TY - JOUR
T1 - A Model-Data Asymptotic-Preserving Neural Network Method Based on Micro-Macro Decomposition for Gray Radiative Transfer Equations
AU - Li , Hongyan
AU - Jiang , Song
AU - Sun , Wenjun
AU - Xu , Liwei
AU - Zhou , Guanyu
JO - Communications in Computational Physics
VL - 5
SP - 1155
EP - 1193
PY - 2024
DA - 2024/06
SN - 35
DO - http://doi.org/10.4208/cicp.OA-2022-0315
UR - https://global-sci.org/intro/article_detail/cicp/23188.html
KW - Gray radiative transfer equation, micro-macro decomposition, model-data, asymptotic-preserving neural network, convergence analysis.
AB - <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>