动能
力矩(物理)
统计物理学
数学
π的近似
熵(时间箭头)
应用数学
物理
热力学
经典力学
作者
William K. Porteous,M. Paul Laiu,Cory D. Hauck
出处
期刊:Communications in Mathematical Sciences
[International Press of Boston, Inc.]
日期:2023-01-01
卷期号:21 (4): 885-913
被引量:2
标识
DOI:10.4310/cms.2023.v21.n4.a1
摘要
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 $C^2$ 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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