Neural network end-to-end acceleration method of AUSM type flux calculation format

Abstract

The invention discloses a neural network end-to-end acceleration method of an AUSM type flux calculation format, and relates to the field of fluid mechanics calculation, and the method comprises the steps: S1, achieving end-to-end input and output mapping based on a feedforward neural network, so as to build a neural network agent model; s2, replacing an AUSM type flux calculation format in a fluid mechanics calculation process by adopting the neural network agent model in the S1; wherein the input data of the neural network agent model is a non-dimensionalized physical quantity under any one of subsonic velocity, transonic velocity, supersonic velocity and hypersonic velocity wind tunnel test working conditions; in the establishment process of the neural network agent model, a Sobol sequence sampling method is optimized in a mode of locally encrypting a calculation dense region. According to the neural network end-to-end acceleration method of the AUSM type flux calculation format, the neural network agent model is introduced, so that the flux which needs six steps to be calculated can be directly obtained in one step through the input condition, and the calculation amount is remarkably reduced.

Description

Technical Field

[0001] The present invention relates to the field of fluid mechanics calculations, and more specifically, to a neural network end-to-end acceleration method in an AUSM-type flux calculation format. Background Art

[0002] In traditional CFD calculations, the time consumption of flux calculation usually accounts for a large proportion of the entire calculation process, generally between 20% and 40%. This proportion varies depending on the specific numerical method, grid resolution, flow complexity, and the degree of solver optimization.

[0003] Among them, the flux calculation includes solving the convective flux and viscous flux in the governing equations, which is one of the most time-consuming parts of the entire CFD solver. Especially in complex flow fields, such as flow environments with shock waves, vortices and turbulence, the accurate calculation of flux becomes particularly important, further increasing the calculation time.

[0004] As an approximate Riemann solver, AUSM (Advection Upstream Splitting Method) is widely used in various flow simulation scenarios from low subsonic to high supersonic in the treatment of compressible flows. From the perspective of format construction, AUSM combines the discontinuous high resolution of Roe format and the computational efficiency of van Leer format, and overcomes the shortcomings of both. It has low numerical dissipation and high resolution of shock waves and contact discontinuities without correction. This format has gradually gained praise for its extremely excellent performance, and has continued to develop many new variants, such as AUSMDV, AUSM+UP, AUSMPW+, etc.

[0005] Optimizing the AUSM format can not only speed up the operation of a single solver, but also affect the solution of various types of fluid mechanics equations, especially in complex aerodynamic design, shock wave capture, boundary layer calculation, etc. If the flux calculation process of the AUSM-type format can be fitted and a large number of nonlinear operations in the traditional calculation process can be replaced, the overall calculation efficiency of many CFD problems will actually be significantly improved.

[0006] Taking the AUSMPW+ format as an example, the flux at the center of the i-th grid cell in three dimensions is The calculation method is as follows: in, represents the average sound speed on the interface; and denote the modified Mach number terms in the positive and negative directions (i.e., left and right directions), respectively, for flux splitting; and are the conserved variables on the left and right sides respectively; represents the pressure correction term of the interface; is the unit normal vector, which represents the direction of pressure.

[0007] The calculation process starts with the average speed of sound at the interface, which is obtained by taking the arithmetic average of the speeds of sound on the left and right sides. The Mach number at the interface is then calculated based on the ratio of the speed to the speed of sound. When dealing with convective flux, the format uses different calculation schemes depending on whether the Mach number exceeds 1. Similarly, the contribution of the pressure term also needs to be treated differently depending on the size of the Mach number. In order to improve the calculation accuracy of the shock wave region, the format also introduces pressure weights and balance factors.

[0008] An important feature of the AUSM format is that special areas will be additionally processed, such as the transonic region (Mach number close to 1), the strong shock wave region, and the region with large pressure gradient. However, this calculation process involves a large number of minimum / maximum operations, absolute value calculations, symbol judgments, and conditional branches, involving data dependencies and frequent interruptions of the calculation pipeline, which will significantly affect the performance of large-scale numerical calculations, especially in a high-concurrency environment. Therefore, if these nonlinear operations can be optimized, the overall calculation efficiency of CFD problems can be greatly improved. Summary of the invention

[0009] An object of the present invention is to solve at least the above problems and / or disadvantages and to provide at least the advantages which will be described hereinafter.

[0010] In order to achieve these objectives and other advantages of the present invention, a neural network end-to-end acceleration method in an AUSM-like flux calculation format is provided, comprising: S1. Implement end-to-end input-output mapping based on feedforward neural network to establish a neural network proxy model; S2, using the neural network proxy model of S1 to replace the AUSM type flux calculation format in the fluid dynamics calculation process; Among them, the input data of the neural network proxy model are: dimensionless physical quantities under any wind tunnel test conditions of subsonic, transonic, supersonic and hypersonic speeds, and the physical quantities include: Mach number Ma ,density ρ ,pressure p The data on the left and right sides of each; the output data are: the three-dimensional flux prediction results of mass, momentum and energy after flux calculation; In the process of establishing the neural network proxy model, the Sobol sequence sampling method is optimized by locally encrypting the densely calculated areas.

[0011] Preferably, the dense area refers to a complex flow field characteristic area similar to a shock wave or an expansion wave; The method for local encryption of densely calculated areas is: S10. When collecting data, the number of pre-collected data in the dense area M Expanded to the total number of sampling points N ; S11, sampling point The sampling probability is assigned the corresponding weight ,and i =1,2… M ; S12, the sampling point is calculated by the following formula The weights are normalized and the normalized results are used as sampling points The random sampling probability : In the above formula, , is the weight of the jth sampling point; S13, randomly select 𝑀 points from 𝑁 sampling points with the random sampling probability obtained in S12; S14. Preset a sampling probability judgment threshold to generate additional sampling points in a random sampling point area where the random sampling probability is greater than the judgment threshold to increase the sampling density.

[0012] Preferably, in S11, the sampling point Feature Base Obtained by the following formula: In the above formula, , are the pressure values ​​on both sides of each set of data, , are the density values ​​of each group of data.

[0013] Preferably, in S10, for different types of examples, the sampling point data is screened by Beta distribution, and the weights It is characterized by the following formula: In the above formula, is the Gamma function, and , is the integrand of the Gamma function, is the parameter that determines the shape of the Beta distribution.

[0014] Preferably, the network structure of the neural network proxy model includes: The feature layer is used to extract features from the left and right sides of the input data; Fully connected layer I that fuses the extracted features together; A residual block layer for improving the nonlinear fitting ability of the network, wherein the residual block layer includes three fully connected layers II; Based on the output of the hidden layer, a fully connected layer III is used to obtain the flux prediction result; Among them, the activation function of the neural network proxy model adopts the Swish function.

[0015] Preferably, the method for generating data in the neural network proxy model is: based on the given input data of each dimension, a six-dimensional data that can be input as an AUSM-type format is obtained by a Sobol sequence sampling method, so as to output the predicted true value through the neural network proxy model: The present invention has at least the following beneficial effects: in the flux calculation process of the direct numerical simulation process, it involves calculating intermediate quantities such as the interface characteristic sound velocity, the interface pressure term and the pressure correction term, and these processes are usually accompanied by complex nonlinear operations and conditional judgments. However, the present invention introduces a neural network proxy model, so that the flux that requires 6 steps to calculate in the prior art can be directly obtained in one step by inputting conditions, which significantly reduces the amount of calculation.

[0016] Other advantages, objectives and features of the present invention will be embodied in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A schematic diagram for comparing the process of applying the neural network proxy model of the present invention in a CFD solver; Figure 2 A network structure diagram of a neural network proxy model of the present invention; Figure 3 A schematic diagram showing the comparison between the direct numerical simulation (DNS) and the local encrypted neural network proxy model; Figure 4 A schematic diagram showing the comparison between direct numerical simulation (DNS) and local encrypted neural network proxy model calculation; Among them, feature layer-1, fully connected layer I-2, residual block layer-3, fully connected layer II-4, and fully connected layer III-5. DETAILED DESCRIPTION

[0018] The present invention is further described in detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0019] The universal approximation theorem has proved that a feedforward neural network with a linear output layer and at least one hidden layer with an activation function of any kind of "squeezing" property can approximate any Borel measurable function from one finite-dimensional space to another finite-dimensional space with arbitrary accuracy as long as the network is given a sufficient number of hidden units. This means that feedforward networks also have the potential to represent AUSMPW+ format operations.

[0020] The calculation of each layer of the neural network mainly relies on linear transformation, that is, mapping input features to outputs through matrix multiplication, and the main computational overhead is concentrated on the activation function. Since the number of neural network layers is far less than the number of nonlinear operations in the AUSMPW+ format, if end-to-end input-output mapping can be achieved through a feedforward neural network, it is expected to significantly accelerate this calculation process, thereby improving the overall computing efficiency.

[0021] In order to achieve the above effects, the present invention needs to construct a corresponding neural network proxy model based on the existing flux calculation in the CFD solver. The design method of the neural network proxy model is as follows: (1) Input and Output Input: Mach number, density, pressure for left and right sides.

[0022] Output: momentum flux, mass flux, energy flux The method for generating data in the neural network proxy model is: based on the given input data of each dimension, the Sobol sequence sampling method is used to obtain six-dimensional data that can be input as AUSM type format, so as to output the predicted true value through the neural network proxy model.

[0023] (2) Sampling method When the input feature dimension is 6, if the traditional Monte Carlo sampling method is used, generating 100 data in each dimension will cause the amount of data to increase dramatically, reaching a scale of 10^12, which will greatly increase the complexity and cost of calculation and storage. In order to improve this problem, it is necessary to consider a more efficient sampling method. There are several different sampling methods, including random uniform sampling (Uniform), Latin hypercube sampling (LHS), Halton sequence and Sobol sequence. After experimental testing, it was found that the sample discreteness of Sobol sequence sampling is the lowest.

[0024] The Sobol sequence is based on the binary digital system and generates point sets in high-dimensional space through a recursive method. It is widely used in high-dimensional numerical integration and Monte Carlo simulation. The key idea is to use direction vectors to generate points with good uniform distribution characteristics. Specifically, the Sobol sequence uses the construction idea of ​​pseudo-random sequences to optimize the uniformity of low-dimensional projections, so that the point set can be evenly covered in each dimension.

[0025] In order to improve the pertinence and efficiency of sampling points, local encryption is performed on the dense areas of calculation based on Sobol sequence sampling (local encryption refers to increasing the original sampling density (or original sampling quantity) of the dense areas. For example, if the original sampling density requires one thousand sampling data, ten thousand sampling data are generated by local encryption, and then one thousand are selected from ten thousand by probability. In this way, the probability of the dense area being selected is higher). According to prior knowledge, shock waves usually appear in areas with large pressure or density gradients, and expansion waves often appear in areas with reduced pressure and accelerated fluids. These similar areas are regarded as dense areas of calculation. In combination with these characteristics, data is screened by Beta distribution for different types of examples.

[0026] During data collection, the number of pre-collected data in dense areas M Expanded to the total number of sampling points N ,For this part, it can be regarded as the regular first increase in sampling density; For each sampling point The probability weight , which can be expressed as: in, i =1,2… M , is the Gamma function. The Gamma function ensures that the probability density function of the Beta distribution integrates to 1, and allows us to use continuous parameters to adjust the distribution shape, which is defined as: The choice of parameters determines the shape of the Beta distribution. a = b =1, the Beta distribution degenerates into a uniform distribution; when a>b When x = around 1; when a aFigure 2 When x =near 0.

[0027] For each sampling point In order to unify the dimensions, the smaller value of the pressure ratio and density ratio on both sides of each set of data is used as the basis, that is: In the above formula, , are the pressure values ​​on both sides of each set of data, , are the density values ​​of each set of data. Specifically, each x is a set of 6-dimensional data, and the pressure and density on both sides of each set are taken.

[0028] On this basis, by reasonably setting up a set of Ma Parameters such as a =2, b =2.5, which can make the larger ratio have a higher probability weight.

[0029] At the same time, in order to ensure that the probability distribution is uniform at all sampling points, the weight of each sampling point is normalized as: in, It is the sampling point The normalized result is taken as the sampling point The random sampling probability of satisfy: Next, a random sampling algorithm is used to randomly select the required M points from the N sampling points. In order to increase the sampling density, a probability threshold is defined , in the random sampling probability Greater than threshold The area generates additional sampling points twice. This part can be regarded as a secondary increase in the sampling density of dense areas: Among them, the threshold coefficient k Determined by actual working conditions: The longer the flow field changes dramatically, k The larger the value.

[0030] (3) Dimensionless data Since the positive and negative values ​​of velocity represent direction, the velocity is normalized to (-1, 1); density and pressure are always greater than 0, so they are normalized to (0, 1); the flux has a large span of magnitude, so the Z-score normalization method is used.

[0031] (4) Network structure like ρ As shown, the network structure of the neural network proxy model of the present invention includes: Feature layer 1 for extracting features from the left and right sides of the input data; Fully connected layer I2 that fuses the extracted features together; A residual block layer 3 for improving the nonlinear fitting ability of the network, wherein the residual block layer comprises three fully connected layers II4; Based on the output of the hidden layer, a fully connected layer III5 is used to obtain the flux prediction result. In actual applications, the feature layer 1 first extracts features of the physical quantities on the left and right sides respectively. After extracting the features, the features are fused together through the fully connected layer I2. Next, a residual block 3 with 3 hidden layers is used to improve the nonlinear fitting ability of the network. Finally, the flux prediction result is obtained through the fully connected layer III5.

[0032] The number of neurons can be adjusted according to the accuracy requirements, and the activation function is the Swish function. Swish is as efficient as ReLU in computation and performs better than ReLU on deeper models.

[0033] With Mach data on the left and right Figure 1 ,density ρ ,pressure p A total of 6-dimensional input is used to train an end-to-end neural network agent model.

[0034] The neural network proxy model of the present invention is applied to the method used in the direct numerical simulation process. Figure 3 shown.

[0035] Example: A typical one-dimensional shock tube problem is used as the initial condition setting. x = 0, there is a discontinuous distribution of density and pressure, and the initial state is: in, Figure 4 , u and p represent density, velocity and pressure respectively.

[0036] Based on this example, the effect of the flux prediction model was verified. As shown in Table 1, compared with direct numerical simulation (DNS), the acceleration ratio of the neural network proxy model of the present invention is about 20x.

[0037] Table 1 like ​ As shown in Figure 2, the convergence results of the neural network without local encryption are compared with the convergence results of the direct data simulation DNS. It can be seen that the deviation between the two is large. ​ As shown in the figure, the convergence results of the local encrypted neural network are compared with the convergence results of the direct data simulation DNS. It can be seen that in the expansion wave region, although there are slight deviations, the change trend captured by the proxy model is almost consistent with the DNS results. More importantly, the model successfully captures the drastic changes in the shock wave region, showing good robustness and accuracy.

[0038] The above solution is only an illustration of a preferred embodiment, but is not limited thereto. When implementing the present invention, appropriate replacement and / or modification can be performed according to user needs.

[0039] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and the embodiments. It can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily realized. Therefore, without departing from the general concept defined by the claims and equivalent scope, the present invention is not limited to the specific details and the illustrations shown and described here.

Claims

1. A neural network end-to-end acceleration method in AUSM-like flux calculation format, characterized in that: include: S1. Implement end-to-end input-output mapping based on feedforward neural network to establish a neural network proxy model; S2, using the neural network proxy model of S1 to replace the AUSM type flux calculation format in the fluid dynamics calculation process; The input data of the neural network proxy model are: dimensionless physical quantities under any wind tunnel test conditions of subsonic, transonic, supersonic and hypersonic speeds, including: data on the left and right sides of Mach number Ma, density ρ and pressure p; the output data are: three-dimensional flux prediction results of mass, momentum and energy after flux calculation; In the process of establishing the neural network proxy model, the Sobol sequence sampling method is optimized by locally encrypting the densely calculated areas.

2. The neural network end-to-end acceleration method in the AUSM-type flux calculation format as claimed in claim 1, characterized in that: The dense area refers to a complex flow field characteristic area similar to shock waves and expansion waves; The method for local encryption of densely calculated areas is: S10. When collecting data, the number of pre-collected data in the dense area M Expanded to the total number of sampling points N ; S11, sampling point The sampling probability is assigned the corresponding weight ,and i =1,2… M ; S12, the sampling point is calculated by the following formula The weights are normalized and the normalized results are used as sampling points The random sampling probability : In the above formula, , is the weight of the jth sampling point; S13, randomly select 𝑀 points from 𝑁 sampling points with the random sampling probability obtained in S12; S14. Preset a sampling probability judgment threshold to generate additional sampling points in a random sampling point area where the random sampling probability is greater than the judgment threshold to increase the sampling density.

3. The neural network end-to-end acceleration method in the AUSM-type flux calculation format as claimed in claim 2, characterized in that: In S11, the sampling point Feature Base Obtained by the following formula: In the above formula, , are the pressure values ​​on both sides of each set of data, , are the density values ​​of each group of data.

4. The neural network end-to-end acceleration method in the AUSM-type flux calculation format as claimed in claim 2, characterized in that: In S10, the Beta distribution is used to filter the sampling point data for different types of cases, and the weight It is characterized by the following formula: In the above formula, is the Gamma function, and , is the integrand of the Gamma function, is the parameter that determines the shape of the Beta distribution.

5. The neural network end-to-end acceleration method in the AUSM-type flux calculation format as claimed in claim 1, characterized in that: The network structure of the neural network proxy model includes: The feature layer is used to extract features from the left and right sides of the input data; Fully connected layer I that fuses the extracted features together; A residual block layer for improving the nonlinear fitting ability of the network, wherein the residual block layer includes three fully connected layers II; Based on the output of the hidden layer, a fully connected layer III is used to obtain the flux prediction result; Among them, the activation function of the neural network proxy model adopts the Swish function.

6. The neural network end-to-end acceleration method in the AUSM-type flux calculation format as claimed in claim 1, characterized in that: The method for generating data in the neural network proxy model is: based on the given input data of each dimension, six-dimensional data that can be input as AUSM type format is obtained through the Sobol sequence sampling method, so as to output the predicted true value through the neural network proxy model.

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