Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure
This work addresses a domain-specific problem in computational physics for researchers in radiative transfer modeling, presenting an incremental improvement over existing methods.
The authors tackled the moment closure problem for the radiative transfer equation by proposing a machine learning approach that directly learns the gradient of the high-order moment using neural networks, achieving good accuracy and generalizability in benchmark tests.
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.