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

• URL: http://arxiv.org/abs/2105.05690v1
• Date: Wed, 12 May 2021 14:24:20 GMT
• Title: Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure
• Abstract summary: We propose to learn the gradient of the high order moment using neural networks. A variety of benchmark tests, including the variable scattering problem, show both good accuracy and generalizability of our machine learning closure model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 and the two material problem, show both good accuracy and generalizability of our machine learning closure model.

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