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. The code and all trained networks are provided on GitHub\footnote{\url{https://github.com/ScSteffen/neuralEntropyClosures}}$^,$\footnote{\url{https://github.com/CSMMLab/KiT-RT}}.

翻译：辐射传输大规模数值模拟的主要挑战在于动力学方程离散化方法对存储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近似的熵闭包方法，以低存储开销和具有竞争力的计算时间精确求解多维矩系统。我们将针对标准熵闭包的方法扩展到正则化熵闭包框架下。核心思想是将正则化熵闭包的结构保持神经网络近似理解为原始熵闭包的两阶段近似。我们对这一近似方法进行了数值分析，并研究了最优参数选择。数值实验表明，该方法在保持竞争性计算时间和仿真精度的同时，其存储开销远低于传统方法。所有代码和训练好的网络均已在GitHub上提供\footnote{\url{https://github.com/ScSteffen/neuralEntropyClosures}}$^,$\footnote{\url{https://github.com/CSMMLab/KiT-RT}}。