Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure
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Abstract (arXiv)
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.
Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 7 of its 62 references that are in the map. First posted on arXiv 12 May 2021.
Builds on
7 of 62 references.
References · 7
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Citing papers per year: 2021: 2; 2022: 0; 2023: 0; 2024: 2; 2025: 1; 2026: 3.
8 papers.
- 2021Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closurescited by 7
- 2021Machine learning moment closure models for the radiative transfer equation III: enforcing hyperbolicity and physical characteristic speedscited by 6
- 2025A brief review of the Deep BSDE method for solving high-dimensional partial differential equationscited by 5
- 2024Hyperbolic Machine Learning Moment Closures for the BGK Equationscited by 3
- 2026Machine learning moment closure models for the radiative transfer equation IV: enforcing symmetrizable hyperbolicity in two dimensionscited by 1
- 2024Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment systemcited by 0
- 2026A Hyperbolic Neural Closure for M1 Radiation Transfercited by 0
- 2026Flux-form spatiotemporal neural operators for coarse-grained dynamics of multiscale PDEscited by 0
- 2026Flux-form spatiotemporal neural operators for coarse-grained dynamics of multiscale PDEs11 Aug 2026
- 2026A Hyperbolic Neural Closure for M1 Radiation Transfer11 Jul 2026
- 2026Machine learning moment closure models for the radiative transfer equation IV: enforcing symmetrizable hyperbolicity in two dimensions22 Apr 2026
- 2025A brief review of the Deep BSDE method for solving high-dimensional partial differential equations7 May 2025
- 2024Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system22 Apr 2024
- 2024Hyperbolic Machine Learning Moment Closures for the BGK Equations9 Jan 2024
- 2021Machine learning moment closure models for the radiative transfer equation III: enforcing hyperbolicity and physical characteristic speeds2 Sep 2021
- 2021Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures30 May 2021