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

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...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Schotthöfer, Steffen, Laiu, M Paul, Martin, Frank, Hauck, Cory D
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.06.2024
Subjects
Approximation
Computer networks
Computer simulation
Computing time
Entropy
Kinetic equations
Neural networks
Numerical analysis
Radiation transport
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2331-8422