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{https://github.com/CSMMLab/KiT-RT}.

通过神经网络逼近方法，本研究提出了一种低内存消耗和高计算效率的方法，精确计算多维矩系统的解。实验结果表明，该方法具有较低的内存占用，且计算时间竞争力强，模拟精度高。

结构保持神经网络用于规范化基于熵的蒙特曼系统闭合

Structure-preserving neural networks for the regularzied entropy-based  closure of the Boltzmann moment system

This paper describes the open-source code Enzo, which uses block-structured
adaptive mesh refinement to provide high spatial and temporal resolution for
modeling astrophysical fluid flows. The code is Cartesian, can be run in 1, 2,
and 3 dimensions, and supports a wide variety of physics including
hydrodynamics, ideal and non-ideal magnetohydrodynamics, N-body dynamics (and,
more broadly, self-gravity of fluids and particles), primordial gas chemistry,
optically-thin radiative cooling of primordial and metal-enriched plasmas (as
well as some optically-thick cooling models), radiation transport, cosmological
expansion, and models for star formation and feedback in a cosmological
context. In addition to explaining the algorithms implemented, we present
solutions for a wide range of test problems, demonstrate the code's parallel
performance, and discuss the Enzo collaboration's code development methodology.

本研究介绍了使用开源代码 Enzo 实现块状结构自适应网格细化，为建模天体物质流动提供高空间、时间分辨率的方法。它包括磁流体力学、N 体动力学、化学反应、辐射传输、宇宙学扩张和星际反馈等物理现象的建模，并演示了并行性能和代码开发方法。