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

Autor:	Huang, Juntao, Cheng, Yingda, Christlieb, Andrew J., Roberts, Luke F.
Rok vydání:	2021
Předmět:	Mathematics - Numerical Analysis Computer Science - Machine Learning Physics - Computational Physics
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jcp.2022.110941
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2105.05690 Zobrazit plný text záznamu View this record from Arxiv