Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system
This work addresses efficiency challenges in large-scale radiation transport simulations, offering a domain-specific incremental improvement.
The authors tackled the high memory and computational demands in radiation transport simulations by developing a neural network-based approximation for the regularized entropy closure of the Boltzmann moment system, achieving a much lower memory footprint with competitive computation times and accuracy.
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.