First-principle-like reinforcement learning of nonlinear numerical schemes for conservation laws
| dc.contributor.author | Wang, Hao-Chen | |
| dc.contributor.author | Yu, Meilin | |
| dc.contributor.author | Xiao, Heng | |
| dc.date.accessioned | 2024-01-22T09:03:47Z | |
| dc.date.available | 2024-01-22T09:03:47Z | |
| dc.date.issued | 2023-12-20 | |
| dc.description.abstract | In this study, we present a universal nonlinear numerical scheme design method enabled by multi-agent reinforcement learning (MARL). Different from contemporary supervised-learning-based and reinforcement-learning-based approaches, no reference data and special numerical treatments are used in the MARL-based method developed here; instead, a first-principle-like approach using fundamental computational fluid dynamics (CFD) principles, including total variation diminishing (TVD) and k-exact reconstruction, is used to design nonlinear numerical schemes. The third-order finite volume scheme is employed as the workhorse to test the performance of the MARL-based nonlinear numerical scheme design method. Numerical results demonstrate that the new MARL-based method is able to strike a balance between accuracy and numerical dissipation in nonlinear numerical scheme design, and outperforms the third-order MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) with the van Albada limiter for shock capturing. Furthermore, we demonstrate for the first time that a numerical scheme trained from one-dimensional (1D) Burger's equation simulations can be directly used for numerical simulations of both 1D and 2D (two-dimensional constructions using the tensor product operation) Euler equations. The working environment of the MARL-based numerical scheme design concepts can incorporate, in general, all types of numerical schemes as simulation machines. | |
| dc.description.sponsorship | HW and HX are funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2075 – 390740016. We acknowledge the support by the Stuttgart Center for Simulation Science (SimTech). | |
| dc.description.uri | https://arxiv.org/abs/2312.13260 | |
| dc.format.extent | 34 pages | |
| dc.genre | journal articles | |
| dc.genre | preprints | |
| dc.identifier.uri | https://doi.org/10.48550/arXiv.2312.13260 | |
| dc.identifier.uri | http://hdl.handle.net/11603/31376 | |
| dc.language.iso | en_US | |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mechanical Engineering Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.rights | This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author. | |
| dc.title | First-principle-like reinforcement learning of nonlinear numerical schemes for conservation laws | |
| dc.type | Text | |
| dcterms.creator | https://orcid.org/0000-0003-3071-0487 |