CN-121980971-A - Physical scene multi-region collaborative computing method based on self-adaptive protection structure

CN121980971ACN 121980971 ACN121980971 ACN 121980971ACN-121980971-A

Abstract

The invention relates to the technical field of computer-aided solution of a physical field or a mathematical equation, and discloses a physical scene multi-region collaborative computing method based on a self-adaptive protection structure. The method comprises the steps of dividing a global solving domain into a plurality of mutually connected and partially overlapped subdomains through domain decomposition, providing each subdomain with an independent physical information neural network model, then circularly executing the steps of extracting multidimensional features based on composite feature indexes in each subdomain, constructing a probability function according to the feature indexes, performing self-adaptive sampling to dynamically update a training set, dynamically optimizing loss function weights according to the variation trend of different loss terms after each round of training is finished, adding physical structure maintaining constraint terms into a total loss function, and circularly executing until convergence conditions are met, and outputting a physical field numerical solution. The method and the device realize accurate capture of the local high gradient region of the physical field, and ensure the stability and physical conservation of the model while improving the calculation precision and efficiency.

Inventors

PENG YAXIN
XIONG YUNKANG
PENG YAN
WEI HONGYU
MA ZHIYING
Nan Haoyu
QU DONG
Xie xie

Assignees

上海大学

Dates

Publication Date: 20260505
Application Date: 20260407

Claims (10)

1. The physical scene multi-region collaborative computing method based on the self-adaptive protection structure is characterized by comprising the following steps of: S1, dividing a global solving domain into a plurality of mutually connected and partially overlapped subdomains by a domain decomposition method, setting coverage areas between adjacent subdomains, and providing each subdomain with an independent physical information neural network PINN model; s2, extracting intra-subdomain characteristics, namely extracting multidimensional characteristics of data after one-round calculation of a neural network in each subdomain based on a characteristic extraction algorithm of a composite characteristic index; s3, self-adaptive sampling and training set updating, namely constructing a probability function according to the characteristic indexes extracted in the S2, and selecting samples and updating the training set in a targeted manner according to the importance degree and the structure deviation degree of different area data; and S4, self-adaptive weight adjustment and model convergence, namely dynamically optimizing the weight of the loss function according to the change trend of different loss items when each round of model training is finished, simultaneously explicitly adding a physical structure maintaining constraint item into the total loss function, and circularly executing the steps S2-S4 until convergence conditions are met, and outputting a physical field numerical solution.
2. The self-adaptive structure-based physical scene multi-region collaborative computing method according to claim 1, wherein the division basis of the region decomposition in S1 is geometric characteristics of a physical problem to be solved, expected physical field distribution or simple space division rules, and the coverage area is used for exchanging boundary information in a training process to ensure continuity of a final solution at a sub-region juncture and global conservation of physical quantity.
3. The self-adaptive structure-based physical scene multi-region collaborative computing method according to claim 1, wherein in S1, an independent physical information neural network PINN model of each sub-region is used for training a local data training set of the sub-region, realizing personalized learning for internal characteristics of the sub-region, and transmitting training results to adjacent sub-regions, so as to realize dynamic coordination of information between the regions.
4. The method for multi-region collaborative calculation of a physical scene based on an adaptive structure according to claim 1, wherein the calculation formula of the composite characteristic index in S2 is: ; Wherein alpha, beta and gamma represent super parameters, the default values are all 1, Representing the gradient operator(s), Representing the laplace operator of the image, Representing the neural network predicted outcome.
5. The adaptive structure-based physical scene multi-region collaborative computing method according to claim 1, wherein the multi-dimensional features in S2 include residual distribution features and gradient change rates, the residual distribution features being a current physical information neural network PINN model predictive solution The degree of controlling partial differential equation is satisfied at the sampling point in the subdomain, and the gradient change rate is the gradient amplitude or the change rate of the physical field variable under the current solution.
6. The adaptive structure-based physical scene multi-region collaborative computing method according to claim 1, wherein the probability function in S3 has a computing formula: ; wherein x is the physical field coordinate , In the form of a spatial coordinate system, And for the time coordinate, ω is the composite characteristic index in S2, k is a structure maintaining weight coefficient, and the default value is 1.
7. The method for multi-region collaborative calculation of a physical scene based on an adaptive protection structure according to claim 1, wherein the adaptive sampling strategy in S3 is to increase sampling points with higher probability in a region with high eigenvalue, and maintain or reduce sampling points in a region with low eigenvalue, wherein the region with high eigenvalue is a region with severe physical field variation or large current solution error.
8. The adaptive structure-based physical scene multi-region collaborative computing method according to claim 1, wherein the total loss function in S4 is computed as: ; Wherein, the Representing the number of neural networks, For the residual loss, In order for the boundary to be lost, For initial loss, θ represents a neural network internal parameter, 、、 And the default value is 0 for super parameters, and the super parameters are updated in the training process.
9. The adaptive structure-based physical scene multi-region collaborative computing method according to claim 1, wherein the physical structure-preserving constraint terms in S4 include a weak form constraint of global mass conservation, momentum conservation.
10. The adaptive structure-based physical scene multi-region collaborative computing method according to claim 1, wherein the convergence condition in S4 is that verification errors and structure constraint residuals of all subfields are lower than a preset threshold.

Description

Physical scene multi-region collaborative computing method based on self-adaptive protection structure Technical Field The invention relates to the technical field of computer-aided solution of a physical field or a mathematical equation, in particular to a physical scene multi-region collaborative computing method based on a self-adaptive protection structure. Background At present, simulation analysis of a physical field mainly depends on various traditional simulation software, such as a commercial simulation platform developed based on numerical methods such as finite element, finite volume or finite difference. The traditional simulation software has higher maturity in engineering design and scientific research application, but has obvious defects in complex scenes. When complex geometries or multi-scale coupling problems are involved, the meshing of models in traditional simulation software requires a great deal of manual participation, and the calculation scale rises sharply with the problem dimension. In order to obtain enough precision, very fine grids and high-order discrete formats are often adopted, so that the solving efficiency of a physical field is low, the single simulation consumes hours or even days, and high-performance computing resource support is needed, so that the computing cost is extremely high. The simulation solving speed of the traditional simulation software has a bottleneck, directly restricts the product research and development and optimization cycle, for example, in hydrodynamic design, the configurations of wings, impellers and the like often need to undergo hundreds of times of pneumatic shape adjustment and performance verification, and if the calculation cycle is overlong each time, the design efficiency and the scheme iteration speed are seriously affected, and the whole research and development process is delayed. At the same time, the traditional solving process is highly sensitive to the change of geometric shapes and boundary conditions, and the reconstruction and meshing are needed after a little modification, so that the calculation burden is further increased. In addition, in the multi-physical field coupling problem (such as fluid-solid coupling or heat flow coupling), the traditional simulation software often needs multi-module joint calculation, the convergence process is unstable, the data interaction is complex, the simulation period is long, the result is inconsistent, and the requirements of high efficiency, flexibility and instantaneity in modern engineering are difficult to meet. In order to overcome the limitation of the traditional simulation software in terms of computational efficiency and expandability, an intelligent solving method based on a physical information neural network (Physics-Informed Neural Networks, PINNs), hereinafter referred to as PINNs method, has appeared in recent years. The method directly embeds the physical constraint of the partial differential equation into the deep learning framework, and realizes gridless solving in a mode of fusing data driving and physical laws, thereby reducing modeling complexity and grid dependence to a certain extent. Meanwhile, the PINNs method can remarkably shorten the solving time under the condition of obtaining similar precision by utilizing the efficient parallel computing characteristic of the neural network, realizes the rapid solving of the complex physical field, and provides a new thought for the efficient solving of the physical field. However, the existing PINNs method still has significant drawbacks in engineering applications. On one hand, a training strategy of global uniform sampling is adopted, so that local high gradient areas in a physical field, such as shock waves, interfaces or boundary layers, are difficult to effectively identify and capture, and the local solving error is large, and the overall accuracy is insufficient. On the other hand, the network structure is usually fixed, the self-adaptive adjustment capability for the physical complexity and physical characteristic difference of different areas is lacking, the problems of oscillation or non-convergence and the like are easy to occur when a multi-scale, complex boundary or nonlinear equation is processed, and the stability is poor. In addition, the phenomena of unbalanced proportion of loss terms, disappearance of gradient, difficulty in explicitly maintaining the original conservation property of a physical system and the like exist in the training process, so that the accuracy and the reliability of the model are further influenced. Disclosure of Invention In view of the above, the invention provides a physical scene multi-region collaborative computing method based on a self-adaptive protection structure, which aims to solve the technical problem in the existing physical field solving method based on a Physical Information Neural Network (PINNs). The problems are caused by the adoption of a fixed sampling strateg