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

• URL: http://arxiv.org/abs/2404.14312v3
• Date: Sun, 2 Jun 2024 00:20:16 GMT
• Title: Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system
• Abstract summary: Main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements. In this work, we derive and investigate a neural network-based approximation to the entropy closure method. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive times and simulation accuracy.
• Score: 3.437372707846067
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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