Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure

TL;DR

This paper introduces a novel machine learning approach that directly learns the gradient of high order moments in the radiative transfer equation, improving accuracy and generalizability in closure models.

Contribution

It proposes a new data-driven method that directly learns the gradient of high order moments, aligning with the exact free streaming limit and enhancing closure modeling.

Findings

Accurate predictions in various benchmark tests

Good generalizability across different problems

Consistent with the free streaming limit

Abstract

In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for radiative transfer equation in slab geometry. Instead of learning the unclosed high order moment, we propose to directly learn the gradient of the high order moment using neural networks. This new approach is consistent with the exact closure we derive for the free streaming limit and also provides a natural output normalization. A variety of benchmark tests, including the variable scattering problem, the Gaussian source problem with both periodic and reflecting boundaries, and the two-material problem, show both good accuracy and generalizability of our machine learning closure model.