WO2021161503A1 - Design program and design method - Google Patents

Abstract

The present invention reduces prediction error for an approximation model that predicts a simulation result.　Simulation result data (14) is acquired, the data including a plurality of first values which indicate a physical amount of a fluid calculated by a simulation and which are associated with a plurality of unequally-spaced lattice points arranged in a region having a border prescribed by a specific object shape. On the basis of the adjacency relationship between the plurality of lattice points, the plurality of first values are rearranged into a multi-dimensional array structure to generate teaching data (15) which includes the plurality of first values of the multi-dimensional array structure. The teaching data (15) and input data (16), which includes second values indicating a specific object shape, are used to generate an approximation model (17) for predicting the distribution of the physical amounts of the fluid from the object shape.

Description

Design program and design method

The present invention relates to a design program and a design method.

One field of computer simulation is computational fluid dynamics (CFD), which solves the behavior of fluids such as air and water by numerical analysis. Computational fluid dynamics uses basic equations that describe the motion of fluids, such as the Navier-Stokes equation, which is a second-order nonlinear differential equation. By discretely expressing the space where the fluid exists by lattice points, generating large-scale simultaneous equations that discretize the basic equations, and finding the approximate solution of the large-scale simultaneous equations by the iterative method, the flow velocity of each lattice point, etc. The physical quantity of is calculated. Computational fluid dynamics may be used in the design of various machines and structures such as aircraft, automobiles and ships.

A fluid simulation method for calculating the physical quantity of a fluid using a shape model represented by a structured grid has been proposed. In addition, an estimation method for estimating the wind speed distribution around a building using a convolutional neural network (CNN) has been proposed. Further, a learning method has been proposed in which the matrix data used for the CNN convolution operation is divided into two to reduce the calculation amount of the convolution operation. Further, an image processing method for converting an input image into an output image using a multilayer CNN has been proposed.

Japanese Unexamined Patent Publication No. 2004-62749 Japanese Unexamined Patent Publication No. 2012-83958 JP-A-2018-4568 Japanese Unexamined Patent Publication No. 2018-16806 Japanese Unexamined Patent Publication No. 2019-8383

Since the fluid simulation includes iterative numerical calculation for many grid points, the amount of calculation is large and the calculation time may be long. Therefore, it may not be practical to perform a fluid simulation comprehensively for many alternatives of object shapes mentioned at the design stage. Therefore, it is conceivable to try a fluid simulation for some object shapes and use the results to generate an approximate model showing the relationship between the object shape and the physical quantity of the fluid. By using the approximate model, the approximate value of the physical quantity of the fluid can be calculated at high speed for a certain object shape, and a good object shape can be narrowed down from a large number of alternatives.

As one simple method of generating an approximate model that predicts the physical quantity of a fluid from the shape of an object, the grid points of an evenly spaced orthogonal grid are placed in the space where the object and the fluid exist, and the physical quantity of each grid point of the orthogonal grid is approximated. A method of performing machine learning so that the model outputs can be considered. In this case, the physical quantity at each lattice point of the orthogonal lattice is sampled from the trial fluid simulation result, and the correspondence between the parameter indicating the object shape and the sampled physical quantity is used as training data for generating an approximate model. become.

However, the gradient of the physical quantity of the fluid (the ratio of the change of the physical quantity to the change of the position) is large near the boundary between the fluid and the object, and the gradient of the physical quantity of the fluid may be small in the region away from the boundary. For this reason, in the approximate model using the orthogonal grids at equal intervals, there is a problem that an error due to sampling occurs because the grid points of the output are coarse, and the prediction error of the physical quantity near the boundary becomes large. On the other hand, if the interval between the orthogonal grids of the approximate model is reduced as a whole, the approximate model becomes large and the cost of machine learning increases in order to generate a highly accurate approximate model.

In one aspect, it is an object of the present invention to provide a design program and a design method that reduce the prediction error of an approximate model that predicts a simulation result.

In one aspect, a design program is provided that causes the computer to perform the following processes. A plurality of first grid points that are arranged in a region having a boundary defined by a specific object shape and that indicate a physical quantity of a fluid calculated by simulation in association with a plurality of grid points that are not evenly spaced. Acquire simulation result data including values. Based on the adjacency between the plurality of grid points, the plurality of first values are rearranged into the multidimensional array structure to generate teacher data including the plurality of first values of the multidimensional array structure. Using the input data including the second value indicating a specific object shape and the teacher data, an approximate model for predicting the distribution of the physical quantity of the fluid from the object shape is generated.

Also, in one aspect, a computer-executed design method is provided.

On one side, the prediction error of the fitted model that predicts the simulation results is reduced.
The above and other objects, features and advantages of the present invention will become apparent by the following description in connection with the accompanying drawings representing preferred embodiments of the present invention.

It is a figure explaining the example of the design apparatus of 1st Embodiment. It is a figure which shows the hardware example of the information processing apparatus of 2nd Embodiment. It is a figure which shows the arrangement example of the lattice point of the fluid simulation. It is a figure which shows the simulation example of a fluid velocity. It is a figure which shows the structural example of the approximate model. It is a figure which shows the example of the convolution operation. It is a figure which shows the prediction example of the fluid velocity by another approximate model. It is a figure which shows the prediction example of the fluid velocity by the approximate model. It is a block diagram which shows the functional example of an information processing apparatus. It is a figure which shows the example of the grid parameter table and the grid point table. It is a figure which shows the example of the distance table and the fluid table. It is a flowchart which shows the procedure example of approximate model learning. It is a flowchart which shows the procedure example of the simulation speedup.

Hereinafter, the present embodiment will be described with reference to the drawings.
[First Embodiment]
The first embodiment will be described.

FIG. 1 is a diagram illustrating an example of a design device according to the first embodiment.
The design device 10 of the first embodiment performs a fluid simulation by numerical fluid dynamics. Further, the design device 10 uses the simulation result for a specific object shape to generate an approximate model that predicts the simulation result from the object shape by machine learning. The design device 10 may be a client device or a server device. The design device 10 can also be referred to as a computer, an information processing device, a simulation device, a machine learning device, or the like.

The design device 10 has a storage unit 11 and a processing unit 12. The storage unit 11 may be a volatile semiconductor memory such as a RAM (RandomAccessMemory) or a non-volatile storage such as an HDD (HardDiskDrive) or a flash memory. The processing unit 12 is, for example, a processor such as a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), or a DSP (Digital Signal Processor). However, the processing unit 12 may include an electronic circuit for a specific purpose such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array). The processor executes a program stored in a memory (may be a storage unit 11) such as a RAM. A set of multiple processors is sometimes referred to as a "multiprocessor" or simply a "processor."

The storage unit 11 stores the simulation result data 14. The simulation result data 14 shows the result of a fluid simulation by numerical fluid dynamics executed for a specific object shape. The object shape is the shape of an object that is supposed to come into contact with a fluid such as air or water, and is, for example, the shape of an aircraft wing or the shape of an automobile.

In the fluid simulation, multiple grid points are placed in the area where the fluid exists, and variables indicating the physical quantity of the fluid such as velocity and pressure are assigned to each grid point. Then, for example, based on a basic equation such as the Navier-Stokes equation, a large-scale simultaneous equation that describes the relationship between variables is generated, and a solution of the variable is obtained by an iterative method using a coefficient matrix that represents the large-scale simultaneous equation. .. In the iterative method, for example, a temporary value is assigned to a variable, an error of the right-hand side vector is calculated based on the assigned value, and the value of the variable is changed so as to reduce the error.

The area to be simulated has a boundary defined by a specific object shape. This boundary is, for example, the boundary between an object and a fluid, and corresponds to the outer circumference of the object. The region is a two-dimensional plane or a three-dimensional space. The grid points arranged in the region are formed by, for example, a structured grid including a plurality of coordinate axes. In that case, each grid point is identified by two-dimensional or three-dimensional coordinates. Seen from a certain grid point, there are grid points adjacent to each coordinate axis. However, the grid points of the first embodiment are not the grid points of the orthogonal grids at equal intervals, and the intervals are not even. At least one coordinate axis does not have to be a straight line. For example, a structured grid having a coordinate axis corresponding to a curve indicating a boundary and a coordinate axis in which the distance between the coordinates becomes narrower as it is closer to the boundary can be considered.

As an example, grid points 13-1 to 13-9 are arranged in the area. Grid points 13-1, 13-2, 13-3 are lined up on the same curve, grid points 13-4, 13-5, 13-6 are lined up on the same curve, grid points 13-7, 13-8, 13-9 are lined up on the same curve. These three curves are along a certain coordinate axis and are, for example, curves parallel to the boundary. In addition, grid points 13-1, 13-4, 13-7 are lined up on the same curve, grid points 13-2, 13-5, 13-8 are lined up on the same curve, and grid points 13-3, 13- 6, 13-9 are lined up on the same curve. These three curves are along a certain coordinate axis, for example, a curve extending outward from the boundary. The grid points 13-1, 13-2, 13-3 are closer to the boundary than the grid points 13-7, 13-8, 13-9. The distance between the grid points 13-1 and the grid points 13-4 is narrower than the distance between the grid points 13-4 and the grid points 13-7. In this way, the closer to the boundary, the narrower the spacing between the grid points may be.

The simulation result data 14 includes a value (first value) indicating the physical quantity of the fluid calculated by the fluid simulation in association with the grid points 13-1 to 13-9. Grid point 13-1 value v1, grid point 13-2 value v2, grid point 13-3 value v3, grid point 13-4 value v4, grid point 13-5 value v5, grid point 13-6 The value v6 of, the value v7 of the grid point 13-7, the value v8 of the grid point 13-8, and the value v9 of the grid point 13-9 are calculated. These values v1 to v9 represent, for example, the velocity of the fluid at the corresponding grid point.

When the processing unit 12 acquires the simulation result data 14, the processing unit 12 sets the values v1 to v9 of the grid points 13-1 to 13-9 in a multidimensional array structure based on the adjacency relationship between the grid points 13-1 to 13-9. Sort to. A multidimensional array containing values v1 to v9 is sometimes called a tensor. The number of dimensions (order) of a multidimensional array depends on the number of dimensions of the region and the number of dimensions of the values v1 to v9. For example, when the area to be simulated is two-dimensional and the values v1 to v9 are one-dimensional scalar values, the values v1 to v9 are stored in a two-dimensional array (second-order tensor).

In sorting into a multidimensional array structure, grid points 13-1 to so that close grid points are associated with close elements of the multidimensional array and distant grid points are associated with distant elements of the multidimensional array. It is preferred that the adjacency of 13-9 is preserved. It is preferred that adjacent grid points are associated with adjacent elements of a multidimensional array. When the coordinates defined by a plurality of coordinate axes are assigned to the grid points 13-1 to 13-9, the processing unit 12 determines the elements of the multidimensional array associated with each grid point based on the coordinates. It may be. For example, when the structured grid has an L axis and a J axis, it is conceivable to associate the L coordinate with the first dimension (row) of the multidimensional array and the J coordinate with the second dimension (column) of the multidimensional array. Be done.

However, since the grid points 13-1 to 13-9 do not form an orthogonal grid at equal intervals, the positions of the elements of the multidimensional array represent the positions of the grid points 13-1 to 13-9 on the region itself. I'm not. The processing unit 12 generates teacher data 15 including the values v1 to v9 of the multidimensional array structure. For example, (1,1) = v1, (1,2) = v2, (1,3) = v3, (2,1) = v4, (2,2) = v5, (2,3) = v6, Values v1 to v9 are lined up, such as (3,1) = v7, (3,2) = v8, (3,3) = v9.

Further, the processing unit 12 generates input data 16 including a value (second value) indicating the specific object shape from the specific object shape targeted for simulation. The input data 16 may include some parameters that reflect the shape of the object. As an example, the processing unit 12 calculates a distance value indicating the distance between the grid points and the boundary for each of the grid points 13-1 to 13-9. The distance value corresponds to the Euclidean distance between the point on the boundary closest to a certain lattice point and the lattice point, and is, for example, the value of a signed distance function (SDF). The processing unit 12 rearranges the distance values of the grid points 13-1 to 13-9 into a multidimensional array structure similar to that of the teacher data 15 to obtain the input data 16. In that case, the elements at the same position between the teacher data 15 and the input data 16 correspond to the same grid point.

The processing unit 12 associates the teacher data 15 with the input data 16 to generate training data including the teacher data 15 and the input data 16. Then, the processing unit 12 uses this training data to generate an approximate model 17 by machine learning. The approximation model 17 is a prediction model that predicts the distribution of the physical quantity of the fluid from the shape of the object, and calculates an approximation value of the result of the fluid simulation without performing the fluid simulation by the iterative method. The teacher data 15 corresponds to the objective variable which is the output of the approximate model 17, and the input data 16 corresponds to the explanatory variable which is the input of the approximate model 17. The approximate model 17 is, for example, a convolutional neural network. The approximation model 17 includes an encoder that converts a multidimensional array of high-dimensional inputs into a low-dimensional feature data by a convolution operation, and a decoder that converts the feature data into a multidimensional array of a high-dimensional output by a deconvolution operation. May include.

According to the design apparatus of the first embodiment, the values of the plurality of lattice points calculated by the fluid simulation are rearranged into a multidimensional array structure based on the adjacency relationship of the plurality of lattice points, and the teacher data. 15 is generated. Then, an approximate model 17 is generated by machine learning from the input data 16 and the teacher data 15 indicating the object shape.

By using the approximate model 17, it is possible to predict the simulation results for other object shapes without executing the fluid simulation by the iterative method. Therefore, the amount of calculation can be reduced, and the approximate value of the physical quantity of the fluid can be calculated at high speed. Therefore, the design work for considering a large number of alternatives for the object shape is streamlined.

Further, in generating the teacher data 15 of the multidimensional array structure, the values included in the simulation result data 14 are sorted according to the adjacency relationship of the lattice points and used as they are. At this time, unlike the case where the elements of the multidimensional array correspond to the lattice points of the orthogonal lattice at equal intervals, it is not necessary to perform sampling for converting the lattice points between the simulation result data 14 and the teacher data 15. Therefore, the occurrence of an error due to sampling can be suppressed, and the prediction accuracy of the approximate model 17 can be improved.

In particular, in fluid simulation, when grid points are arranged at high density in a part of the area such as near the boundary, the prediction error of the part of the area can be reduced. Further, the scale of the approximate model 17 can be reduced and the cost of machine learning can be reduced as compared with the case where the teacher data 15 adopts orthogonal grids at equal intervals and attempts to improve the accuracy by reducing the grid intervals. ..

[Second Embodiment]
Next, a second embodiment will be described.
The information processing apparatus of the second embodiment simulates the airflow around the wing of an aircraft based on computational fluid dynamics. Further, the information processing apparatus of the second embodiment generates an approximate model for predicting the airflow around the blade from the shape of the blade by machine learning using the simulation results for several blades having different shapes. The information processing device of the second embodiment may be a client device or a server device. The information processing device of the second embodiment can also be referred to as a computer, a simulation device, a machine learning device, a design device, or the like.

FIG. 2 is a diagram showing a hardware example of the information processing apparatus according to the second embodiment.
The information processing apparatus 100 of the second embodiment includes a CPU 101, a RAM 102, an HDD 103, an image interface 104, an input interface 105, a medium reader 106, and a communication interface 107. These units included in the information processing apparatus 100 are connected to the bus. The information processing device 100 corresponds to the design device 10 of the first embodiment. The CPU 101 corresponds to the processing unit 12 of the first embodiment. The RAM 102 or the HDD 103 corresponds to the storage unit 11 of the first embodiment.

The CPU 101 is a processor that executes program instructions. The CPU 101 loads at least a part of the programs and data stored in the HDD 103 into the RAM 102 and executes the program. The CPU 101 may include a plurality of processor cores, and the information processing device 100 may include a plurality of processors. A collection of multiple processors is sometimes referred to as a "multiprocessor" or simply a "processor."

The RAM 102 is a volatile semiconductor memory that temporarily stores a program executed by the CPU 101 and data used by the CPU 101 for calculation. The information processing device 100 may include a type of memory other than RAM, or may include a plurality of memories.

HDD 103 is a non-volatile storage that stores software programs such as OS (Operating System), middleware, and application software, and data. The information processing device 100 may include other types of storage such as a flash memory and an SSD (Solid State Drive), or may include a plurality of storages.

The image interface 104 outputs an image to the display device 111 connected to the information processing device 100 in accordance with a command from the CPU 101. As the display device 111, any kind of display device such as a CRT (Cathode Ray Tube) display, a liquid crystal display (LCD: Liquid Crystal Display), an organic EL (OEL: Organic Electro-Luminescence) display, and a projector can be used. .. An output device other than the display device 111 such as a printer may be connected to the information processing device 100.

The input interface 105 receives an input signal from the input device 112 connected to the information processing device 100. As the input device 112, any kind of input device such as a mouse, a touch panel, a touch pad, and a keyboard can be used. A plurality of types of input devices may be connected to the information processing device 100.

The medium reader 106 is a reading device that reads programs and data recorded on the recording medium 113. As the recording medium 113, any kind of recording medium such as a magnetic disk such as a flexible disk (FD) or HDD, an optical disk such as a CD (Compact Disc) or a DVD (Digital Versatile Disc), or a semiconductor memory is used. Can be done. The medium reader 106 copies, for example, a program or data read from the recording medium 113 to another recording medium such as the RAM 102 or the HDD 103. The read program is executed by, for example, the CPU 101. The recording medium 113 may be a portable recording medium, and may be used for distribution of programs and data. Further, the recording medium 113 and the HDD 103 may be referred to as a computer-readable recording medium.

The communication interface 107 is connected to the network 114 and communicates with other information processing devices via the network 114. The communication interface 107 may be a wired communication interface connected to a wired communication device such as a switch or a router, or may be a wireless communication interface connected to a wireless communication device such as a base station or an access point.

Next, the fluid simulation will be described.
FIG. 3 is a diagram showing an example of arrangement of grid points in a fluid simulation.
In the fluid simulation, shape data 151 showing the shape of the blade to be simulated is given. The shape data 151 is generated by, for example, CAD (Computer Aided Design) software. The shape data 151 includes, for example, data of a curve indicating the outer circumference of the blade. It is assumed that air, which is a fluid, exists on the outside of the wing, and the curve indicating the outer circumference of the wing corresponds to the boundary between the wing and the fluid. In the second embodiment, for the sake of simplicity, a two-dimensional shape of the wing as viewed from the lateral direction is assumed.

From the shape data 151, a plurality of lattice points are arranged in the two-dimensional region where the fluid exists. These grid points are formed by a structured grid that is a non-orthogonal grid. The generation of grid points of a structured grid is described in, for example, the following non-patent document. Kazuhiro Nakahashi, "Lattice Generation in Computational Fluid Dynamics", Information Processing, Vol. 30 No. 7, pp. 767-774, July 1989.

The structural grid of the second embodiment is a structural grid of a boundary-fitting curvilinear coordinate system in which the coordinate axes are determined based on the boundary curve, and is a boundary curve J-axis and an L-axis extending outward from the boundary. It has two coordinate axes. The J-axis is a curve that follows the outer circumference of the wing shown in FIG. 3 in the order of lower right, lower left, upper left, and upper right. The lower right grid point of the wing has J coordinate = 40, and the upper right grid point of the wing has J coordinate = 471. 432 J coordinates are arranged at equal intervals on the J axis. The L-axis is a curve extending outward from the J-axis. The grid point closest to the boundary has L coordinate = 1, and the grid point farthest from the boundary has L coordinate = 48. Forty-eight L coordinates are arranged on the L axis. The intervals of the L coordinates are not equal. The closer to the boundary, the smaller the L-coordinate interval, and the farther from the boundary, the larger the L-coordinate interval. The L coordinate interval is determined by a predetermined calculation formula such as an exponential function.

Curve 152-1 is a curve with L coordinate = 1. Curve 152-2 is a curve with L coordinate = 2. Curve 152-3 is a curve with L coordinate = 3. Curve 152-4 is a curve with L coordinate = 4. The curve 152-5 is a curve with L coordinate = 5. The curve 152-6 is a curve with L coordinate = 6. Curves 152-1 to 152-6 are, for example, parallel to the boundary. The distance between two adjacent curves 152-1 to 152-6 increases as the distance from the boundary increases.

Curve 153-1 is a curve with J coordinate = 40. The curve 153-2 is a curve with J coordinate = 41. The curve 153-3 is a curve with J coordinate = 42. The curve 153-4 is a curve with J coordinate = 43. The curve 153-5 is a curve with J coordinate = 44. Curves 153-1 to 153-5 are generated, for example, to intersect curves 152-1 to 152-6 at right angles.

The intersection between the curve corresponding to the L coordinate of the integer and the curve corresponding to the J coordinate of the integer is adopted as the grid point. Therefore, in the range shown in FIG. 3, 30 intersections between the curves 152-1 to 152-6 and the curves 153-1 to 153-5 are adopted as the grid points. As described above, the lattice points used in the fluid simulation are not the lattice points of the orthogonal lattices at equal intervals, but are the lattice points of the structured lattice given a certain order by the L-axis and the J-axis. With respect to a certain grid point, at most two grid points having the same L coordinate and at most two grid points having the same J coordinate are adjacent to each other.

The grid points used in the fluid simulation can be represented by a matrix 154 based on the L and J coordinates. The matrix 154 is a matrix of 48 rows and 432 columns. The rows of the matrix 154 correspond to the L coordinates, and the columns of the matrix 154 correspond to the J coordinates. For example, the elements (1,1) of the matrix 154 correspond to the grid points of L coordinate = 1, J coordinate = 40, that is, the intersections of the curve 152-1 and the curve 153-1. The elements (6, 5) of the matrix 154 correspond to the grid points of L coordinate = 6, J coordinate = 44, that is, the intersections of the curves 152-6 and the curves 153-5. Since it is an approximate model described later, the number of L coordinates and the number of J coordinates are constant regardless of the shape of the wing.

When the grid points are generated from the shape data 151, the information processing apparatus 100 calculates a velocity vector indicating the fluid velocity at each grid point by fluid simulation. The velocity vector is a two-dimensional vector including an X component and a Y component. The X-axis is in the right direction of the shape data 151 in FIG. 3, and the Y-axis is in the upward direction of the shape data 151 in FIG.

In the fluid simulation, the information processing device 100 assigns a variable indicating a velocity vector to each grid point. The information processing device 100 disperses the Navier-Stokes equations, which are second-order nonlinear differential equations that describe the behavior of a fluid, and generates simultaneous equations that show the relationships between variables. The information processing apparatus 100 generates a coefficient matrix representing simultaneous equations, a solution vector, and a right-hand side vector, and obtains a solution of simultaneous equations by an iterative method. In the iterative method, a temporary value is assigned to the solution vector, the error of the right-hand side vector is calculated based on the assigned value, and the value of the solution vector is changed so that the error becomes small until the error converges. repeat.

FIG. 4 is a diagram showing a simulation example of the fluid velocity.
Graph 171 is a graph that visualizes the velocity vector near the boundary calculated by the fluid simulation. In graph 171 the velocity vector is represented by arrows. The arrow line of graph 171 shown in FIG. 4 is from the lower left to the upper right. Therefore, these velocity vectors include a positive X component and a positive Y component. The grid points are at the left end of the arrow. The velocity vector at the grid points is represented by the direction and length of the arrow.

As shown in Graph 171, the closer to the boundary, the larger the gradient of the velocity vector, that is, the greater the amount of change in the velocity vector when the position is changed by a small amount, and the farther from the boundary, the smaller the gradient of the velocity vector. By arranging the grid points at high density near the boundary, it is possible to accurately express the distribution of the velocity vector near the boundary.

Next, an approximate model will be described.
In the design of the wing, a preferable shape is narrowed down from various shape candidates. On the other hand, the fluid simulation by the iterative method requires a large amount of calculation and a long calculation time. Therefore, it is not realistic to perform the above-mentioned fluid simulation for a large number of shape candidates. Therefore, the information processing apparatus 100 tries fluid simulation for some blade shapes, uses the simulation results as training data, and generates an approximate model for predicting the velocity vector from the blade shapes by machine learning. By using the approximate model, it is possible to calculate the approximate value of the velocity vector for various shapes at high speed without performing the fluid simulation by the iterative method, and the simulation result can be predicted.

FIG. 5 is a diagram showing a structural example of an approximate model.
The approximate model 160 is a multi-layer convolutional neural network (DCNN). The approximation model 160 includes an encoder 161 and a decoder 162. The encoder 161 includes a plurality of convolution layers that perform a convolution operation, and converts the input tensor 163 into feature data having a size smaller than that of the input tensor 163. The decoder 162 includes a plurality of convolution layers that perform deconvolution operations, and converts the feature data into an output tensor 164 having a size larger than that of the feature data.

The input tensor 163 is a tensor having a height of 48 × a width of 432 × 1 channel. The input tensor 163 corresponds to a two-dimensional array (second-order tensor) and corresponds to one set of a matrix 154 having 48 rows × 432 columns. The output tensor 164 is a tensor having a height of 48 × a width of 432 × 2 channels. The output tensor 164 corresponds to a three-dimensional array (third-order tensor), and corresponds to two sets of a matrix 154 having 48 rows × 432 columns. The height and width of the output tensor 164 are the same as those of the input tensor 163.

The input tensor 163 input to the approximate model 160 is input data indicating the shape of the wing. In the second embodiment, the SDF value defined by the signed distance function is used as an index representing the shape of the wing. The SDF value is calculated for each grid point. The SDF value indicates the distance from the boundary to the grid point, that is, the distance between the point on the boundary closest to the grid point and the grid point. The generation of the signed distance function is described, for example, in the following non-patent document. Kohei Okita, Kenji Ono, "Accuracy of Fluid Solver Using Shape Representation by Signed Distance Function", RIKEN Symposium 2008 VCAD System Research (3rd), November 2008. The SDF value is positive outside the boundary and negative inside the boundary. Since the fluid is outside the boundary, the second embodiment deals with a positive SDF value.

The input tensor 163 is a rearrangement of SDF values of a plurality of grid points based on the coordinates of those grid points. In the input tensor 163, the SDF values of the near grid points are placed close together and the SDF values of the distant grid points are placed apart. The height direction of the input tensor 163 corresponds to the L axis, and the width direction of the input tensor 163 corresponds to the J axis. For example, the element (1,1) of the input tensor 163 is the SDF value of the grid point of L coordinate = 1, J coordinate = 40. The elements (6, 5) of the input tensor 163 are the SDF values of the grid points of the L coordinate = 6, J coordinate = 44.

The output tensor 164 output from the approximate model 160 is output data showing the distribution of the velocity vector of the fluid. The first channel of the output tensor 164 represents the X component of the velocity vector, and the second channel of the output tensor 164 represents the Y component of the velocity vector. The output tensor 164 is a rearrangement of velocity vectors of a plurality of grid points based on the coordinates of those grid points. In the output tensor 164, the velocity vectors of the near grid points are placed close together and the velocity vectors of the distant grid points are placed apart. The height direction of the output tensor 164 corresponds to the L axis, and the width direction of the output tensor 164 corresponds to the J axis.

For example, the element (1,1,1) of the output tensor 164 is the X component of the velocity vector of the lattice point of the L coordinate = 1, J coordinate = 40. The elements (1, 1, 2) of the output tensor 164 are the Y components of the velocity vector of the grid point. The elements (6, 5, 1) of the output tensor 164 are the X component of the velocity vector of the lattice point of the L coordinate = 6, J coordinate = 44. The elements (6, 5, 2) of the output tensor 164 are the Y components of the velocity vector of the grid point.

In generating the approximate model 160 by machine learning, the information processing apparatus 100 prepares training data in which an explanatory variable corresponding to the input tensor 163 and an objective variable corresponding to the output tensor 164 are associated with each other. Performing a fluid simulation on one shape of the wing produces a set of input and output tensors. The information processing apparatus 100 executes, for example, a fluid simulation a plurality of times (for example, 2000 times) to generate training data including a plurality of sets of input tensors and output tensors. At this time, the information processing apparatus 100 automatically generates another shape by giving distortion to one shape created by the user.

FIG. 6 is a diagram showing an example of a convolution operation.
At each convolution layer included in the encoder 161 of the approximate model 160, a convolution operation, which is a multiply-accumulate operation, is performed. The tensor 165 is a tensor input to the convolution layer. Kernel 166 is a filter applied to the input tensor 165. Kernel 166 is prepared for each convolution layer. The feature map 167 is a tensor output from the convolution layer and is the result of a convolution operation between the tensor 165 and the kernel 166. Normally, the sides of the kernel 166 are shorter than the sides of the tensor 165. The sides of the feature map 167 are the same length as the sides of the tensor 165 or shorter than the sides of the tensor 165.

In the convolution operation, the kernel 166 is first superimposed on the upper left of the tensor 165. Multiplication is performed between the overlapping elements of the tensor 165 and the elements of the kernel 166, and the sum of these products is the upper left element of the feature map 167. After that, the product-sum operation is repeated by shifting the kernel 166 on the tensor 165 by a predetermined stride. This convolution operation can be expressed as a neural network.

For example, assume that the kernel 166 has a size of 3x3 and a stride of 2. First, the center of the kernel 166 is aligned with the element a22 of the tensor 165. Then, a11 * k11 + a12 * k12 + a13 * k13 + a21 * k21 + a22 * k22 + a23 * k23 + a31 * k31 + a32 * k32 + a33 * k33, which is the sum of the products of the nine sets of elements, is calculated. This total value becomes element b11 of the feature map 167.

Next, by shifting the kernel 166 to the right by 2 and aligning the center of the kernel 166 with the element a24 of the tensor 165, the element b12 of the feature map 167 is calculated. Similarly, by aligning the center of the kernel 166 with the element a42 of the tensor 165, the element b21 of the feature map 167 is calculated, and by aligning the center of the kernel 166 with the element a44 of the tensor 165, the element b22 of the feature map 167 is calculated. Is calculated. The element b22 is calculated as a33 * k11 + a34 * k12 + a35 * k13 + a43 * k21 + a44 * k22 + a45 * k23 + a53 * k31 + a54 * k32 + a55 * k33.

When the stride is 1, the height and width of the feature map 167 will be the same as the tensor 165. When the stride is 2, the height and width of the feature map 167 is 1/2 that of the tensor 165. When the stride is 3, the height and width of the feature map 167 is 1/3 of the tensor 165. Thus, the size of the feature map 167 depends on the stride. By setting the number of channels of the kernel 166 to 2 or more, the number of channels of the feature map 167 can be increased more than the number of channels of the tensor 165.

The element of kernel 166 corresponds to the weight of the edge included in the neural network, and is a parameter whose value is adjusted in machine learning. On the other hand, the size and stride of kernel 166 are hyperparameters whose values do not change in machine learning. The size and stride of kernel 166 are pre-adjusted so that the height and width of the output tensor 164 match the height and width of the input tensor 163, based on the number of L and J coordinates of the grid points. .. The information processing apparatus 100 may automatically determine the kernel size and stride of each convolution layer based on the number of L coordinates and the number of J coordinates. The height and width of the output tensor 164 can also be adjusted by padding to extend the height and width by adding elements of predetermined value around the existing tensor.

In each convolution layer included in the decoder 162 of the approximate model 160, a deconvolution operation, which is a multiply-accumulate operation, is performed. The deconvolution operation is sometimes called a transposed convolution operation. The deconvolution operation corresponds to the reverse operation of the above convolution operation. In the deconvolution operation, one element included in the input tensor is multiplied by a plurality of elements included in the kernel, and a multiplication result having the same size as the kernel is obtained. This multiplication is performed on all the elements contained in the input tensor. The result of this multiplication is shifted by the stride, and the overlapping parts are summed to obtain the output tensor.

When the stride is 1, the height and width of the output tensor will be the same as the input tensor. With a stride of 2, the height and width of the output tensor is twice that of the input tensor. With a stride of 3, the height and width of the output tensor is three times that of the input tensor. Thus, even in the deconvolution operation, the size of the output tensor depends on the stride.

A general convolutional neural network may include a pooling layer and a fully connected layer in addition to the convolutional layer. On the other hand, the approximate model 160 includes a convolution layer, but does not include a pooling layer or a fully connected layer. The fitted model 160 may include only the convolution layer. The approximate model 160 does not include the pooling layer because the operation equivalent to that of the pooling layer can be realized by adjusting the kernel size and stride of the convolution layer. The approximate model 160 does not include the fully connected layer because the input tensor 163 and the output tensor 164 have substantially the information on the adjacency between the grid points, but the information on the adjacency is lost in the fully connected layer. This is because there is a risk that it will end up. Further, by mounting only the convolution layer, the structure of the approximate model 160 can be simplified.

Here, the significance of defining the input / output of the approximate model by rearranging the lattice points of the non-orthogonal lattice used in the fluid simulation according to the L coordinate and the J coordinate will be described.
As another method of defining the input / output of the approximate model, separately from the grid points of the non-orthogonal grid used in the fluid simulation, the grid points of the orthogonal grid at equal intervals are generated from the shape data, and the grid points of the orthogonal grid are input. A method of associating the elements of the tensor and the output tensor can be considered. In this case, the element of the input tensor becomes the SDF value at the lattice point of the orthogonal lattice, and the element of the output tensor becomes the velocity vector at the lattice point of the orthogonal lattice. By adopting the grid points of the orthogonal grid, unlike the method of the second embodiment, the positions of the elements of the input tensor and the output tensor directly correspond to the positions in the space including the blade.

However, when the approximate model adopts the grid points of the orthogonal grid, there is a gap between the grid points shown by the simulation result and the grid points shown by the output of the approximate model. Therefore, when generating training data from the simulation results, interpolation processing is performed to estimate the velocity vector of the lattice points of the orthogonal lattice from the velocity vector of the lattice points of the non-orthogonal lattice. Further, in using the simulation result predicted by the approximate model, an interpolation process is performed to estimate the velocity vector of the lattice points of the non-orthogonal lattice from the velocity vector of the lattice points of the orthogonal lattice.

For the interpolation process, for example, a bilinear interpolation method or a linear interpolation method is used. In the bilinear interpolation method, four lattice points around the position of interest are detected, and the weighted average of the velocity vectors of these four lattice points is calculated according to the distance between the position of interest and the four lattice points. , Estimate the velocity vector at the position of interest.

If this interpolation process is performed when the training data is generated, a sampling error may occur in the training data, and the prediction accuracy of the approximate model may decrease due to the sampling error. In particular, since the gradient of the velocity vector is large near the boundary, the sampling error due to the interpolation processing becomes large, and the prediction accuracy of the approximate model may be significantly lowered near the boundary. Further, in order to improve the prediction accuracy of the approximate model while adopting the grid points of the orthogonal grid, the grid spacing must be reduced. However, reducing the grid spacing increases the height and width of the input and output tensors, increasing the number of nodes included in the fitted model. For this reason, the execution time of machine learning for generating an approximate model becomes long, and the amount of training data to be prepared also increases.

On the other hand, according to the method of the second embodiment, it is possible to avoid the sampling error due to the interpolation processing and improve the prediction accuracy of the approximate model. In addition, maintaining the adjacency between the grid points of the non-orthogonal grid makes it easier to improve the prediction accuracy of the approximate model. In the following, an example of the prediction accuracy when the grid points of the orthogonal grid are used for the input / output of the approximate model and the prediction accuracy when the grid points of the fluid simulation are used for the input / output of the approximate model will be described.

FIG. 7 is a diagram showing an example of prediction of fluid velocity by another approximate model.
Graph 172 is a graph that visualizes the velocity vector near the boundary predicted by an approximate model using lattice points of an orthogonal lattice for input and output. Graph 172 shows the distribution of velocity vectors for the same blade shape as Graph 171. Here, in order to compare with Graph 171, the velocity vector at the lattice point of the non-orthogonal lattice is estimated from the velocity vector at the lattice point of the orthogonal lattice output by the approximate model by the bilinear interpolation method. Comparing the graph 171 and the graph 172, the difference in the velocity vector depending on the position is not properly expressed in the graph 172. Therefore, the prediction accuracy of the velocity vector near the boundary is low.

FIG. 8 is a diagram showing an example of prediction of fluid velocity by an approximate model.
Graph 173 is a graph that visualizes the velocity vector near the boundary predicted by an approximate model using grid points of a non-orthogonal lattice for input and output. Graph 173 shows the distribution of velocity vectors for the same blade shape as graphs 171 and 172. Since the approximate model directly calculates the velocity vector of the grid points for fluid simulation, the output of the approximate model is not interpolated. Comparing Graph 171 and Graph 173, Graph 173 appropriately expresses the difference in velocity vector depending on the position. Therefore, it can be said that the prediction accuracy of the velocity vector near the boundary is higher than that of the approximate model used in Graph 172.

The orthogonal lattice adopted by the approximate model of Graph 172 includes 256 X-coordinates and 256 Y-coordinates, and has 65536 lattice points. The spacing between the orthogonal grids is larger than the grid spacing on the fluid simulation near the boundary. That is, in the vicinity of the boundary, the lattice points of the orthogonal lattice of the approximate model are coarser than those of the non-orthogonal lattice of the fluid simulation. On the other hand, the non-orthogonal lattice adopted by the approximate model of the second embodiment includes 48 L coordinates and 432 J coordinates, and has 20736 lattice points. Therefore, in the method of the second embodiment, the scale of the approximate model is smaller and the prediction accuracy is higher.

Next, the function of the information processing apparatus 100 will be described.
FIG. 9 is a block diagram showing a functional example of the information processing device.
The information processing device 100 includes a shape data storage unit 121, a grid parameter storage unit 122, a grid point data storage unit 123, a distance data storage unit 124, a fluid data storage unit 125, a training data storage unit 126, and an approximate model storage unit 127. .. These storage units are realized by using, for example, the storage area of the RAM 102 or the HDD 103. Further, the information processing apparatus 100 includes a grid generation unit 131, a distance calculation unit 132, a simulation execution unit 133, a tensor conversion unit 134, a learning unit 135, and a prediction unit 136. These processing units are realized, for example, by using a program executed by the CPU 101.

The shape data storage unit 121 stores shape data created by the user using CAD software. The shape data represents the shape of the blade including the outer circumference of the blade. The shape data storage unit 121 may store shape data for at least one shape.

The grid parameter storage unit 122 stores parameters for automatically generating grid points. The parameters include the number of L coordinates and the number of J coordinates. This parameter is commonly applied to various shapes. Therefore, the number of L coordinates and the number of J coordinates are common. The grid point data storage unit 123 stores grid point data indicating grid points for fluid simulation automatically generated from the shape data. This grid point is a grid point of a structured grid that is not evenly spaced and is not an orthogonal grid. Lattice point data is generated for each blade shape.

The distance data storage unit 124 stores distance data indicating the SDF value of each grid point calculated by the signed distance function. Distance data is generated for each wing shape. The fluid data storage unit 125 stores fluid data indicating the velocity vector of each grid point calculated by the fluid simulation. Fluid data is generated for each blade shape.

The training data storage unit 126 stores training data in which an input tensor corresponding to an explanatory variable and an output tensor corresponding to an objective variable are associated with each other. The output tensor corresponds to the teacher data. The training data includes a plurality of sets of input tensors and output tensors (for example, 2000 sets). The input tensor is generated from the distance data and the output tensor is generated from the fluid data. The approximate model storage unit 127 stores the approximate model generated by machine learning. The approximate model contains model parameters such as kernel elements for each convolution layer.

The grid generation unit 131 reads the user-created shape data from the shape data storage unit 121. The grid generation unit 131 generates a large number of shape data (for example, 2000 patterns of shape data) indicating different blade shapes by applying distortion to the blade shape indicated by the user-created shape data. However, it is also possible for the user to create shape data of different blade shapes. The grid generation unit 131 reads out the grid parameters from the grid parameter storage unit 122. The grid generation unit 131 sets the L-axis and the J-axis for each shape data, sets the L-coordinates and the J-coordinates as many as the number specified by the grid parameters, and generates the grid points of the structured grid. The grid generation unit 131 stores grid point data indicating the positions of the generated grid points in the grid point data storage unit 123.

The distance calculation unit 132 reads the shape data from the shape data storage unit 121 and reads the grid point data from the grid point data storage unit 123. The distance calculation unit 132 generates a signed distance function for calculating the distance from the boundary which is the outer circumference of the blade shape according to a predetermined algorithm for each shape data. The distance calculation unit 132 calculates the SDF value of each grid point using the signed distance function, and stores the distance data indicating the SDF value in the distance data storage unit 124.

The simulation execution unit 133 reads the grid point data from the grid point data storage unit 123. The simulation execution unit 133 assigns a velocity vector variable to each lattice point for each lattice point data, and uses the Navier-Stokes equation as a basic equation to generate a coefficient matrix and a right-hand side vector of simultaneous equations. The simulation execution unit 133 obtains a solution of simultaneous equations by an iterative method, and stores fluid data indicating the solution in the fluid data storage unit 125.

However, the initial value of the solution may be given by the prediction unit 136. The initial value given by the prediction unit 136 is an approximate value of the velocity vector of each grid point calculated by the prediction unit 136. In that case, the simulation execution unit 133 substitutes the initial value given by the prediction unit 136 into the variable and starts the solution by the iterative method. Starting a fluid simulation using an approximate value of a variable is sometimes called a "warm start". By using an approximate value, the number of iterations can be reduced as compared with the case where a predetermined initial value is used. Using an approximate value is equivalent to omitting the middle stage of the iterative operation.

The tensor conversion unit 134 reads the distance data from the distance data storage unit 124. The tensor conversion unit 134 rearranges the SDF values included in the distance data based on the L coordinate and the J coordinate to generate an input tensor. Further, the tensor conversion unit 134 reads fluid data from the fluid data storage unit 125. The tensor conversion unit 134 rearranges the velocity vectors included in the fluid data based on the L coordinate and the J coordinate to generate an output tensor. In the sorting, the lattice parameters stored in the lattice parameter storage unit 122 are referred to.

At the time of learning the approximate model, the tensor conversion unit 134 associates the input tensor and the output tensor for the same blade shape and stores them in the training data storage unit 126. When using the approximate model, the tensor conversion unit 134 provides the input tensor to the prediction unit 136.

The learning unit 135 reads training data from the training data storage unit 126. The learning unit 135 adjusts hyperparameters such as the kernel size and stride of each convolution layer of the approximate model according to the size of the input tensor and the size of the output tensor. Then, the learning unit 135 adjusts parameters such as kernel elements of each convolution layer of the approximate model using the training data. The learning unit 135 stores the approximate model in the approximate model storage unit 127.

The prediction unit 136 reads the approximate model from the approximate model storage unit 127. The prediction unit 136 acquires an input tensor from the tensor conversion unit 134 and inputs it to the approximate model. The prediction unit 136 reads the output tensor from the approximation model, rearranges the velocity vectors included in the output tensor, and generates approximation data indicating the prediction of the simulation result.

When performing a warm start, the prediction unit 136 provides approximate data to the simulation execution unit 133. When the warm start is not performed, for example, the prediction unit 136 visualizes the velocity vector indicated by the approximate data on the shape data as shown in the graph 173, and displays the visualization data on the display device 111. The prediction unit 136 may store the approximate data in the non-volatile storage, or may transmit the approximate data to another information processing device.

The grid generation unit 131 can be implemented by using the grid generation library program. Further, the distance calculation unit 132 can be implemented by using the SDF library program. Further, the simulation execution unit 133 can be implemented by using the CFD library program.

FIG. 10 is a diagram showing an example of a grid parameter table and a grid point table.
The grid parameter storage unit 122 stores the grid parameter table 141. The number of L coordinates and the number of J coordinates are registered as lattice parameters in the lattice parameter table 141. The L-coordinate number and the J-coordinate number are determined in advance according to the type of the object to be designed. If the types of objects are the same, the L-coordinate number and the J-coordinate number are not changed even if the shapes are different. As described above, for example, the L coordinate number is 48 and the J coordinate number is 432.

The grid point data storage unit 123 stores the grid point table 142. The grid point ID, L coordinate, J coordinate, X coordinate, and Y coordinate of each of the plurality of grid points are registered in the grid point table 142. The grid point ID is an identification number that identifies the grid points. The L coordinate is the coordinate of the structural grid and is defined by the L axis extending outward from the boundary. The J coordinate is the coordinate of the structural grid and is the coordinate defined by the J axis along the boundary. The X coordinate is the coordinate of the orthogonal grid and is the coordinate defined by the X axis in the left-right direction of the CAD drawing. The Y coordinate is the coordinate of the orthogonal grid and is the coordinate defined by the Y axis in the vertical direction of the CAD drawing.

FIG. 11 is a diagram showing an example of a distance table and a fluid table.
The distance data storage unit 124 stores the distance table 143. The grid point ID and SDF value of each of the plurality of grid points are registered in the distance table 143. The grid point ID corresponds to the grid point ID of the grid point table 142. The SDF value is the distance between the grid points and the boundary, that is, the Euclidean distance between the point on the boundary closest to the grid point and the grid point. The SDF value is a positive real number because the grid points are outside the boundary.

The fluid data storage unit 125 stores the fluid table 144. In the fluid table 144, the lattice point ID, the velocity X component, and the velocity Y component of each of the plurality of lattice points are registered. The grid point ID corresponds to the grid point ID of the grid point table 142. The velocity X component is the X component of the velocity vector, that is, the component in the left-right direction on the CAD drawing. The velocity Y component is the Y component of the velocity vector, that is, the component in the vertical direction on the CAD drawing.

Next, the processing procedure of the information processing apparatus 100 will be described.
FIG. 12 is a flowchart showing an example of a procedure for learning an approximate model.
(S10) The grid generation unit 131 reads out the shape data created by the CAD software. Further, the lattice generation unit 131 reads out the number of L coordinates and the number of J coordinates, which are the lattice parameters registered in the lattice parameter table 141.

(S11) The grid generation unit 131 generates a variation of the shape data by giving a distortion to the object shape indicated by the shape data read in step S10. By combining the original shape data and variations, for example, about 2000 different object shapes are prepared.

(S12) The grid generation unit 131 selects one object shape.
(S13) The grid generation unit 131 generates grid points of a structured grid in which each coordinate axis is a curve and the grid points are not evenly spaced, based on the grid parameters read in step S10 and the boundary of the object shape selected in step S12. do. For example, the grid generation unit 131 sets the curve indicating the boundary as the J-axis, and sets the J-coordinates on the J-axis at equal intervals by the number of J-coordinates in step S10. The J coordinate is a non-negative integer that increases by 1 clockwise. Further, the grid generation unit 131 sets the L-coordinate on the L-axis by the number of L-coordinates in step S10, with the curve extending outward from the boundary as the L-axis. The intervals of the L coordinates are not even, and the closer to the boundary, the narrower the intervals. The L coordinate is a non-negative integer that increases by 1 from the boundary to the outside. The grid generation unit 131 generates a grid point table 142 showing the L coordinate, J coordinate, X coordinate, and Y coordinate of the generated grid points.

(S14) The distance calculation unit 132 generates a signed distance function that defines the distance from the boundary based on the object shape selected in step S12. The distance calculation unit 132 calculates the SDF value of each grid point based on the grid point table 142 generated in step S13 and the signed distance function, and generates a distance table 143 showing the calculated SDF value.

(S15) The simulation execution unit 133 assigns a velocity vector variable to each grid point based on the grid point table 142 generated in step S13. The simulation execution unit 133 generates simultaneous equations describing the constraints between variables based on the Navier-Stokes equation, which is a basic equation, and finds a solution of the simultaneous equations by an iterative method. The solution of the simultaneous equations is a velocity vector indicating the fluid velocity at each grid point. The simulation execution unit 133 generates a fluid table 144 showing the calculated velocity vector.

(S16) The tensor conversion unit 134 associates the lattice points with the elements of the tensor based on the number of L coordinates and the number of J coordinates registered in the lattice parameter table 141. The first dimension (row) of the tensor corresponds to the L coordinate, and the second dimension (column) of the tensor corresponds to the J coordinate.

(S17) The tensor conversion unit 134 rearranges the SDF values of the plurality of grid points included in the distance table 143 generated in step S14 into the tensor format according to the correspondence in step S16. This distance tensor becomes the input tensor. Further, the tensor conversion unit 134 rearranges the velocity vectors of the plurality of lattice points included in the fluid table 144 generated in step S15 into the tensor format according to the correspondence in step S16. The first channel of the tensor corresponds to the X component, and the second channel of the tensor corresponds to the Y component. This fluid velocity tensor becomes the output tensor. The tensor conversion unit 134 associates the distance tensor with the fluid velocity tensor and adds them to the training data.

(S18) The grid generation unit 131 determines whether all the object shapes have been selected in step S12. When all the object shapes are selected, the process proceeds to step S19, and when unselected object shapes remain, the process returns to step S12.

(S19) The learning unit 135 determines the hyperparameters of the approximate model based on the size of the distance tensor and the size of the fluid velocity tensor. Hyperparameters include the kernel size and stride of each convolution layer. The learning unit 135 determines the parameters of the approximate model by machine learning using the training data generated in step S17. The parameters include kernel elements for each convolution layer. The approximate model is a predictive model that predicts the fluid velocity tensor from the distance tensor. The learning unit 135 stores the generated approximate model in the approximate model storage unit 127.

FIG. 13 is a flowchart showing an example of a procedure for speeding up the simulation.
(S20) The grid generation unit 131 reads out the shape data created by the CAD software. Further, the lattice generation unit 131 reads out the number of L coordinates and the number of J coordinates, which are the lattice parameters registered in the lattice parameter table 141.

(S21) The lattice generation unit 131 is a lattice point of a structural lattice in which each coordinate axis is a curve and the lattice points are not evenly spaced based on the object shape indicated by the shape data read in step S20 and the lattice parameter read out in step S20. To generate. The grid generation unit 131 generates a grid point table 142 showing the L coordinate, J coordinate, X coordinate, and Y coordinate of the generated grid points.

(S22) The distance calculation unit 132 generates a signed distance function that defines the distance from the boundary based on the object shape indicated by the shape data. The distance calculation unit 132 calculates the SDF value of each grid point based on the grid point table 142 generated in step S21 and the signed distance function, and generates a distance table 143 showing the calculated SDF value.

(S23) The tensor conversion unit 134 associates the lattice points with the elements of the tensor based on the number of L coordinates and the number of J coordinates registered in the lattice parameter table 141.
(S24) The tensor conversion unit 134 rearranges the SDF values of the plurality of grid points included in the distance table 143 generated in step S22 into the tensor format according to the correspondence in step S23. This distance tensor becomes the input tensor.

(S25) The prediction unit 136 reads the approximate model from the approximate model storage unit 127. The prediction unit 136 inputs the distance tensor generated in step S24 into the approximation model to generate a fluid velocity tensor indicating an approximate value of the velocity vector of each grid point.

(S26) The prediction unit 136 rearranges the velocity vectors included in the fluid velocity tensor generated in step S25 in the order for fluid simulation based on the number of L coordinates and the number of J coordinates. The format of the sorted velocity vector is, for example, fluid table 144. The simulation execution unit 133 assigns a velocity vector variable to each grid point based on the grid point table 142 generated in step S21. The simulation execution unit 133 generates simultaneous equations describing the constraints between variables based on the Navier-Stokes equations. The simulation execution unit 133 substitutes the approximate value of the velocity vector calculated by the prediction unit 136 into the variable as the initial value. As a result, the simulation execution unit 133 can perform a warm start.

(S27) The simulation execution unit 133 starts the iterative method from the state in which the initial value is assigned to the variable in step S26, and finds the solution of the simultaneous equations. The solution calculated here is a velocity vector with higher accuracy than the approximate value calculated by the prediction unit 136. By performing a warm start, the number of iterations is smaller than when an initial value deviating from the approximate value is used.

(S28) The prediction unit 136 visualizes the velocity vector of each grid point calculated in step S27 and displays it on the display device 111. It is also possible to omit steps S26 and S27 and visualize the approximate value of the velocity vector of each grid point calculated in step S25.

According to the information processing apparatus of the second embodiment, grid points of a structured grid that is not an orthogonal grid are generated, and the fluid velocity of each grid point is calculated by fluid simulation. Therefore, the lattice points can be arranged at high density near the boundary, and the fluid velocity near the boundary having a large gradient can be calculated with high accuracy. In addition, an approximate model is generated from the simulation results for some object shapes, and the distribution of the fluid velocity is predicted from the object shapes by the approximate model. Therefore, it is not necessary to comprehensively execute the fluid simulation by the iterative method for a large number of shape proposals, the amount of calculation can be reduced, and the approximate value of the fluid velocity can be calculated at high speed. Therefore, the design work for examining a large number of shape proposals is streamlined.

In addition, when generating training data used for machine learning of an approximate model, the fluid velocity included in the simulation result is used as it is after being sorted according to the adjacency relationship of the grid points of the structured grid. Therefore, unlike the case where the orthogonal grid is used for the input / output of the approximate model, it is not necessary to perform the interpolation process for estimating the fluid velocity at a position different from the fluid simulation, and the sampling error due to the interpolation process can be suppressed. Therefore, the prediction accuracy of the approximate model is improved. In particular, the prediction accuracy near the boundary where the gradient of the fluid velocity is large is greatly improved.

In addition, the scale of the approximate model can be reduced compared to the case where an orthogonal grid is used for the input and output of the approximate model and the accuracy is improved by reducing the grid spacing. Therefore, the execution time of machine learning is shortened, and the training data size can be reduced. In addition, the output of the approximate model directly corresponds to the grid points of the structured grid used in the fluid simulation. Therefore, the warm start of the fluid simulation using the output of the approximate model can be executed without the interpolation processing, and the output of the approximate model can be smoothly used.

In addition, the SDF value is used as the input of the approximate model, and a plurality of SDF values are arranged according to the adjacency relationship of the grid points. Therefore, it is possible to accurately represent the shape of an object without adopting an orthogonal lattice. Also, the approximate model includes a convolutional layer, but does not include a pooling layer or a fully connected layer. Therefore, it is possible to prevent the loss of information on the adjacency relationship between a plurality of grid points in the calculation process inside the approximate model. Further, by using the convolution layer, the approximate model can be flexibly adjusted according to the size of the input / output.

The above merely indicates the principle of the present invention. Moreover, numerous modifications and modifications are possible to those skilled in the art, and the present invention is not limited to the exact configurations and applications described and described above, and all corresponding modifications and equivalents are attached. It is considered to be the scope of the present invention according to the claims and their equivalents.

10 Design equipment 11 Storage unit 12 Processing unit 13-1 to 13-9 Lattice points 14 Simulation result data 15 Teacher data 16 Input data 17 Approximate model

Claims (6)

1. On the computer
   A plurality of first grid points that are arranged in a region having a boundary defined by a specific object shape and that indicate a physical quantity of a fluid calculated by simulation in association with a plurality of grid points that are not evenly spaced. Get simulation result data including values
   Based on the adjacency relationship between the plurality of grid points, the plurality of first values are rearranged into a multidimensional array structure to generate teacher data including the plurality of first values of the multidimensional array structure. death,
   Using the input data including the second value indicating the specific object shape and the teacher data, an approximate model for predicting the distribution of the physical quantity of the fluid from the object shape is generated.
   A design program that executes processing.
2. The plurality of grid points are generated based on a plurality of coordinate axes including a first coordinate axis corresponding to a curve indicating the boundary and a second coordinate axis in which the distance between the coordinates becomes narrower as the distance between the coordinates becomes closer to the boundary.
   In the generation of the teacher data, each of the plurality of grid points is associated with an element in the multidimensional array structure based on the coordinates defined by the plurality of coordinate axes.
   The design program according to claim 1.
3. In addition to the computer
   A plurality of distance values indicating distances from the boundary are calculated as the second value in association with the plurality of grid points.
   Based on the adjacency, the plurality of distance values are rearranged into the multidimensional array structure to generate the input data including the plurality of distance values of the multidimensional array structure.
   The design program according to claim 1, wherein the process is executed.
4. The approximation model is an encoder that generates feature data smaller in size than the input multidimensional array from the input multidimensional array by one or more convolution operations, and the feature data by one or more deconvolution operations. Includes a decoder that produces a multidimensional array of outputs larger in size than the feature data.
   The design program according to claim 1.
5. In addition to the computer
   Other input data including a fourth value indicating another object shape is input to the approximate model to generate output data including a plurality of third values arranged in the multidimensional array structure.
   The simulation is executed by rearranging the plurality of third values according to the shape of the other object and using the rearranged plurality of third values as initial values of physical quantities of the fluid.
   The design program according to claim 1, wherein the process is executed.
6. The computer
   A plurality of first grid points that are arranged in a region having a boundary defined by a specific object shape and that indicate a physical quantity of a fluid calculated by simulation in association with a plurality of grid points that are not evenly spaced. Get simulation result data including values
   Based on the adjacency relationship between the plurality of grid points, the plurality of first values are rearranged into a multidimensional array structure to generate teacher data including the plurality of first values of the multidimensional array structure. death,
   Using the input data including the second value indicating the specific object shape and the teacher data, an approximate model for predicting the distribution of the physical quantity of the fluid from the object shape is generated.
   Design method.

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