The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the context of regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy closure as a two-stage approximation to the original entropy closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy.

翻译：辐射输运大规模数值模拟的主要挑战在于动理学方程离散化方法对内存和计算时间的高要求。本文推导并研究了一种基于神经网络的熵闭合方法近似，以低内存占用和具有竞争力的计算时间精确计算多维矩系统的解。我们将针对标准熵基闭合开发的方法扩展到正则化熵基闭合的框架中。核心思想是将正则化熵闭合的结构保持神经网络近似解释为对原始熵闭合的两阶段逼近。我们对该近似进行了数值分析，并探究了最优参数选择。数值实验表明，与传统方法相比，本方法在保持相当计算时间和模拟精度的同时，显著降低了内存占用。