Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system
<|reference_start|>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 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.<|reference_end|>
@article{schotthöfer2024structure-preserving,
    title={Structure-preserving neural networks for the regularized entropy-based
  closure of the Boltzmann moment system},
    author={Steffen Schotth"ofer and M. Paul Laiu and Martin Frank and Cory D.
  Hauck},
    journal={arXiv preprint arXiv:2404.14312},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.14312},
    primaryClass={math.NA cs.LG cs.NA}
}