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We propose a model-data asymptotic-preserving neural network(MD-APNN) methodto solve the nonlinear gray radiative transfer equations(GRTEs). The system ischallenging to be simulated with both the traditional numerical schemes and thevanilla physics-informed neural networks(PINNs) due to the multiscalecharacteristics. Under the framework of PINNs, we employ a micro-macrodecomposition technique to construct a new asymptotic-preserving(AP) lossfunction, which includes the residual of the governing equations in themicro-macro coupled form, the initial and boundary conditions with additionaldiffusion limit information, the conservation laws, and a few labeled data. Aconvergence analysis is performed for the proposed method, and a number ofnumerical examples are presented to illustrate the efficiency of MD-APNNs, andparticularly, the importance of the AP property in the neural networks for thediffusion dominating problems. The numerical results indicate that MD-APNNslead to a better performance than APNNs or pure data-driven networks in thesimulation of the nonlinear non-stationary GRTEs.

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