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

TL;DR

BF-APNN is a novel neural network framework that significantly accelerates solving high-dimensional, nonlinear radiative transfer equations while maintaining high accuracy, by employing basis function expansion to reduce computational costs.

Contribution

The paper introduces BF-APNN, a low-memory neural network method that leverages basis function expansion to efficiently solve complex, high-dimensional RTEs, improving speed and accuracy over existing methods.

Findings

BF-APNN reduces training time compared to RT-APNN.

BF-APNN effectively handles nonlinear, discontinuous, and multiscale RTEs.

BF-APNN maintains high solution accuracy in challenging scenarios.

Abstract

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.