Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations

2021/06/16 by William A. Porteous, Porteous, William A., M. Paul Laiu +3 · 2 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2106.08973

openalex publication_date 2021/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a data-driven approach to construct entropy-based closures for the moment system from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment system, and thus does not depend on the space-time discretization of the moment system and specific problem configurations such as initial and boundary conditions. With convex and C² approximations, this data-driven closure inherits several structural properties from entropy-based closures, such as entropy dissipation, hyperbolicity, and H-Theorem. We construct convex approximations to the Maxwell-Boltzmann entropy using convex splines and neural networks, test them on the plane source benchmark problem for linear transport in slab geometry, and compare the results to the standard, optimization-based M_N closures. Numerical results indicate that these data-driven closures provide accurate solutions in much less computation time than the M_N closures.

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• Learning interpretable closures for thermal radiation transport in optically-thin media using WSINDy
• Maximum likelihood discretization of the transport equation

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