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 https://github.com/ScSteffen/neuralEntropyClosures and https://github.com/CSMMLab/KiT-RT.

翻译：辐射输运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内存和计算时间的高需求。本文推导并研究了一种基于神经网络的熵闭合方法近似方案，能够以低内存占用和具有竞争力的计算时间精确求解多维矩系统。我们将标准熵基闭合方法扩展到正则化熵基闭合框架中。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原始熵闭合的两阶段近似。我们对该近似进行了数值分析，并探讨了最优参数选择。数值实验表明，与传统方法相比，本方法在保持计算时间和模拟精度的同时，内存占用显著降低。所有代码及训练好的网络模型已发布于GitHub：https://github.com/ScSteffen/neuralEntropyClosures 和 https://github.com/CSMMLab/KiT-RT。