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

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.

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• A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure based on Data-Driven Shape Function
• Continuous data assimilation for hydrodynamics: consistent discretization and application to moment recovery
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• Embedding physical symmetries into machine-learned reduced plasma physics models via data augmentation
• Reduced order models for nonlinear radiative transfer based on moment equations and POD/DMD of Eddington tensor