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.

翻译：本文提出了一种渐近保持随机特征方法（APRFM），用于高效求解多尺度辐射输运方程。该方法通过采用微宏观分解策略，有效应对了辐射输运方程固有的刚性和多尺度特性所带来的挑战。该策略将分布函数分解为平衡分量与非平衡分量，使得两部分均可在最小二乘极小化框架下通过随机特征方法（RFM）进行逼近。所提方法在不同尺度下均展现出卓越的鲁棒性，且相较于原始RFM，能以更少的自由度和配置点实现高精度。此外，与基于深度神经网络的方法相比，本方法在参数效率和计算速度方面具有显著优势。这些优势已通过对一维及二维问题的多项数值实验得到验证。