Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations
- Univ. of Texas, Austin, TX (United States)
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
In this study, we present a data-driven approach for approximating entropy-based closures of moment systems 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 spacetime discretization of the moment system or 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, entropy-based systems which solve a convex optimization problem to find the closure. Numerical results indicate that these data-driven closures provide accurate solutions in much less computation time than that required by the optimization routine.
- Research Organization:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- AC05-00OR22725
- OSTI ID:
- 1999103
- Journal Information:
- Communications in Mathematical Sciences, Journal Name: Communications in Mathematical Sciences Journal Issue: 4 Vol. 21; ISSN 1539-6746
- Publisher:
- International PressCopyright Statement
- Country of Publication:
- United States
- Language:
- English
A structure-preserving surrogate model for the closure of the moment system of the Boltzmann equation using convex deep neural networks
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text | January 2021 |
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