A Micro-Macro Decomposition-Based Asymptotic-Preserving Random Feature Method for Multiscale Radiative Transfer Equations

TL;DR

This paper presents an asymptotic-preserving random feature method that efficiently solves multiscale radiative transfer equations by combining micro-macro decomposition with the random feature approach, improving accuracy and computational efficiency.

Contribution

The paper introduces a novel APRFM that integrates micro-macro decomposition with RFM, enhancing robustness and efficiency in multiscale radiative transfer simulations.

Findings

Achieves high accuracy with fewer degrees of freedom.

Demonstrates robustness across different scales.

Outperforms deep neural network methods in speed and parameter efficiency.

Abstract

This paper introduces the Asymptotic-Preserving Random Feature Method (APRFM) for the efficient resolution of multiscale radiative transfer equations. The APRFM effectively addresses the challenges posed by stiffness and multiscale characteristics inherent in radiative transfer equations through the application of a micro-macro decomposition strategy. This approach decomposes the distribution function into equilibrium and non-equilibrium components, allowing for the approximation of both parts through the random feature method (RFM) within a least squares minimization framework. The proposed method exhibits remarkable robustness across different scales and achieves high accuracy with fewer degrees of freedom and collocation points than the vanilla RFM. Additionally, compared to the deep neural network-based method, our approach offers significant advantages in terms of parameter efficiency and computational speed. These benefits have been substantiated through numerous numerical experiments conducted on both one- and two-dimensional problems.