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

TL;DR

This paper introduces a neural network approach for the regularized entropy closure of the Boltzmann moment system, significantly reducing memory requirements while maintaining accuracy and computational efficiency.

Contribution

It extends entropy closure neural network methods to regularized closures, providing a two-stage approximation with proven numerical effectiveness.

Findings

Lower memory footprint compared to traditional methods

Competitive computational times

Accurate solutions demonstrated in numerical experiments

Abstract

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.