present invention is an estimation device that estimates the analysis value distribution in the object to be analyzed, including an estimation information acquisition unit that acquires input information including the value of at least one parameter that affects the analysis value distribution, and based on the relationship between the parameter included in the input information and the low-dimensional information obtained by reducing the dimension of the analysis value distribution for the object to be analyzed, a low-dimensional estimation unit that estimates the low-dimensional input information that is the low-dimensional information corresponding to the input information, and a conversion unit that calculates an estimation result of the analysis value distribution corresponding to the input information using a learned conversion model capable of estimating the analysis value distribution from the low-dimensional input information. The conversion model includes a first conversion model that estimates an intermediate vector based on the low-dimensional input information, and a second conversion model that calculates an estimation result of the analysis value distribution based on the intermediate vector. The number of dimensions of the intermediate vector is larger than the number of dimensions of the low-dimensional input information and smaller than the number of dimensions of the analysis value distribution. A second example of the estimation device of the present invention is an estimation device that estimates the analysis value distribution in the object to be analyzed, including an estimation information acquisition unit that acquires input information including the value of at least one parameter that affects the analysis value distribution, and based on the relationship between the parameter included in the input information and the low-dimensional information obtained by reducing the dimension of the analysis value distribution for the object to be analyzed, a low-dimensional estimation unit that estimates the low-dimensional input information that is the low-dimensional information corresponding to the input information, and a conversion unit that calculates an estimation result of the analysis value distribution corresponding to the input information using a learned conversion model capable of estimating the analysis value distribution from the low-dimensional input information. The number of dimensions of the low-dimensional input information is smaller than the number of dimensions of the parameters constituting the input information.

[0009] The learning device of the present invention is a learning device that calculates a learning model for estimating an analysis value distribution in an object to be analyzed, and includes a learning information acquisition unit that acquires at least one parameter that affects the analysis value distribution and the analysis value distribution, a first learning unit that creates a conversion model by learning the relationship between the low-dimensional information obtained by reducing the dimension of the analysis value distribution of the object to be analyzed and the analysis value distribution corresponding to the low-dimensional information using the analysis value distribution acquired by the learning information acquisition unit, and a second learning unit that creates an estimation model by learning the relationship between the parameter and the low-dimensional information using the parameter and the analysis value distribution acquired by the learning information acquisition unit and the conversion model. The first learning unit creates a first conversion model by learning the relationship between an intermediate vector obtained by reducing the dimension of the analysis value distribution of the object to be analyzed and the analysis value distribution before being reduced to the intermediate vector using the analysis value distribution acquired by the learning information acquisition unit, and creates a second conversion model by learning the relationship between the low-dimensional information obtained by reducing the dimension of the intermediate vector and the intermediate vector before being reduced to the low-dimensional information using the intermediate vector. The number of dimensions of the intermediate vector is larger than the number of dimensions of the low-dimensional information and smaller than the number of dimensions of the analysis value distribution.

[0010] A first example of the estimation method of the present invention is an estimation method for estimating an analysis value distribution in an object to be analyzed, including an estimation information acquisition step of acquiring input information including values of at least one parameter that affects the analysis value distribution, and based on the relationship between the parameter included in the input information and low-dimensional information obtained by reducing the dimension of the analysis value distribution for the object to be analyzed, a low-dimensional estimation step of estimating low-dimensional input information that is low-dimensional information corresponding to the input information, and a conversion step of calculating an estimation result of the analysis value distribution corresponding to the input information using a learned conversion model capable of estimating the analysis value distribution from the low-dimensional input information. The conversion model includes a first conversion model for estimating an intermediate vector based on the low-dimensional input information, and a second conversion model for calculating an estimation result of the analysis value distribution based on the intermediate vector. The number of dimensions of the intermediate vector is larger than the number of dimensions of the low-dimensional input information and smaller than the number of dimensions of the analysis value distribution. A second example of the estimation method of the present invention is an estimation method for estimating an analysis value distribution in an object to be analyzed, including an estimation information acquisition step of acquiring input information including values of at least one parameter that affects the analysis value distribution, and based on the relationship between the parameter included in the input information and low-dimensional information obtained by reducing the dimension of the analysis value distribution for the object to be analyzed, a low-dimensional estimation step of estimating low-dimensional input information that is low-dimensional information corresponding to the input information, and a conversion step of calculating an estimation result of the analysis value distribution corresponding to the input information using a learned conversion model capable of estimating the analysis value distribution from the low-dimensional input information. The number of dimensions of the low-dimensional input information is smaller than the number of dimensions of the parameters constituting the input information.

[0011] The learning method of the present invention is a learning method for calculating a learning model for estimating an analysis value distribution in an object to be analyzed, the method comprising: a learning information acquisition step of acquiring at least one parameter that affects the analysis value distribution and the analysis value distribution; a first learning step of creating a conversion model by learning the relationship between low-dimensional information obtained by reducing the dimensionality of the analysis value distribution for the object to be analyzed and the analysis value distribution corresponding to the low-dimensional information, using the analysis value distribution obtained in the learning information acquisition step; and a second learning step of creating an estimation model by learning the relationship between the parameter and the low-dimensional information, using the parameter and the analysis value distribution obtained in the learning information acquisition step and the conversion model. The first learning step includes creating a first conversion model by learning the relationship between an intermediate vector obtained by reducing the dimensionality of the analysis value distribution for the object to be analyzed and the analysis value distribution before being reduced to the intermediate vector, using the analysis value distribution obtained in the learning information acquisition step, and creating a second conversion model by learning the relationship between low-dimensional information obtained by reducing the dimensionality of the intermediate vector and the intermediate vector before being reduced to the low-dimensional information, using the intermediate vector. The number of dimensions of the intermediate vector is larger than the number of dimensions of the low-dimensional information and smaller than the number of dimensions of the analysis value distribution.

[0012] A first example of the program of the present invention causes a computer to function as each part of the estimation device. A second example of the program of the present invention causes a computer to function as each part of the learning device.

Advantages of the Invention

[0013] According to the present invention, it is possible to reduce the computational load during learning required to calculate the analysis value distribution in the object to be analyzed. Therefore, for example, it is possible to obtain an estimation model of the distribution of analysis values in the object to be analyzed, such as the magnetic flux density distribution in a motor core, in a shorter time.

Brief Description of the Drawings

[0014]

Figure 1

Figure 2

Figure 3A

Figure 3B

Figure 4A

Figure 4B

Figure 5

Mode for Carrying Out the Invention

[0015] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. Note that, regarding length, position, size, interval, etc., when the comparison targets are the same, in addition to the case where they are exactly the same, those that are different within a range not departing from the gist of the invention (for example, those that are different within the tolerance range determined at the time of design) are also included.

[0016] (Inspiration) First, the inspiration obtained by the inventors when arriving at this embodiment will be described. As described in the problems to be solved by the invention, in the technique described in Patent Document 1, numerical analysis such as the finite element method is performed at all calculation positions (positions of mesh nodes in the finite element method) in the analysis target to solve the governing equation, and information on a plurality of variable values (distribution of analysis values such as magnetic flux density) calculated in this way is used as learning data. The larger the number of calculation positions in the analysis target, the larger the combination of analysis values for each position of the analysis target in the analysis value distribution, so many combinations of input information values to a plurality of learning models prepared to explain this are required. Also, usually, the larger the amount of information (number of dimensions) input to the learning model, the more learning data is required. Therefore, it is not easy to create a significant learning model without using a large amount of learning data when performing supervised learning.

[0017] Therefore, the inventors considered that if the amount of information input to the learning model (conversion model T in FIG. 4 described later) could be reduced, the learning load of the learning model could be reduced. Thus, the inventors focused on the fact that in the region to be numerically analyzed, there is a region where the result of numerical analysis can be estimated to some extent from physical knowledge or the like without performing numerical analysis. For example, almost no magnetic flux passes through the slots of a motor. Also, in the teeth of the stator core, the direction of the magnetic flux is generally in the radial direction of the motor. Therefore, even without performing numerical analysis using Maxwell's equations (so-called electromagnetic field analysis) or numerical analysis itself for the magnetic flux density distribution over the details in the slots and teeth, some estimation can be made. In this case, the distribution of the magnetic flux density in the slots and teeth becomes a certain determined distribution. That is, the region where the above-mentioned prediction of the result of numerical analysis to some extent is considered to have little contribution to the output result of the learning model, and it is considered that it may be expressed in relation to other regions.

[0018] Based on this, in order to reduce the computational load for calculating the distribution of analysis values to be estimated, such as the magnetic flux density distribution in a motor core, the inventors conceived of calculating low-dimensional information obtained by reducing the dimension of the analysis value distribution (calculating a distribution of a lower dimension than the analysis value distribution) based on the input information including the value of at least one parameter that affects the analysis value distribution to be estimated, and calculating the analysis value distribution based on the calculated low-dimensional information.

[0019] As a specific example for doing this, in order to reduce the total number of learning data (total number of records) during learning, the inventors of the present invention considered creating a conversion model (learning model) by learning (machine learning) the relationship between low-dimensional information obtained by reducing the dimension of information to be estimated (analytical value distribution), such as the magnetic flux density distribution in a motor core, and the information itself to be estimated. Also, in reality, the analytical value distribution itself changes depending on analytical conditions such as numerical analysis conditions where numerical analysis assumes driving conditions of the motor, etc. From this, by learning (machine learning) the relationship between input information including the value of at least one parameter that affects the analytical value distribution and the aforementioned low-dimensional information, an estimation model (learning model) for estimating low-dimensional input information, which is low-dimensional information corresponding to the input information, is created, and it was conceived to generate the input (low-dimensional input information) of the conversion model according to the analytical conditions for which the analytical value distribution is desired using the estimation model. Thereby, using the estimation model, the low-dimensional information (low-dimensional input information) corresponding to the input information can be quickly obtained, and by inputting the obtained low-dimensional input information into the conversion model, it becomes possible to quickly obtain the analytical value distribution corresponding to the input information.

[0020] As described above, even if the amount of information is reduced by dimensionality reduction (dimension compression), there is no problem in reality as long as the output of the learning model is within an acceptable range, and the low-dimensional input information obtained by the learning model can be converted into the analytical value distribution with appropriate accuracy. Therefore, during learning, after reducing the amount of information (dimension) of the output information in the learning data, the above-mentioned relationship is learned, so the amount of learning data (the number of records indicating the correspondence between the input and the output) can be reduced, and the learning load can be reduced. Also, during estimation, by using the learning model to obtain the low-dimensional input information corresponding to the analytical value distribution to be estimated and converting the low-dimensional input information into the analytical value distribution, an estimation result with a predetermined accuracy can be obtained.

[0021] Here, in order to obtain the distribution of the analysis value (analysis value distribution) in the analysis target, such as the magnetic flux density distribution in the motor core, at least a part of the information that can change the analysis value distribution other than the analysis value distribution to be estimated is used as input to obtain an estimated value of the analysis value distribution. The information that can change the analysis value distribution may specifically be a parameter treated as a constant (constant when formulated in numerical analysis) in the governing equation. At the time of estimation, in order to obtain information to be estimated such as the magnetic flux density distribution using the conversion model from such input information, the input information needs to be associated with the information to be estimated via the low-dimensional input information that becomes the input of the conversion model.

[0022] Thus, as an example of the information that can change the analysis value distribution, when using a parameter treated as a constant in the governing equation, in numerical analysis for solving the governing equation by numerical analysis, the number of discretization regions (e.g., meshes) may be set to a number less than the number of discretization regions that ensures the estimation accuracy by numerical analysis to calculate the above-mentioned low-dimensional input information. Alternatively, a correspondence table associating the input information and the low-dimensional information may be used to calculate the low-dimensional input information corresponding to the input information. For input information not in the correspondence table, after obtaining input information close to the input information in the correspondence table, the low-dimensional input information may be calculated using the correspondence table.

[0023] However, in order to reduce the computational load more, it is preferable to use the above-mentioned estimation model. The above-mentioned estimation model in this case is, for example, a learning model that has learned the relationship between at least one predetermined parameter among the parameters and n-dimensional low-dimensional information capable of calculating variables of N dimensions higher than the n-th order (n < N). By using such a conversion model, the dimension of the data handled by the learning model can be reduced to a low dimension.

[0024] Here, the N-dimensional variable is the variable to be estimated. Also, the n-dimensional reduced input information may be any information that can calculate the N-dimensional analysis value distribution. For example, when representing the magnetic flux density distribution as an image, the n-dimensional reduced input information may be an n-dimensional image obtained by compressing the N-dimensional image representing the magnetic flux density distribution (for example, by omitting the information of some pixels). Also, the n-dimensional reduced input information may be, for example, the feature amount of the N-dimensional image representing the magnetic flux density distribution.

[0025] When calculating the n-dimensional reduced input information dimensionally compressed as described above, it is necessary to calculate the N-dimensional variables from the n-dimensional reduced input information. For example, when the n-dimensional reduced input information is calculated by compressing the N-dimensional image as described above, for example, using a known method used when expanding an image in the field of image processing, the N-dimensional analysis value distribution may be calculated from the n-dimensional reduced input information.

[0026] However, when compressing an N-dimensional image into n dimensions, if the value of n is too small, it may not be possible to calculate the N-dimensional analysis value distribution from the n-dimensional low-dimensional information, or the calculation accuracy of the N-dimensional analysis value distribution may be significantly reduced. On the other hand, if the value of n is too large, the reduction of the calculation load cannot be sufficiently realized. That is, in order to balance the reduction of the calculation load and the calculation accuracy of the N-dimensional analysis value distribution, it is necessary to appropriately determine the value of n. However, when determining the value of n by trial and error, the calculation load for determining the value of n becomes large. Therefore, the inventors conceived of making the aforementioned conversion model include a first conversion model and a second conversion model. The first conversion model is a learning model that learns the relationship between the intermediate vector obtained by reducing the dimension of the analysis value distribution and the analysis value distribution before being reduced to the intermediate vector. The second conversion model is a learning model that learns the relationship between the low-dimensional information obtained by reducing the dimension of the intermediate vector and the intermediate vector before being reduced to the low-dimensional information. In this case, the dimension number m of the intermediate model is larger than the dimension number n of the low-dimensional information and smaller than the dimension number N of the analysis value distribution (n < m < N). By using such an intermediate vector with the dimension number m, it becomes possible to search for a smaller dimension number as the dimension number n of the low-dimensional information.

[0027] For example, the Intrinsic Dimension described in Non-Patent Document 2 is the lowest degree that can represent a dataset. However, in Non-Patent Document 2, as a calculation formula for Intrinsic Dimension, a calculation formula for a dataset with specific characteristics is proposed. On the other hand, in the analysis value distribution, the values are often similar between adjacent positions, and it is difficult to consider it as independent and identically distributed. Even in such a case, if the analysis value distribution is compressed into an intermediate vector with dimensions m (n < m < N) that is larger than n and smaller than N, it becomes possible to make the intermediate vector independent and identically distributed even when the analysis value distribution is not independent and identically distributed. Thereby, based on the intermediate vector, the Intrinsic Dimension can be derived, and the derived Intrinsic Dimension can be determined as the value of n. Note that the method for determining the value of n does not have to be a method for calculating the Intrinsic Dimension.

[0028] The conversion model may be, for example, a learning model using an autoencoder. By using an autoencoder, it is possible to create a more accurate estimation model while suppressing information loss. However, the conversion model is not limited to a learning model using an autoencoder as long as it is a learning model capable of performing data dimensional compression and expansion. For example, the estimation model may be a learning model that performs data dimensional compression and expansion using principal component analysis (PCA).

[0029] On the other hand, the estimation model may be, for example, any machine learning model. For example, the estimation model may be a learning model using SVR (Support Vector Regression), or a learning model using random forest. The estimation model may be a learning model other than a machine learning model.

[0030] Hereinafter, the present invention made based on the above-described findings will be described by taking as an example the case where the analysis target is a motor and the analysis value distribution is the magnetic flux density distribution in the motor. Here, the analysis value is, for example, an analysis value of a variable to be estimated or a variable that can be mutually converted with the variable (hereinafter, these variables are also referred to as estimation target variables). The estimation target variable is, for example, magnetic flux density. In this case, the analysis value distribution is, for example, a magnetic flux density distribution. Note that the distribution is a distribution in a one-dimensional, two-dimensional, or three-dimensional region. When calculating the magnetic flux density distribution of the motor, the governing equation is the Maxwell equation. In the Maxwell equation, in addition to the magnetic flux density, the magnetic field strength is included as a variable. Therefore, the estimation target variable is not limited to the magnetic flux density and may be, for example, the magnetic field strength.

[0031] Also, the magnetic flux density vector B is expressed as B = rotA using the vector potential A. Therefore, as a variable that can be mutually converted with the variable to be estimated (magnetic flux density vector B), for example, the vector potential may be used as the estimation target variable.

[0032] Also, the calculation target of the analysis value distribution (distribution of the variable to be estimated) is not limited to motors such as IPMSM. For example, the calculation target of the analysis value distribution (distribution of the variable to be estimated) may be a rotating electrical machine other than a motor (i.e., a generator). Also, the calculation target of the analysis value distribution (distribution of the variable to be estimated) may be a device other than a rotating electrical machine, such as a transformer.

[0033] Also, the governing equation is not limited to Maxwell's equations. For example, the governing equation may be Newton's equations of motion or the Navier-Stokes equations. The variable to be estimated is determined according to the governing equation. The region of the calculation target of the analysis value distribution (variable to be estimated) is not limited to the region inside an object (solid) or the region around the object, and may be a liquid region or a gas region.

[0034] (IPMSM) In this embodiment, the case of calculating (estimating) the magnetic flux density distribution of an IPMSM (Interior Permanent Magnet Synchronous Motor) is exemplified. Therefore, first, the IPMSM will be outlined.

[0035] FIG. 1 is a diagram showing an example of the configuration of the IPMSM 100. In FIG. 1, a so-called V-shaped IPMSM in which permanent magnets as the poles of the rotor are arranged in a V shape is illustrated. Further, in FIG. 1, a case where the number of poles of the IPMSM 100 (rotor 110) is 8 poles is illustrated (note that the number of poles of the IPMSM 100 is not limited). In FIG. 1, the range PR between the double arrow lines is a part constituting one pole of the IPMSM 100. Note that when the number of poles of the IPMSM 100 (rotor 110) is n poles, the IPMSM 100 has a rotational symmetry relationship of n-fold symmetry with the rotation axis 0 of the IPMSM 100 as the axis of rotational symmetry. n is an integer of 2 or more, and in the example shown in FIG. 1, n is 8 (n = 8). FIG. 1 shows one of four regions obtained by equally dividing a cross section perpendicular to the rotation axis 0 of the IPMSM 100 into four parts. That is, FIG. 1 shows a region constituting two poles of the rotor 110 among the regions of the IPMSM 100. These four regions have a four-fold symmetry relationship with the rotation axis 0 of the IPMSM 100 as the axis of rotational symmetry (4 = 8 poles÷2). Therefore, in FIG. 1, by rotating the region shown in FIG. 1 by 90° each with the center line of the IPMSM 100 as the rotation axis 0, the overall configuration of the cross section of the IPMSM 100 when cut perpendicular to the rotation axis 0 of the IPMSM 100 can be obtained.

[0036] In FIG. 1, the IPMSM 100 includes a rotor 110 and a stator 120. The stator 120 includes a stator core 121 and a stator coil (not shown). The stator 120 generates a rotating magnetic field. Note that in FIG. 1, the illustration of the stator coil included in the stator 120 is omitted. The stator coil (not shown) is installed in each slot 122 of the stator core 121 (for convenience of notation, only one slot is labeled in FIG. 1). The winding method of the stator coil is not limited. The winding method of the stator coil may be a distributed winding or a concentrated winding.

[0037] The rotor 110 rotates about the rotation axis 0 of the IPMSM 100 as the rotation axis. Therefore, the rotation axis 0 of the rotor 110 coincides with the rotation axis 0 of the IPMSM 100. The position of the origin 0 of the coordinates shown in FIG. 1 is the position of the rotation axis 0, but for convenience of notation, these positions are shown as different positions. In FIG. 1, an x-y coordinate system (rectangular coordinate system) with the horizontal direction of FIG. 1 as the x-axis and the vertical direction as the y-axis, and an r-θ coordinate system (polar coordinate (circular coordinate)) with the radial direction of the IPMSM 100 as the radial direction and the rotation angle as the deflection angle are shown together.

[0038] The rotor 110 includes a rotor core 111 and a plurality of permanent magnets per pole. In FIG. 1, the case where the number of permanent magnets per pole is 2 is illustrated (see permanent magnets 112a to 112b). However, the number of permanent magnets per pole is not limited. In the following description, when the permanent magnets 112a to 112b are not distinguished, the permanent magnets 112a to 112b are each referred to as a permanent magnet 112. The rotor core 111 is made of a soft magnetic material. The rotor core 111 is formed, for example, by laminating a plurality of electromagnetic steel sheets.

[0039] As described above, FIG. 1 illustrates the case where a plurality of permanent magnets 112 per pole are installed in the rotor core 111. Therefore, in the rotor core 111, a plurality of magnet holes per pole are formed along a direction parallel to the rotation axis 0 of the rotor core 111 (in the following description, the direction parallel to the rotation axis 0 is referred to as the z-axis direction as needed). The magnet hole is a through hole penetrating in the z-axis direction. The plurality of permanent magnets 112 are each inserted into the magnet hole formed in the rotor core 111 and thereby installed (embedded) in the rotor core 111. As described above, FIG. 1 shows the region constituting two poles of the rotor 110 in the region of the IPMSM 100. FIG. 1 illustrates the case where two permanent magnets 112 per pole are embedded. Therefore, FIG. 1 illustrates the case where a total of 16 permanent magnets are embedded in the rotor core 111. In FIG. 1, for convenience of notation, only the portion constituting one pole of the rotor 110 is labeled, and the labels for the other seven poles of the rotor 110 are omitted.

[0040] In the magnet holes formed in the rotor core 111, the spaces where the permanent magnets 112 do not exist become flux barriers 113a to 113d. The flux barriers 113a to 113d are regions where magnetic flux does not pass, or regions where magnetic flux passes with more difficulty than the regions around the flux barriers 113a to 113d. In the following description, when the flux barriers 113a to 113d are not distinguished, the flux barriers 113a to 113d are referred to as flux barrier 113 as necessary. Here, a case where there is no physical object in the flux barrier 113 is exemplified (that is, a case where the flux barrier 113 is a void (air region) is exemplified). However, a non-magnetic material may be installed in the flux barrier 113. Note that the IPMSM itself may be a known IPMSM and is not limited to the IPMSM 100 illustrated in FIG. 1.

[0041] (Learning device 210 and estimation device 220) Next, the learning device 210 and the estimation device 220 of the present embodiment will be described. FIG. 2 is a diagram showing an example of the functional configuration of the learning device 210 and the estimation device 220. FIG. 3A is a flowchart for explaining an example of the learning method. FIG. 3B is a flowchart for explaining an example of the estimation method.

[0042] The learning device 210 and the estimation device 220 each include, as hardware, for example, one or more hardware processors and one or more memories. The learning device 210 and the estimation device 220 execute various operations by executing one or more programs stored in the memory by one or more hardware processors. Various operations are executed by executing one or more programs stored in the memory by one or more hardware processors. The hardware processor may be, for example, a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit). Also, the learning device 210 and the estimation device 220 may include a CPU and a GPU. Also, the memory may be, for example, a RAM (Random Access Memory) or a ROM (Read Only Memory). Also, the learning device 210 and the estimation device 220 may include a RAM and a ROM. Also, the learning device 210 and the estimation device 220 may include a storage medium other than a RAM and a ROM. Also, the learning device 210 and the estimation device 220 may be realized by dedicated hardware such as an ASIC (Application Specific Integrated Circuit).

[0043] An input device 230a and an input device 230b are communicably connected to the learning device 210 and the estimation device 220, respectively. In the following description, when the input devices 230a and 230b are not distinguished, the input devices 230a and 230b are referred to as the input device 230 as necessary. Also, an output device 240 is communicably connected to the estimation device 220.

[0044] The input device 230 is a device for inputting various types of information into the learning device 210 and the estimation device 220. For example, the input device 230 may include a database. Also, the input device 230 may include a user interface. In this case, the input device 230 includes, for example, a keyboard and a mouse. Also, the input device 230 may include an information processing device (computer) separate from the learning device 210 and the estimation device 220. The number of input devices 230 may be one or two or more. Also, at least one of the input devices 230 may be a device inside the learning device 210 or the estimation device 220. Also, the communication between the input device 230 and the learning device 210 and the estimation device 220 may be wired communication or wireless communication.

[0045] The output device 240 is a device that performs processing based on the information output from the estimation device 220. For example, the output device 240 may include a computer display. Also, the output device 240 may include an information processing device (computer) separate from the estimation device 220. Also, the output device 240 may include a storage medium. The number of output devices 240 may be one or two or more. Also, at least one of the output devices 240 may be a device inside the estimation device 220. Also, the communication between the output device 240 and the estimation device 220 may be wired communication or wireless communication.

[0046] Note that in this embodiment, a case where the learning device 210 and the estimation device 220 are separate devices is illustrated. However, the learning device 210 and the estimation device 220 may be realized as one device. Also, the input device 230a and the output device 240 may also be realized as one device including the learning device 210 and the estimation device 220.

[0047] ((Learning Device and Learning Method)) First, an example of the learning device and the learning method of this embodiment will be described. In the learning device and the learning method, the above-described conversion model T and estimation model E are created. In FIG. 2, in this embodiment, an example is given where the learning device 210 includes a learning information acquisition unit 211, a first learning unit 212, a second learning unit 213, a storage unit 214, and an output unit 215. In this embodiment, an example is given where the storage unit 214 is a storage medium provided in the learning device 210. However, the storage unit 214 may be external to the learning device 210.

[0048] <Learning information acquisition unit 211, step S311> The learning information acquisition unit 211 acquires at least one parameter (hereinafter also simply referred to as a parameter) that affects the analysis value distribution in the object to be analyzed and the analysis value distribution. As described above, in this embodiment, an example is given where the analysis value distribution is a magnetic flux density distribution. At least one predetermined parameter among the parameters treated as constants in the governing equation and the N-dimensional analysis value (estimated target variable) corresponding to the parameter are acquired (step S311).

[0049] The parameter may include the driving conditions of the object to be analyzed and the object conditions of the object to be analyzed itself. The driving conditions may include at least one of the amplitude and the advance angle of the stator current. The object conditions may include information for specifying the shape of the rotor. In this embodiment, an example is given where the parameter includes the amplitude of the stator current, the advance angle, and information for specifying the shape of the rotor. In a soft magnetic material such as an annular electromagnetic steel sheet constituting the rotor core, generally, bridges, flux barriers, magnet holes, etc. are formed, but the information for specifying the shape of the rotor may be information for specifying the regions (shape, position, size) occupied by these components in the soft magnetic material or information for specifying the physical properties of the components.

[0050] Also, the parameters are determined according to the analysis purpose. For example, when it is desired to know the influence of current, the parameters related to current are set as the parameters. If it is the shape, the shape is set as the parameter. Also, let the number of dimensions of the parameters constituting the input information be p. The number of dimensions p of the parameters constituting the input information corresponds to the number of parameters constituting the input information (the number of parameters that need to be input to the estimation model E to estimate the low-dimensional information (low-dimensional input information)). For example, when the input information is constituted by the amplitude and phase angle of the stator current, the width and length of the permanent magnet 112, and the width and length of the flux barrier 113, the number of dimensions p of the parameters constituting the input information is 6. However, the shapes and sizes of all the permanent magnets 112 are the same, and the shapes and sizes of all the flux barriers 113 are the same. Also, in the present embodiment, the case where the number of dimensions n of the low-dimensional information is smaller than the number of dimensions p of the parameters constituting the input information (the case of n < p) is exemplified.

[0051] The N-dimensional analysis value (estimated target variable) corresponding to the parameter is, for example, the N-dimensional analysis value calculated by performing numerical analysis using the parameter as a constant of the governing equation. The method of numerical analysis may be a known method such as the finite element method. In the following description, in order to distinguish from the parameters acquired by the estimation information acquisition unit 221 described later, the parameters acquired by the learning information acquisition unit 211 are referred to as learning parameters as necessary.

[0052] The parameters may be all or some of the parameters treated as constants in the governing equation. As described above, in this embodiment, the case of calculating (estimating) the magnetic flux density distribution of the IPMSM 100 is exemplified. In this case, the learning parameters may include, for example, information for specifying the amplitude of the stator current (excitation current), the advance angle, and the shape of the rotor 110. The shape of the rotor 110 includes, for example, the width and length of the permanent magnet 112 and the width and length of the flux barrier 113. Also, for example, parameters such as the number of poles, the outer diameter and inner diameter of the stator core 121, the outer diameter and inner diameter of the rotor core 111, the number of slots 122, the rotational speed of the IPMSM 100, and the physical property values of the materials may be separately set in the learning device 210 as fixed values. In this case, these parameters are excluded from at least one parameter that affects the analytical value distribution in the object to be analyzed described above. However, these parameters may be included in the learning parameters. Note that the parameters treated as constants when solving the governing equation include not only the constants included in the governing equation but also the constants in the mathematical formula describing the boundary conditions when performing numerical analysis.

[0053] The analytical value (variable to be estimated) is, for example, a variable calculated by performing numerical analysis on the governing equation. When using the finite element method as the numerical analysis method, the analytical value is, for example, the variable to be estimated at each node of the mesh. In this case, N is the total number of nodes of the mesh. As described above, in this embodiment, the case of calculating (estimating) the magnetic flux density distribution of the IPMSM 100 is exemplified. Also, as described later, in this embodiment, the case where the conversion model T is a learning model using a convolutional autoencoder is exemplified. Therefore, in this embodiment, the case where the analytical value is image information is exemplified.

[0054] In the image constituting the analytical value distribution (distribution of the variable to be estimated), for example, one pixel corresponds to one node. Note that the image constituting the analytical value distribution may be compressed. In this case, N is less than the total number of nodes of the mesh. In this case, one or more of the plurality of nodes of the mesh are not represented by the image. Further, the pixel value (gray level value) of each pixel is, for example, a value corresponding to an analysis value (in this embodiment, magnetic flux density). The pixel value (gray level value) of each pixel may be a value corresponding to the magnitude (absolute value) of the magnetic flux density vector, or may be a value corresponding to the value of a predetermined direction component of the magnetic flux density vector. Such a method of representing the magnetic flux density distribution in an image may be realized by a known method as described in Non-Patent Document 1. Further, in this embodiment, a case where the number of dimensions (=N) of the analysis value distribution is the total number of pixels of the image constituting the analysis value distribution is illustrated. For example, when an image representing a magnetic flux density distribution is an image of 128×128 pixels, it is assumed that the image represents an analysis value distribution of 16,384 (=128×128) dimensions. In the following description, an image representing such a magnetic flux density distribution is referred to as an N-dimensional image as necessary.

[0055] In this embodiment, a case where the learning information acquisition unit 211 acquires the above learning parameters and the analysis value distribution from the input device 230a is illustrated. As described above, the input device 230a may include a database. In this case, the learning information acquisition unit 211 may acquire, for example, the learning parameters and the analysis value distribution stored in the database. Further, the input device 230a may include a user interface. In this case, the learning information acquisition unit 211 may acquire, for example, the learning parameters input-operated with respect to the user interface. Further, the input device 230a may include an information processing device. In this case, the learning information acquisition unit 211 may receive, for example, the learning parameters and the analysis value distribution transmitted from the information processing device.

[0056] Further, the learning information acquisition unit 211 may acquire the analysis value distribution by performing numerical analysis using, for example, the finite element method (by the learning information acquisition unit 211 itself) without acquiring the analysis value distribution from the input device 230a. In this case, the learning information acquisition unit 211 may acquire information necessary for performing numerical analysis (information such as the position, size, and shape of the mesh) from the input device 230a.

[0057] <First learning unit 212, storage unit 214, step S312> The first learning unit 212 creates a conversion model T that learns the relationship between the low-dimensional information obtained by reducing the dimensionality of the analysis value distribution for the object to be analyzed and the analysis value distribution corresponding to the low-dimensional input information, using the analysis value distribution acquired by the learning information acquisition unit 211 (step S312). Specifically, the conversion model T is, for example, a learning model that learns the relationship between an N-dimensional analysis value distribution, an n-dimensional low-dimensional information calculated based on the N-dimensional analysis value distribution and having a lower order than N, and the N-dimensional analysis value distribution corresponding to the n-dimensional low-dimensional information. Note that the n-dimensional low-dimensional information may be information obtained by compressing the N-dimensional analysis value distribution so that it can be converted into the N-dimensional analysis value distribution. The n-dimensional low-dimensional information may be, for example, a feature amount of an N-dimensional image.

[0058] FIG. 4A is a diagram for explaining an example of the concept of a learning model. In FIG. 4A, both the information input to the conversion model T and the information output from the conversion model T are N-dimensional analysis value distributions (N-dimensional images in the present embodiment). FIG. 4B is a diagram for explaining an example of the learning method (creation method) of the conversion model T.

[0059] In the present embodiment, the conversion model T includes a first conversion model T1 and a second conversion model T2. The first conversion model T1 is a learning model that learns the relationship between an intermediate vector obtained by reducing the dimensionality of the analysis value distribution for the object to be analyzed and the analysis value distribution before reducing the dimensionality to the intermediate vector, using the analysis value distribution acquired by the learning information acquisition unit 211. The second conversion model T2 is a learning model that learns the relationship between the low-dimensional information obtained by reducing the dimensionality of the intermediate vector and the intermediate vector before reducing the dimensionality to the low-dimensional information, using the intermediate vector.

[0060] In the present embodiment, a case where the conversion model T is a learning model using an autoencoder is exemplified. In this case, the conversion model T includes, for example, a first conversion model T1 including a first encoder 411 and a first decoder 412, and a second conversion model T2 including a second encoder 413 and a second decoder 414. Note that the conversion model T is not limited to a learning model using an autoencoder.

[0061] The first encoder 411 performs dimensionality compression on the N-dimensional analytical value distribution. As a result, low-dimensional information of m(>n) dimensions is calculated. Although the intermediate vector is also low-dimensional information obtained by reducing the dimensionality of the N-dimensional analytical value distribution, hereinafter, in order to distinguish it from the aforementioned low-dimensional information of n dimensions, the low-dimensional information of m dimensions is referred to as an intermediate vector here. When the conversion model T (the first conversion model T1) is a learning model using a convolutional autoencoder, the m-dimensional intermediate vector is, for example, information representing the feature amount of an N-dimensional image. For example, an N-dimensional image of 128×128 pixels is dimensionally compressed into feature amounts of the dimension (m) specified by the user.

[0062] The second encoder 413 performs dimensionality compression on the m-dimensional intermediate vector. As a result, low-dimensional information of n dimensions is calculated. When the conversion model T (the second conversion model T1) is a learning model using an autoencoder, the low-dimensional information of n dimensions is, for example, information representing the feature amount of the intermediate vector. Also, the value of n is determined using, for example, the value of n' in the following formula (1).

[0063]

Equation

[0064] Here, A is the number of teacher data. [x (1) , x (2) , ···, x (i) , ···, x (A) is a group of intermediate vectors that is a set of intermediate vectors in each teacher data. In formula (1), the number of analytical value distributions that are teacher data is set as A. For each of the A analytical value distributions, the A intermediate vectors obtained by applying the first encoder 411 are included in the group of intermediate vectors [x (1) , x (2) , ···, x (i) , ···, x (A) . x (i) is the i-th intermediate vector (m dimensions) (the i-th element of the group of intermediate vectors). T j (x(i) ) is the Euclidean distance between the i-th intermediate vector and the intermediate vector that has the j-th largest Euclidean distance among the A intermediate vectors with the i-th intermediate vector.

[0065] The second decoder 414 converts n-dimensional low-dimensional information into an m-dimensional intermediate vector. In the present embodiment, the second decoder 414 calculates an m-dimensional feature amount.

[0066] The first decoder 412 converts an m-dimensional intermediate vector into an N-dimensional analysis value distribution. In the present embodiment, the first decoder 412 calculates an N-dimensional image.

[0067] The first learning unit 212 creates a conversion model T by performing learning using the analysis value distribution acquired by the learning information acquisition unit 211 as learning data. In the present embodiment, a case is exemplified in which the first learning unit 212 creates a conversion model T by performing learning using only learning data without using teacher data (correct labels) (that is, unsupervised learning). However, the first learning unit 212 may create a conversion model T by performing supervised learning.

[0068] In the learning of the conversion model T, first, the first learning unit 212 learns the first encoder 411 and the first decoder 412 using the analysis value distribution. Next, the first learning unit 212 determines the value of n using the intermediate vector obtained by the learning of the first encoder 411 and the first decoder 412 and the formula (1). The value of n needs to be larger than the value of n' calculated by the formula (1). For example, the first learning unit 212 may determine the value of n as the ceiling value of the value of n' calculated by the formula (1). In the present embodiment, a case is exemplified in which the first encoder 411 and the first decoder 412 are convolutional autoencoders.

[0069] After the first learning unit 212 learns the first encoder 411 and the first decoder 412 as described above to determine the value of n, it learns the second encoder 413 and the second decoder 414 using the value of n. In this embodiment, a case where the second encoder 413 and the second decoder 414 are normal autoencoders is exemplified. Since the learning methods of the first encoder 411, the first decoder 412, the second encoder 413, and the second decoder 414 themselves can be realized by various known methods as learning methods of autoencoders, detailed descriptions thereof are omitted here.

[0070] As described above, in this embodiment, a case where the magnetic flux density distribution of the IPMSM 100 is calculated (estimated) as an N-dimensional analysis value distribution is exemplified. In this case, it is preferable to calculate the magnetic flux density distribution of the IPMSM 100 over one period of the time period. Therefore, in this embodiment, a case where the magnetic flux density distribution of the IPMSM 100 is calculated at each of a plurality of timings obtained by dividing (for example, equally dividing) one period of the magnetic flux density is exemplified. In this case, the first learning unit 212 creates a conversion model T at each of the plurality of timings. In FIG. 4, the timing ts corresponds to the first timing of one period. The timing te corresponds to the last timing of one period. Also, assuming that the time step is Δt and the timing te is ts + M × Δt (M is a natural number). In this case, the first learning unit 212 creates, for example, M + 1 conversion models T at each of the timings from the timing ts, the timing ts + Δt, the timing ts + 2 × Δt, ··· the timing ts + (M - 1) × Δt, and the timing ts + M × Δt (= te). At this time, the first learning unit 212 creates the conversion model T at the timing t by using the N-dimensional image representing the magnetic flux density distribution at the timing t as learning data. The first learning unit 212 stores the conversion model T created as described above in the storage unit 214.

[0071] <The second learning unit 213, the storage unit 214, step S313> The second learning unit 213 creates an estimation model E by learning the relationship between at least one parameter that affects the analysis value distribution in the object to be analyzed, and the dimension-reduced input information that is the dimension-reduced information of the analysis value distribution for the object to be analyzed, using the parameter and the analysis value distribution obtained by the learning information acquisition unit 211, and the conversion model T (step S313).

[0072] In FIG. 4, at least one parameter that affects the analysis value distribution in the object to be analyzed is input to the estimation model E. Further, n-dimensional dimension-reduced input information is output from the estimation model E. The n-dimensional dimension-reduced input information is the n-dimensional information to be calculated in the second encoder 413 of the conversion model T (second conversion model T2). In the present embodiment, the case where the n-dimensional dimension-reduced input information is information representing the feature amount of the N-dimensional image is exemplified.

[0073] In the present embodiment, the case where the second learning unit 213 creates the estimation model E by performing learning using the learning parameter and the analysis value distribution obtained by the learning information acquisition unit 211, and the conversion model T created by the first learning unit 212 is exemplified.

[0074] For example, the second learning unit 213 extracts the analysis value distribution corresponding to the learning parameter obtained by the learning information acquisition unit 211 from the analysis value distribution obtained by the learning information acquisition unit 211. The analysis value distribution corresponding to the learning parameter is, for example, an N-dimensional analysis value distribution calculated by performing numerical analysis using the learning parameter as a constant of the governing equation.

[0075] The second learning unit 213 obtains the n-dimensional dimensionality-reduced input information calculated by the second encoder 413 by inputting the extracted N-dimensional analysis value distribution into the first conversion model T1 (first encoder 411) and then inputting the m-dimensional intermediate vector calculated by the first encoder 411 into the second conversion model T2 (second encoder 413). The second learning unit 213 uses, as input data, the parameters specified by the learning parameters used as keys when extracting the analysis value distribution. Further, the second learning unit 213 uses, as teacher data (correct labels), the n-dimensional dimensionality-reduced information calculated by the second encoder 413 by inputting the m-dimensional intermediate vector calculated by the first encoder 411 by inputting the extracted N-dimensional analysis value distribution into the first conversion model T1 (first encoder 411) and then inputting it into the second conversion model T2 (second encoder 413). The second learning unit 213 calculates the estimation model E by performing supervised learning using these input data and teacher data. In this embodiment, a case where the N-dimensional analysis value distribution is an N-dimensional image is exemplified. In this case, the second learning unit 213 may specify the relationship between the pixel information such as the color represented by each pixel of the N-dimensional image and the value of the magnetic flux density using a table or the like that associates the two, and it becomes possible to convert the pixel information of each pixel into the value of the magnetic flux density. Further, such specification may be performed outside the second learning unit 213. In this embodiment, a case where the N-dimensional analysis value distribution is an N-dimensional image is exemplified. In this embodiment, a case where the n-dimensional dimensionality-reduced input information is a feature amount of an N-dimensional image is exemplified. Therefore, the n-dimensional dimensionality-reduced input information (feature amount of the N-dimensional image) is converted into an N-dimensional image by a known method.

[0076] Note that in FIG. 4A, the dashed line from the "dimensionality-reduced information (n dimensions)" in the conversion model T to the output "dimensionality-reduced input information (n dimensions)" of the estimation model E indicates that the n-dimensional dimensionality-reduced information calculated by inputting the m-dimensional intermediate vector calculated by the first encoder 411 into the second encoder 413 is the teacher data (correct label) used when creating the estimation model E. As described above, in this embodiment, an example is given in which the first encoder 411 and the second encoder 413 are used during the learning of the estimation model E, and the first decoder 412 and the second decoder 414 are not used.

[0077] As described above, in this embodiment, an example is given in which the magnetic flux density distribution of the IPMSM 100 is calculated at each of a plurality of timings obtained by dividing (for example, equally dividing) one period of the magnetic flux density. In this case, the second learning unit 213 creates an estimation model E at each of the plurality of timings. In the example shown in FIG. 4, the second learning unit 213 creates, in the same manner as the conversion model T, for example, M + 1 estimation models E at each of the timings from the timing ts, the timing ts + Δt, the timing ts + 2×Δt, ··· the timing ts + (M - 1)×Δt, and the timing ts + M×Δt (= te). At this time, the second learning unit 213 uses, as teacher data (correct label) for creating the estimation model E at the timing t, the m-dimensional intermediate vector calculated by inputting the N-dimensional image representing the magnetic flux density distribution at the timing t to the first encoder 411 and the n-dimensional information calculated by inputting the result to the second encoder 413. Further, the second learning unit 213 uses, as input data for creating the estimation model E at the timing t, the parameter corresponding to the magnetic flux density distribution (N-dimensional analysis value distribution) at the timing t among the parameters included in the learning parameters acquired by the learning information acquisition unit 211. Note that parameters that do not change in one period have the same value at each timing in one period.

[0078] As described above, the estimation model E may be, for example, any machine learning model created by supervised learning. Since the learning method of the estimation model E itself can be realized by various known methods as the learning method of a machine learning model, detailed description thereof is omitted here. The second learning unit 213 stores the estimation model E created as described above in the storage unit 214.

[0079] Here, it is preferable that the learning parameters acquired by the learning information acquisition unit 211 include the number of parameters necessary for the second learning unit 213 to create the estimation model E. For example, when the learning parameters include information for specifying the amplitude of the stator current (excitation current), the advance angle, and the shape of the rotor 110, for example, the amplitude of the stator current (excitation current), the advance angle, and the shape of the rotor 110 at one timing t become the parameters at one timing t. The learning information acquisition unit 211 acquires the parameters at each timing t for one cycle as such parameters. The learning information acquisition unit 211 acquires a set of the number of parameters necessary for the learning to create the estimation model E, with the parameters at each timing t for one cycle as a set. The larger the number of sets of parameters acquired in this way, the higher the calculation accuracy of the n-dimensional reduced-dimensional input information calculated (estimated) by the estimation model E, but the higher the calculation load during learning. Conversely, the smaller the number of sets of parameters, the lower the calculation load during learning, but the lower the calculation accuracy of the n-dimensional reduced-dimensional input information calculated (estimated) by the estimation model E. The number of sets of parameters specified by the learning parameters acquired by the learning information acquisition unit 211 may be determined from such a perspective. This also applies to the number of N-dimensional analysis value distributions (N-dimensional images) acquired by the learning information acquisition unit 211.

[0080] <Output unit 215> The output unit 215 outputs the conversion model T and the estimation model E stored in the storage unit 214 to the estimation device 220. The output unit 215 may output the conversion model T and the estimation model E to the estimation device 220 in response to a request from the estimation device 220. Also, the output unit 215 may output the conversion model T and the estimation model E to the estimation device 220 regardless of a request from the estimation device 220. For example, the output unit 215 may output the conversion model T and the estimation model E to the estimation device 220 when a model output instruction is input from the input device 230a. Also, the estimation device 220 may be able to refer to the conversion model T and the estimation model E stored in the storage unit 214. In this case, the learning device 210 may not include the output unit 215.

[0081] ((Estimation Device and Estimation Method)) Next, an example of the estimation device and estimation method of the present embodiment will be described. In the estimation device and estimation method, an N-dimensional analysis value distribution is calculated (estimated). In FIG. 2, in the present embodiment, a case where the estimation device 220 includes an estimation information acquisition unit 221, a low-dimensional estimation unit 222, a conversion unit 223, and an output unit 224 is illustrated as an example.

[0082] <Estimation Information Acquisition Unit 221, Step S321> The estimation information acquisition unit 221 acquires input information including the value of at least one parameter that is treated as a constant when solving the governing equation (step S321). In the following description, the parameter acquired by the estimation information acquisition unit 221 is referred to as an estimation parameter as necessary.

[0083] Here, it is preferable that the types of learning parameters and the types of estimation parameters are the same. For example, when the learning parameters include the amplitude of the stator current (excitation current), the advance angle, and the shape of the rotor 110, the estimation information acquisition unit 221 acquires the amplitude of the stator current (excitation current), the advance angle, and the shape of the rotor 110 as estimation parameters (input information). Also, the number of sets of estimation parameters acquired by the estimation information acquisition unit 221 may be, for example, one set or two or more sets.

[0084] In this embodiment, a case where the estimation information acquisition unit 221 acquires the above-described estimation parameters from the input device 230b is exemplified. As described above, the input device 230b may include a database. In this case, the estimation information acquisition unit 221 may acquire, for example, the estimation parameters stored in the database. Further, the input device 230b may include a user interface. In this case, the estimation information acquisition unit 221 may acquire, for example, the estimation parameters input-operated on the user interface. Further, the input device 230b may include an information processing device. In this case, the estimation information acquisition unit 221 may receive, for example, the estimation parameters transmitted from the information processing device.

[0085] <Low-dimensional estimation unit 222, step S322> The low-dimensional estimation unit 222 calculates low-dimensional input information, which is low-dimensional information obtained by reducing the dimensionality of the analysis value distribution, based on the estimation parameters acquired by the estimation information acquisition unit 221 (step S322). In this embodiment, a case where, when the estimation parameters are input to the estimation model E, a feature amount of an N-dimensional image is output as an example of the low-dimensional input information of n dimensions from the estimation model E is exemplified. Further, in this embodiment, a case where the low-dimensional estimation unit 222 calculates the feature amounts of the N-dimensional image at each of a plurality of timings t obtained by dividing (for example, equally dividing) one cycle period of the magnetic flux density using the estimation model E at the timing t is exemplified.

[0086] <Conversion unit 223, step S323> The conversion unit 223 calculates an N (N>n)-dimensional analysis value distribution based on the n-dimensional dimensionality-reduced input information calculated by the low-dimensional estimation unit 222 (step S323). In the present embodiment, as an example of the n-dimensional dimensionality-reduced input information, when the feature amount of the N-dimensional image calculated by the low-dimensional estimation unit 222 is input to the first decoder 412, as an example of the m-dimensional intermediate vector, an m-dimensional vector is output from the first decoder 412, and when the m-dimensional intermediate vector output from the first decoder 412 is input to the second decoder 414, as an example of the N-dimensional analysis value distribution, the case where an N-dimensional image is output from the second decoder 414 is illustrated. Further, in the present embodiment, an example is illustrated in which the conversion unit 223 calculates the N-dimensional image at each of a plurality of timings t obtained by dividing (for example, equally dividing) one period of the magnetic flux density using the conversion model T at the timing t.

[0087] Note that in FIG. 4, the solid line from the output “dimensionality-reduced input information (n dimensions)” of the estimation model E to the “low-dimensional information (n dimensions)” in the conversion model T indicates that the n-dimensional dimensionality-reduced input information (in the present embodiment, the feature amount of the N-dimensional image) calculated by the estimation model E is input to the first decoder 412 when calculating (estimating) the N-dimensional analysis value distribution (in the present embodiment, the N-dimensional image).

[0088] As described above, in the present embodiment, an example is illustrated in which the first decoder 412 and the second decoder 414 are used and the first encoder 411 and the second encoder 413 are not used when calculating (estimating) the N-dimensional image.

[0089] <Output unit 224, step S324> The output unit 224 outputs information for specifying the N-dimensional analysis value distribution calculated by the conversion unit 223. As described above, the output device 240 may include a computer display. In this case, the output unit 224 causes, for example, information for specifying the N-dimensional analysis value distribution to be displayed on the computer display. Further, the output device 240 may include an information processing device. In this case, the output unit 224 may transmit, for example, information for specifying the N-dimensional analysis value distribution to the information processing device. Further, the output device 240 may include a storage medium. In this case, the output unit 224 may store, for example, information for specifying the N-dimensional analysis value distribution in the storage medium.

[0090] (Calculation example) Next, a calculation example will be described. In this calculation example, the magnetic flux density distribution of the IPMSM 100 shown in FIG. 1 was calculated by each of the method of the present embodiment and the method of performing numerical analysis (electromagnetic field analysis) using the finite element method.

[0091] In this calculation example, the number of poles of the IPMSM was set to 8. Further, the number of slots of the IPMSM was set to 24. Further, as the excitation conditions, the values of the currents of the U-phase, V-phase, and W-phase were set to 0 A, -17.3 A, and 17.3 A, respectively. Although the configuration and analysis conditions of the IPMSM to be analyzed other than this are not explicitly shown, these are the same in any method.

[0092] As the conversion model T, an autoencoder (a convolutional autoencoder and a normal autoencoder) in which the dimension of the data input to the first encoder 411 and the dimension of the data output from the first decoder 412 are each 16384 (= 128 × 128) dimensions, and the dimension of the data input to the second encoder 413 and the dimension of the data output from the second decoder 414 (i.e., the dimension of the intermediate vector) are each 128 dimensions, and an autoencoder in which the dimension of the data output from the first encoder 411 and the dimension of the data input to the first decoder 412 (i.e., the dimension of the feature data) are each 8 dimensions were created by unsupervised learning and used as an estimation model. As a result of using the intermediate vector and equation (1), the Intrinsic Dimension was calculated to be 7.62. Therefore, by rounding up 7.62 and converting it to an integer, 8 was determined as the number of dimensions n of the feature data. Also, a machine learning model using a neural network was created by supervised learning and used as a conversion model. In the supervised learning for creating the conversion model, 400 sets of data sets were used as a set of input data and teacher data (correct labels). Also, as a parameter input to the conversion model, a parameter related to the shape of the rotor was used. Also, the number of dimensions p of the parameters constituting the input information was set to 36.

[0093] FIG. 5 is a diagram showing an example of the estimation result of the magnetic flux density distribution of the IPMSM. In FIGS. 5(a) and 5(b), the magnitude (value) of the x-component B of the magnetic flux density vector is represented by density. x of the magnetic flux density vector is represented by density.

[0094] Also, the horizontal axes in FIGS. 5(a) and 5(b) are the radial distance r of the polar coordinates shown in FIG. 1. In the region close to the rotation axis of the IPMSM (refer to the rotation axis 0 in FIG. 1), that is, in the peripheral region of the shaft, almost no magnetic flux passes through. Therefore, in FIGS. 5(a) and 5(b), the minimum value of the horizontal axis is set to a position that is 0.3 times the radius R of the stator (=0.3R) away from the rotation axis of the IPMSM along the radial direction (radial distance direction) of the IPMSM. Note that the “→ outer peripheral side” shown in FIGS. 5(a) and 5(b) indicates that the larger the value of the horizontal axis (the right side), the more it is the position on the outer peripheral side of the IPMSM.

[0095] Also, the vertical axes in FIGS. 5(a) and 5(b) are the angular deviation θ of the polar coordinates shown in FIG. 1. Here, in FIGS. 5(a) and 5(b), the minimum value and the maximum value of the vertical axis are set to 0° and 45°, respectively. That is, FIGS. 5(a) and 5(b) show the magnetic flux density distribution for one pole.

[0096] Comparing FIGS. 5(a) and 5(b), the magnetic flux density distribution of the IPMSM calculated by the method of this embodiment (FIG. 5(b)) is similar to the magnetic flux density distribution of the IPMSM calculated using the finite element method (FIG. 5(a)). Also, in the method of this embodiment, when the parameters are input into the conversion model, the magnetic flux density distribution can be instantaneously calculated from the dimension calculation model. Therefore, with the method of this embodiment, a magnetic flux density distribution that can reproduce the characteristics of the magnetic flux density distribution calculated using the finite element method can be calculated in a short time.

[0097] (Summary) As described above, in this embodiment, the estimation device 220 calculates the n-dimensional (n < N) low-dimensional input information, which is the low-dimensional information corresponding to the parameter, based on the relationship between at least one parameter (input information) that affects the analysis value distribution in the analysis object and the N-dimensional analysis value distribution of the analysis object reduced to a low dimension. Then, the estimation device 220 calculates the estimation result of the N-dimensional analysis value distribution corresponding to the parameter using the learned conversion model T that can estimate the N-dimensional analysis value distribution from the low-dimensional input information based on the n-dimensional low-dimensional input information.

[0098] Therefore, for example, without performing supervised learning that uses the N-dimensional analysis value distribution as the correct label for a parameter set consisting of one or more that constitutes the input information, by obtaining the relationship between the parameter set and the low-dimensional input information through learning or the like, the N-dimensional analysis value distribution corresponding to the input information can be calculated (estimated). Thus, the computational load during learning required to calculate the analysis value distribution (for example, variables (unknowns) included in the governing equation) can be reduced. For example, the distribution of analysis values in the analysis object, such as the magnetic flux density distribution in the motor core, can be obtained in a significantly shorter time compared to the case of exactly solving the governing equation.

[0099] At this time, the dimension number n of the low-dimensional input information is set using, as the conversion model T, a first conversion model T1 that estimates an m-dimensional (n < m < N) intermediate vector based on the low-dimensional input information and a second conversion model T2 that calculates the estimation result of the analysis value distribution based on the intermediate vector. By configuring in this way, the dimension number n of the low-dimensional input information that can calculate the N-dimensional analysis value distribution with high accuracy can be determined without obtaining the value of n through trial and error. Therefore, the load during learning can be further reduced.

[0100] Also, in the present embodiment, the number of dimensions n of the dimension-reduced input information is made smaller than the number of dimensions p of the parameters constituting the input information (the number of parameters constituting the input information). By doing so, the number of dimensions of the input information can be compressed, so that the effect of reducing the computational load during learning can be enhanced. For example, when optimizing the shape of a soft magnetic material (electromagnetic steel sheet) constituting the core of a rotating electrical machine, the characteristics of the rotating electrical machine are calculated while changing this shape. According to the above-described embodiment, the relationship between the shape of the soft magnetic material and the distribution of analytical values such as the magnetic flux density distribution can be efficiently obtained, so that the efficiency of shape optimization can be enhanced.

[0101] Also, in the present embodiment, the estimation device 220 uses, as the conversion model T, a learning model using an autoencoder. Therefore, the feature amount of the N-dimensional analytical value distribution can be calculated as the n-dimensional dimension-reduced input information. Thus, the number of dimensions of the n-dimensional dimension-reduced input information can be made lower.

[0102] Also, in the present embodiment, the estimation device 220 calculates the Intrinsic Dimension based on the intermediate vector and calculates the value of n using the Intrinsic Dimension. Therefore, by setting n based on the value calculated thereby, an appropriate n such as the minimum n (for example, the value of the Intrinsic Dimension or the smallest integer value larger than the value of the Intrinsic Dimension) can be set. Thus, the computational load required for calculating the analytical value distribution can be more effectively reduced.

[0103] (Other Embodiments) The above-described embodiment of the present invention can be realized by a computer executing a program. A computer-readable recording medium having the program recorded thereon and a computer program product such as the program can also be applied as an embodiment of the present invention. Examples of the recording medium that can be used include a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a non-volatile memory card, and a ROM. The embodiment of the present invention can be realized by a PLC (Programmable Logic Controller) or dedicated hardware such as an ASIC (Application Specific Integrated Circuit). Furthermore, the above-described embodiments of the present invention are merely examples of the implementation of the present invention, and the technical scope of the present invention should not be interpreted as being limited by these. In other words, the present invention can be implemented in various forms without departing from its technical concept or main features.

[0104] The disclosure of the above embodiment can be, for example, as follows. [Disclosure 1] An estimation device for estimating an analytical value distribution in an analysis object, comprising: an estimation information acquisition unit that acquires input information including a value of at least one parameter that affects the analytical value distribution; a low-dimensional estimation unit that estimates reduced-dimensional input information, which is low-dimensional information corresponding to the input information, based on a relationship between a parameter included in the input information and low-dimensional information obtained by reducing the dimensionality of an analytic value distribution for the analysis object; a conversion unit that calculates an estimation result of the analytical value distribution according to the input information by using a trained conversion model capable of estimating the analytical value distribution from the reduced-dimensional input information, The transformation model is a first transformation model that estimates an intermediate vector based on the reduced-dimensional input information; A second conversion model that calculates an estimation result of the analysis value distribution based on the intermediate vector, An estimation device, wherein the number of dimensions of the intermediate vector is larger than the number of dimensions of the dimensionality-reduced input information and smaller than the number of dimensions of the analysis value distribution. [Disclosure 2] The estimation device according to Disclosure 1, wherein the number of dimensions of the dimensionality-reduced input information is smaller than the number of dimensions of the parameters constituting the input information. [Disclosure 3] The estimation device according to Disclosure 1 or 2, wherein the first conversion model and the second conversion model are learning models using an autoencoder. [Disclosure 4] An estimation device for estimating an analysis value distribution in an object to be analyzed, An estimation information acquisition unit that acquires input information including values of at least one parameter that affects the analysis value distribution, A dimensionality reduction estimation unit that estimates dimensionality-reduced input information, which is dimensionality-reduced information corresponding to the input information, based on the relationship between the parameters included in the input information and the dimensionality-reduced information obtained by reducing the dimensionality of the analysis value distribution of the object to be analyzed, A conversion unit that calculates an estimation result of the analysis value distribution corresponding to the input information using a learned conversion model capable of estimating the analysis value distribution from the dimensionality-reduced input information, An estimation device, wherein the number of dimensions of the dimensionality-reduced input information is smaller than the number of dimensions of the parameters constituting the input information. [Disclosure 5] The dimensionality reduction estimation unit according to any one of Disclosures 1 to 4, calculates dimensionality-reduced input information, which is dimensionality-reduced information corresponding to the input information, based on an estimation model that has learned the relationship between the parameters included in the input information and the dimensionality-reduced input information. [Disclosure 6] The estimation device according to any one of Disclosures 1 to 5, wherein the analysis value distribution includes a distribution of a first variable included in a governing equation or a second variable that can be mutually converted with the first variable. [Disclosure 7] The governing equation includes a Maxwell equation, The estimation device according to Disclosure 6, wherein the analyzed value distribution is a distribution of magnetic flux density or vector potential. [Disclosure 8] The estimation device according to any one of Disclosures 1 to 7, wherein the dimension number N of the analyzed value distribution is 50 times or more the dimension number n of the dimension-reduced input information. [Disclosure 9] The analysis object includes a rotor of a rotating electrical machine, The estimation device according to any one of Disclosures 1 to 8, wherein the input information includes information for specifying the shape of the rotor. [Disclosure 10] A learning device that calculates a learning model for estimating an analyzed value distribution in an analysis object, A learning information acquisition unit that acquires at least one parameter that affects the analyzed value distribution and the analyzed value distribution; A first learning unit that creates a conversion model by learning the relationship between the dimension-reduced information obtained by dimension-reducing the analyzed value distribution of the analysis object and the analyzed value distribution corresponding to the dimension-reduced information, using the analyzed value distribution acquired by the learning information acquisition unit; A second learning unit that creates an estimation model by learning the relationship between the parameter and the dimension-reduced information, using the parameter and the analyzed value distribution acquired by the learning information acquisition unit and the conversion model; Comprising The first learning unit creates a first conversion model by learning the relationship between an intermediate vector obtained by dimension-reducing the analyzed value distribution of the analysis object and the analyzed value distribution before dimension-reducing the intermediate vector, using the analyzed value distribution acquired by the learning information acquisition unit, and creates a second conversion model by learning the relationship between the dimension-reduced information obtained by dimension-reducing the intermediate vector and the intermediate vector before dimension-reducing the dimension-reduced information, using the intermediate vector. The learning device, wherein the dimension number of the intermediate vector is larger than the dimension number of the dimension-reduced information and smaller than the dimension number of the analyzed value distribution. [Disclosure 11] The first learning unit is the learning device according to Disclosure 10, which determines the number n of dimensions of the low-dimensional information using the Intrinsic Dimension of the intermediate vector. [Disclosure 12] The Intrinsic Dimension is such that the number of the analysis value distributions is A, and among the A intermediate vectors obtained by reducing the dimensionality of the A analysis value distributions, for the i-th intermediate vector x (i) among the A intermediate vectors, the Euclidean distance between the intermediate vector whose Euclidean distance from the i-th intermediate vector is the j-th largest and the i-th intermediate vector is T j (x (i) ) and is calculated based on Equation (1), which is the learning device according to Disclosure 11. [Disclosure 13] An estimation method for estimating an analysis value distribution in an object to be analyzed, comprising: an estimation information acquisition step of acquiring input information including values of at least one parameter that affects the analysis value distribution; a low-dimensional estimation step of estimating low-dimensional input information, which is low-dimensional information corresponding to the input information, based on the relationship between the parameter included in the input information and the low-dimensional information obtained by reducing the dimensionality of the analysis value distribution for the object to be analyzed; a conversion step of calculating an estimation result of the analysis value distribution corresponding to the input information using a learned conversion model capable of estimating the analysis value distribution from the low-dimensional input information, the conversion model comprising: a first conversion model that estimates an intermediate vector based on the low-dimensional input information; and a second conversion model that calculates an estimation result of the analysis value distribution based on the intermediate vector, wherein the number of dimensions of the intermediate vector is larger than the number of dimensions of the low-dimensional input information and smaller than the number of dimensions of the analysis value distribution. The estimation method. [Disclosure 14] An estimation method for estimating an analysis value distribution in an object to be analyzed, comprising: an estimation information acquisition step of acquiring input information including values of at least one parameter that affects the analysis value distribution; A low-dimensional estimation step of estimating low-dimensional input information, which is low-dimensional information corresponding to the input information, based on the relationship between the parameters included in the input information and the low-dimensional information obtained by reducing the dimensionality of the analysis value distribution for the object to be analyzed; A conversion step of calculating an estimation result of the analysis value distribution corresponding to the input information using a learned conversion model capable of estimating the analysis value distribution from the low-dimensional input information, the estimation method comprising: The dimensionality of the low-dimensional input information is smaller than the dimensionality of the parameters constituting the input information. [Disclosure 15] A learning method for calculating a learning model for estimating an analysis value distribution in an object to be analyzed, the method comprising: A learning information acquisition step of acquiring at least one parameter that affects the analysis value distribution and the analysis value distribution; A first learning step of creating a conversion model by learning the relationship between the low-dimensional information obtained by reducing the dimensionality of the analysis value distribution for the object to be analyzed and the analysis value distribution corresponding to the low-dimensional information using the analysis value distribution obtained in the learning information acquisition step; A second learning step of creating an estimation model by learning the relationship between the parameter and the low-dimensional information using the parameter and the analysis value distribution obtained in the learning information acquisition step and the conversion model; The first learning step includes creating a first conversion model by learning the relationship between an intermediate vector obtained by reducing the dimensionality of the analysis value distribution for the object to be analyzed and the analysis value distribution before being reduced to the intermediate vector using the analysis value distribution obtained in the learning information acquisition step, and creating a second conversion model by learning the relationship between the low-dimensional information obtained by reducing the dimensionality of the intermediate vector and the intermediate vector before being reduced to the low-dimensional information using the intermediate vector, wherein the dimensionality of the intermediate vector is larger than the dimensionality of the low-dimensional information and smaller than the dimensionality of the analysis value distribution. The dimensionality of the intermediate vector is larger than the dimensionality of the low-dimensional information and smaller than the dimensionality of the analysis value distribution. [Disclosure 16] A program for causing a computer to function as each part of the estimation device according to any one of Disclosures 1 to 9. [Disclosure 17] A program for causing a computer to function as each part of the learning device according to any one of Disclosures 10 to 12.

Explanation of Signs

[0105] 0 Axis of rotation, origin of coordinates 100 IPMSM 110 Rotor 111 Rotor core 112(112a~112b) Permanent magnet 113(113a~113d) Flux barrier 120 Stator 121 Stator core 122 Slot 210 Learning device 211 Learning information acquisition unit 212 First learning unit 213 Second learning unit 214 Memory unit 215 Output unit 220 Learning device 221 Estimation information acquisition unit 222 Low-dimensional estimation unit 223 Conversion unit 224 Output unit 230(230a~230b) Input device 240 Output device 411 First encoder 412 Second encoder 413 First decoder 414 Second decoder r Radial distance θ Angular deviation E Estimation model T Conversion model T1 First conversion model T2 Second conversion model PR Portion constituting one pole of IPMSM100

Claims

1. An estimation device for estimating an analytical value distribution in an object to be analyzed, comprising: An estimation information acquisition unit that acquires input information including values of at least one parameter that affects the analytical value distribution; A low-dimensional estimation unit that estimates low-dimensional input information, which is low-dimensional information corresponding to the input information, based on the relationship between the parameter included in the input information and the low-dimensional information obtained by reducing the dimensionality of the analytical value distribution of the object to be analyzed; A conversion unit that calculates an estimation result of the analytical value distribution corresponding to the input information using a learned conversion model capable of estimating the analytical value distribution from the low-dimensional input information. The conversion model includes: A first conversion model that estimates an intermediate vector based on the low-dimensional input information; A second conversion model that calculates an estimation result of the analytical value distribution based on the intermediate vector. The number of dimensions of the intermediate vector is larger than the number of dimensions of the low-dimensional input information and smaller than the number of dimensions of the analytical value distribution.

2. The estimation device according to claim 1, wherein the number of dimensions of the low-dimensional input information is smaller than the number of dimensions of the parameter constituting the input information.

3. The estimation device according to claim 1 or 2, wherein the first conversion model and the second conversion model are learning models using an autoencoder.

4. An estimation device for estimating an analytical value distribution in an object to be analyzed, comprising: An estimation information acquisition unit that acquires input information including values of at least one parameter that affects the analytical value distribution; A low-dimensional estimation unit that estimates low-dimensional input information, which is low-dimensional information corresponding to the input information, based on the relationship between the parameter included in the input information and the low-dimensional information obtained by reducing the dimensionality of the analytical value distribution of the object to be analyzed; A conversion unit that calculates an estimation result of the analysis value distribution corresponding to the input information by using a learned conversion model capable of estimating the analysis value distribution from the low-dimensional input information. An estimation device, wherein the number of dimensions of the low-dimensional input information is smaller than the number of dimensions of the parameters constituting the input information. **Claim 5** The low-dimensional estimation unit calculates low-dimensional input information, which is low-dimensional information corresponding to the input information, based on an estimation model that has learned the relationship between the parameters included in the input information and the low-dimensional input information. The estimation device according to claim 1, 2, or 4. **Claim 6** The analysis value distribution includes the distribution of a first variable included in the governing equation or a second variable that can be mutually converted with the first variable. The estimation device according to claim 1, 2, or 4. **Claim 7** The governing equation includes Maxwell's equations. The analysis value distribution is the distribution of magnetic flux density or vector potential. The estimation device according to claim 6. **Claim 8** The number of dimensions N of the analysis value distribution is 50 times or more the number of dimensions n of the low-dimensional input information. The estimation device according to claim 1, 2, or 4. **Claim 9** The object to be analyzed includes a rotor of a rotating electrical machine. The input information includes information for specifying the shape of the rotor. The estimation device according to claim 1, 2, or 4. **Claim 10** A learning device that calculates a learning model for estimating an analysis value distribution in an object to be analyzed, A learning information acquisition unit that acquires at least one parameter that affects the analysis value distribution and the analysis value distribution; A first learning unit that creates a conversion model by learning the relationship between the low-dimensional information obtained by reducing the dimension of the analysis value distribution of the object to be analyzed and the analysis value distribution corresponding to the low-dimensional information, using the analysis value distribution acquired by the learning information acquisition unit. A second learning unit that creates an estimation model by learning the relationship between the parameter and the low-dimensional information using the parameter and the analysis value distribution acquired by the learning information acquisition unit and the conversion model; comprising; The first learning unit learns the relationship between the intermediate vector obtained by dimensionality reduction of the analysis value distribution for the object to be analyzed and the analysis value distribution before dimensionality reduction of the intermediate vector using the analysis value distribution acquired by the learning information acquisition unit to create a first conversion model, and learns the relationship between the low-dimensional information obtained by dimensionality reduction of the intermediate vector and the intermediate vector before dimensionality reduction of the low-dimensional information using the intermediate vector to create a second conversion model; A learning device, wherein the number of dimensions of the intermediate vector is larger than the number of dimensions of the low-dimensional information and smaller than the number of dimensions of the analysis value distribution.

11. The learning device according to claim 10, wherein the first learning unit determines the number of dimensions n of the low-dimensional information using the Intrinsic Dimension of the intermediate vector.

12. The Intrinsic Dimension is calculated based on the following formula (1), where A is the number of analysis value distributions, the i-th intermediate vector among the A intermediate vectors obtained by dimensionality reduction of the A analysis value distributions is x (i) , and among the A intermediate vectors, the Euclidean distance between the i-th intermediate vector and the intermediate vector whose Euclidean distance from the i-th intermediate vector is the j-th largest is T j (x (i) ). The learning device according to claim 11. 【Equation 1】

13. An estimation method for estimating an analysis value distribution in an object to be analyzed, comprising: An estimation information acquisition step of acquiring input information including the value of at least one parameter that affects the analysis value distribution; A low-dimensional estimation step of estimating low-dimensional input information, which is low-dimensional information corresponding to the input information, based on the relationship between the parameters included in the input information and the low-dimensional information obtained by reducing the dimension of the analysis value distribution for the object to be analyzed; A conversion step of calculating an estimation result of the analysis value distribution corresponding to the input information by using a learned conversion model capable of estimating the analysis value distribution from the low-dimensional input information, comprising: The conversion model includes: A first conversion model that estimates an intermediate vector based on the low-dimensional input information; A second conversion model that calculates an estimation result of the analysis value distribution based on the intermediate vector, and The dimension number of the intermediate vector is larger than the dimension number of the low-dimensional input information and smaller than the dimension number of the analysis value distribution. The estimation method.

14. An estimation method for estimating an analysis value distribution in an object to be analyzed, comprising: An estimation information acquisition step of acquiring input information including values of at least one parameter that affects the analysis value distribution; A low-dimensional estimation step of estimating low-dimensional input information, which is low-dimensional information corresponding to the input information, based on the relationship between the parameters included in the input information and the low-dimensional information obtained by reducing the dimension of the analysis value distribution for the object to be analyzed; A conversion step of calculating an estimation result of the analysis value distribution corresponding to the input information by using a learned conversion model capable of estimating the analysis value distribution from the low-dimensional input information, comprising: The dimension number of the low-dimensional input information is smaller than the dimension number of the parameters constituting the input information. The estimation method.

15. A learning method for calculating a learning model for estimating an analysis value distribution in an object to be analyzed, comprising: A learning information acquisition step of acquiring at least one parameter that affects the analysis value distribution and the analysis value distribution; A first learning step of creating a conversion model that learns the relationship between the low-dimensional information obtained by reducing the dimensionality of the analysis value distribution for the object to be analyzed and the analysis value distribution corresponding to the low-dimensional information, using the analysis value distribution obtained in the learning information acquisition step. A second learning step of creating an estimation model that learns the relationship between the parameter and the low-dimensional information, using the parameter and the analysis value distribution obtained in the learning information acquisition step and the conversion model. Comprising: In the first learning step, creating a first conversion model that learns the relationship between the intermediate vector obtained by reducing the dimensionality of the analysis value distribution for the object to be analyzed and the analysis value distribution before reducing the dimensionality of the intermediate vector, using the analysis value distribution obtained in the learning information acquisition step; and creating a second conversion model that learns the relationship between the low-dimensional information obtained by reducing the dimensionality of the intermediate vector and the intermediate vector before reducing the dimensionality of the low-dimensional information, using the intermediate vector. A learning method in which the dimensionality of the intermediate vector is larger than the dimensionality of the low-dimensional information and smaller than the dimensionality of the analysis value distribution.

16. A program for causing a computer to function as each part of the estimation device according to claim 1, 2, or 4.

17. A program for causing a computer to function as each part of the learning device according to any one of claims 10 to 12.

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