BF-APNN: A Low-Memory Method for Accelerating the Solution of Radiative Transfer Equations

The Radiative Transfer Equations (RTEs) exhibit high dimensionality and multiscale characteristics, rendering conventional numerical methods computationally intensive. Existing deep learning methods perform well in low-dimensional or linear RTEs, but still face many challenges with high-dimensional or nonlinear RTEs. To overcome these challenges, we propose the Basis Function Asymptotically Preserving Neural Network (BF-APNN), a framework that inherits the advantages of Radiative Transfer Asymptotically Preserving Neural Network (RT-APNN) and accelerates the solution process. By employing basis function expansion on the microscopic component, derived from micro-macro decomposition, BF-APNN effectively mitigates the computational burden associated with evaluating high-dimensional integrals during training. Numerical experiments, which involve challenging RTE scenarios featuring, nonlinearity, discontinuities, and multiscale behavior, demonstrate that BF-APNN substantially reduces training time compared to RT-APNN while preserving high solution accuracy. Moreover, BF-APNN exhibits superior performance in addressing complex, high-dimensional RTE problems, underscoring its potential as a robust tool for radiative transfer computations.