A model-data asymptotic-preserving neural network method based on micro-macro decomposition for gray radiative transfer equations

• URL: http://arxiv.org/abs/2212.05523v1
• Date: Sun, 11 Dec 2022 15:08:09 GMT
• Title: A model-data asymptotic-preserving neural network method based on micro-macro decomposition for gray radiative transfer equations
• Authors: Hongyan Li, Song Jiang, Wenjun Sun, Liwei Xu, Guanyu Zhou
• Abstract summary: We propose a model-data-preserving neural network(MD-APNN) method to solve the nonlinear gray radiative transfer equations(GRTEs)
• Score: 4.220781196806984
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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