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

arXiv: https://arxiv.org/abs/2404.14312 · HTML: https://mlsanity.com/paper/2404.14312/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 50 references that are in the map.
- First posted on arXiv 22 Apr 2024.

## Builds on (most cited first, 8 of 8)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure](https://mlsanity.com/paper/2105.05690/) (2021)
- [Integrating Machine Learning with Physics-Based Modeling](https://mlsanity.com/paper/2006.02619/) (2020)
- [Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-equilibrium Flows](https://mlsanity.com/paper/2009.13415/) (2020)
- [Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures](https://mlsanity.com/paper/2105.14410/) (2021)
- [Machine learning moment closure models for the radiative transfer equation III: enforcing hyperbolicity and physical characteristic speeds](https://mlsanity.com/paper/2109.00700/) (2021)
- [Hyperbolic Machine Learning Moment Closures for the BGK Equations](https://mlsanity.com/paper/2401.04783/) (2024)

## Abstract (arXiv)

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.