@Article{CiCP-35-5,
author = {Li, Hongyan and Song, Jiang and Wenjun, Sun and Xu, Liwei and Zhou, Guanyu},
title = {A Model-Data Asymptotic-Preserving Neural Network Method Based on Micro-Macro Decomposition for Gray Radiative Transfer Equations},
journal = {Communications in Computational Physics},
year = {2024},
volume = {35},
number = {5},
pages = {1155--1193},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0315},
url = {https://global-sci.com/article/90951/a-model-data-asymptotic-preserving-neural-network-method-based-on-micro-macro-decomposition-for-gray-radiative-transfer-equations}
}