A Model-Data Asymptotic-Preserving Neural Network Method Based on Micro-Macro Decomposition for Gray Radiative Transfer Equations
Year: 2024
Author: Hongyan Li, Song Jiang, Wenjun Sun, Liwei Xu, Guanyu Zhou
Communications in Computational Physics, Vol. 35 (2024), Iss. 5 : pp. 1155–1193
Abstract
We propose a model-data asymptotic-preserving neural network (MD-APNN) method to solve the nonlinear gray radiative transfer equations (GRTEs). The system is challenging to be simulated with both the traditional numerical schemes and the vanilla physics-informed neural networks (PINNs) due to the multiscale characteristics. Under the framework of PINNs, we employ a micro-macro decomposition technique to construct a new asymptotic-preserving (AP) loss function, which includes the residual of the governing equations in the micro-macro coupled form, the initial and boundary conditions with additional diffusion limit information, the conservation laws, and a few labeled data. A convergence analysis is performed for the proposed method, and a number of numerical examples are presented to illustrate the efficiency of MD-APNNs, and particularly, the importance of the AP property in the neural networks for the diffusion dominating problems. The numerical results indicate that MD-APNNs lead to a better performance than APNNs or pure Data-driven networks in the simulation of the nonlinear non-stationary GRTEs.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0315
Communications in Computational Physics, Vol. 35 (2024), Iss. 5 : pp. 1155–1193
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 39
Keywords: Gray radiative transfer equation micro-macro decomposition model-data asymptotic-preserving neural network convergence analysis.