CN-121683627-B - Method for predicting shock waves through multi-region conservation enhanced physical information neural network

CN121683627BCN 121683627 BCN121683627 BCN 121683627BCN-121683627-B

Abstract

The invention discloses a method for predicting shock waves through a multi-region conservation enhanced physical information neural network, which belongs to the field of flow field prediction of shock waves and strong nonlinear physical phenomena in high-speed flow, and comprises the steps of S1, carrying out numerical simulation through fluid dynamics software to obtain a reference flow field solution of an N-S control equation to be solved, verifying a model solving result, S2, constructing a neural network comprising an integration layer, a micro-layer and a loss function error layer, S3, constructing the physical information neural network, S4, training after setting training parameters of the physical information neural network, and determining whether convergence criteria are met through constructing a joint loss function corresponding to the physical information neural network, and S5, applying a trained neural network model to shock wave prediction of the high-speed flow field simulation under different working conditions. According to the invention, the width of the shock wave transition region is effectively compressed through the constraint of multi-region local conservation, so that the relative error of the physical quantity is obviously reduced compared with the prior method.

Inventors

LI YUBO
LIU FENG
Xiong Hengli
TANG HONGWEI
ZHENG YINGLONG
JIANG WANQIU

Assignees

中国空气动力研究与发展中心超高速空气动力研究所

Dates

Publication Date: 20260505
Application Date: 20260209

Claims (6)

1. A method for predicting shock waves through a multi-region conservation enhanced physical information neural network, comprising: s1, performing numerical simulation through fluid dynamics software to obtain a reference flow field solution of an N-S control equation to be solved, and verifying a model solving result; s2, constructing a neural network comprising an integral/micro layering and a loss function error layer; s3, combining the neural network constructed in the S2 with an N-S control equation, boundary conditions and a multi-region conservation constraint unit to obtain a physical information neural network; s4, setting training parameters of the physical information neural network based on simulation parameters of the S1, determining whether convergence criteria are met by constructing a joint loss function corresponding to the physical information neural network, and verifying with a reference flow field solution of the S1 after convergence; Wherein the joint Loss function Loss is characterized by: In the above-mentioned method, the step of, And The basic constraint weight and the conservation constraint weight are respectively, MSE bc is the boundary condition mean square error, MSE pde is the residual mean square error of the N-S control equation, and MSE conservation is the multi-region conservation constraint mean square error; After the integration part of the integration/micro layering performs integration treatment on sampling points in the multi-region conservation constraint unit, the loss function error layer maps an integration result into multi-region conservation constraint mean square error; After the integral/micro-layering differential part carries out differential processing on sampling points in a calculation domain, a loss function error layer maps differential processing results into residual mean square errors; s5, applying the trained physical neural network model to shock wave prediction of high-speed flow field simulation under different working conditions; the multi-region conservation constraint unit comprises a region dividing module, a local conservation constraint construction module and a self-adaptive enhancement module; The working content of the multi-region conservation constraint unit comprises: S30, determining a calculation domain of the sampling data based on the pre-solved flow problem; S31, dividing the calculation domain into a plurality of closed and locally conservation sub-regions by a region division module according to a preset division strategy; S32, embedding three types of local conservation integral constraints into each sub-region by the local conservation constraint construction module so as to convert the volume integral into a boundary line integral based on the Gaussian divergence theorem; And S33, the self-adaptive enhancement module is used for adaptively enhancing the sub-region based on the pressure gradient distribution in the calculation domain in the training process of the neural network.
2. The method for predicting shock waves by the multi-region conservation-enhanced physical information neural network of claim 1, wherein in S33, the specific constraint contents of the local conservation constraint construction module include mass conservation constraint, momentum conservation constraint, and energy conservation constraint; Wherein the conservation of mass constraint is characterized by the following formula: In the above-mentioned method, the step of, And The inflow boundary and the outflow boundary of the sub-region respectively, In order to achieve a density of the particles, As a velocity vector of the velocity vector, Is the vector of the normal outside the boundary, Arc length along the boundary of the subarea; the conservation of momentum constraint is characterized by the following equation: In the above formula, p is pressure, u is an x-direction velocity component, v is a y-direction velocity component, n x is a component of an out-of-boundary normal vector in the x-direction, and n y is a component of an out-of-boundary normal vector in the y-direction; The conservation of energy constraint is characterized by the following formula: in the above formula, E is the total energy and satisfies the state equation Gamma is the adiabatic index.
3. The method of predicting shock waves by a multi-region conservation enhanced physical information neural network of claim 1, wherein in S33, the adaptive enhancement is performed by: S330, monitoring pressure gradient distribution in a calculation domain in real time, and positioning high gradient regions related in each sub-region based on statistical distribution characteristics of pressure gradient module lengths; s331, carrying out additional region subdivision on the inside of each positioned high gradient region; S332, dynamically adjusting conservation constraint weights of the high gradient regions through self-adaptive parameters in the neural network so as to inhibit numerical oscillation and dissipation.
4. The method of predicting shock waves by a multi-region conservation enhanced physical information neural network of claim 3, wherein in S330, the localization of high gradient regions is achieved by: In the above-mentioned method, the step of, Represents the pressure gradient, μ represents the average level of the full-field pressure gradient, σ represents the fluctuation amplitude of the full-field pressure gradient, and k represents the standard deviation.
5. The method of predicting shock waves by a multi-region conservation enhanced physical information neural network of claim 1, wherein the multi-region conservation constrained mean square error is characterized by: Where N is the total number of divided sub-regions, i is the sub-region index, For the mass conservation residual of the i-th sub-region, And Momentum conservation residuals of the ith sub-region in the x-direction and the y-direction respectively, The energy conservation residual for the i-th sub-region.
6. The method for predicting shock waves by a multi-region conservation enhanced physical information neural network of claim 1, wherein the sampling points of the physical information neural network during training mainly comprise sampling points of a local conservation region, residual sampling points of a control equation and boundary sampling points.

Description

Method for predicting shock waves through multi-region conservation enhanced physical information neural network Technical Field The invention relates to the field of flow field prediction of shock waves and strong nonlinear physical phenomena in high flow. More particularly, the present invention relates to a method of predicting shock waves through a multi-region conservation enhanced physical information neural network. Background In the field of aerospace, accurately simulating the motion law of a high-speed flow field is a key for optimizing the design of an aircraft and improving the propulsion efficiency. The Navier-Stokes (N-S) equation is taken as a core theoretical basis of fluid mechanics, and strictly describes mass, momentum and energy conservation rules, but the traditional numerical method has the problems of strong grid dependence, low efficiency and the like under complex geometry and variable boundary conditions due to the nonlinear and strong coupling characteristics. In recent years, the Physical Information Neural Network (PINN) realizes the fusion of data driving and physical constraint by embedding a physical equation into a loss function, and has application potential in the field of fluid mechanics. However, the existing PINN and improved models face significant bottlenecks in solving the high-speed flow field: 1. the capturing capability of the shock wave equal-strength discontinuity is insufficient, namely, the traditional PINN is difficult to describe the severe gradient change of the physical quantity in the high-speed flow field, so that the shock wave boundary is blurred, the transition area is widened, and the numerical dissipation is serious; 2. The existing improvement method is mainly used for improving the performance by enhancing the observation data, the training overhead is increased, and the acquisition of experimental data of a high-speed flow field is limited by the equipment precision and experimental conditions, so that the cost is extremely high; 3. the stability contradicts with the precision, namely when facing a complex flow field, the model is easy to have precision decline and numerical oscillation; 4. The global conservation constraint is weak, that is, the traditional PINN only depends on the global constraint of an N-S equation, and the conservation reinforcement of a local area is lacked, so that the physical rule of a key area (such as a shock wave core area) deviates from a real solution. The above problems lead to the difficulty in meeting the requirements of engineering application on high precision and high stability of high-speed flow field fine structure simulation in the prior art, and a high-efficiency flow field solving method which does not depend on additional observation data and can strengthen local conservation constraint is needed. Disclosure of Invention It is an object of the present invention to address at least the above problems and/or disadvantages and to provide at least the advantages described below. To achieve these objects and other advantages and in accordance with the purpose of the invention, there is provided a method of predicting shock waves by a multi-region conservation-enhanced physical information neural network, comprising: s1, performing numerical simulation through fluid dynamics software to obtain a reference flow field solution of an N-S control equation to be solved, and verifying a model solving result; s2, constructing a neural network comprising an integral/micro layering and a loss function error layer; s3, combining the neural network constructed in the S2 with an N-S control equation, boundary conditions and a multi-region conservation constraint unit to obtain a physical information neural network; s4, setting training parameters of the physical information neural network based on simulation parameters of the S1, determining whether convergence criteria are met by constructing a joint loss function corresponding to the physical information neural network, and verifying with a reference flow field solution of the S1 after convergence; Wherein the joint Loss function Loss is characterized by: In the above-mentioned method, the step of, AndThe basic constraint weight and the conservation constraint weight are respectively, MSE bc is the boundary condition mean square error, MSE pde is the residual mean square error of the N-S control equation, and MSE conservation is the multi-region conservation constraint mean square error; After the integration part of the integration/micro layering performs integration treatment on sampling points in the multi-region conservation constraint unit, the loss function error layer maps an integration result into multi-region conservation constraint mean square error; After the integral/micro-layering differential part carries out differential processing on sampling points in a calculation domain, a loss function error layer maps differential processing results into residual m