RT-APNN for Solving Gray Radiative Transfer Equations

TL;DR

The paper introduces RT-APNN, a novel neural network framework that efficiently solves high-dimensional, nonlinear Gray Radiative Transfer Equations, outperforming existing methods in accuracy and computational speed, and successfully simulating complex problems like the Marshak wave.

Contribution

It presents the first deep learning method capable of solving high-dimensional, nonlinear GRTEs with improved accuracy and efficiency, incorporating advanced training techniques.

Findings

RT-APNN outperforms existing methods in accuracy and speed.

Successfully simulates the complex Marshak wave problem.

Effective in high-dimensional, nonlinear scenarios.

Abstract

The Gray Radiative Transfer Equations (GRTEs) are high-dimensional, multiscale problems that pose significant computational challenges for traditional numerical methods. Current deep learning approaches, including Physics-Informed Neural Networks (PINNs) and Asymptotically Preserving Neural Networks (APNNs), are largely restricted to low-dimensional or linear GRTEs. To address these challenges, we propose the Radiative Transfer Asymptotically Preserving Neural Network (RT-APNN), an innovative framework extending APNNs. RT-APNN integrates multiple neural networks into a cohesive architecture, reducing training time while ensuring high solution accuracy. Advanced techniques such as pre-training and Markov Chain Monte Carlo (MCMC) adaptive sampling are employed to tackle the complexities of long-term simulations and intricate boundary conditions. RT-APNN is the first deep learning method to successfully simulate the Marshak wave problem. Numerical experiments demonstrate its superiority over existing methods, including APNNs and MD-APNNs, in both accuracy and computational efficiency. Furthermore, RT-APNN excels at solving high-dimensional, nonlinear problems, underscoring its potential for diverse applications in science and engineering.