Dyn$\mathrm{AMO}$: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws

Dzanic, T.; Mittal, K.; Kim, D.; Yang, J.; Petrides, S.; Keith, B.; Anderson, R.

doi:10.1016/j.jcp.2024.112924

Title: Dyn$$\mathrm{AMO}$$: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws

Journal Article · 16 March 2024 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2024.112924 · OSTI ID:2335990

^[1]; Mittal, K. ^[1]; Kim, D. ^[2]; Yang, J. ^[1]; Petrides, S. ^[1]; Keith, B. ^[2]; Anderson, R. ^[1]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Brown University, Providence, RI (United States)

Here we introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial differential equations. However, traditional adaptive mesh refinement approaches for time-dependent problems typically rely only on instantaneous error indicators to guide adaptivity. As a result, standard strategies often require frequent remeshing to maintain accuracy. In the DynAMO approach, multi-agent reinforcement learning is used to discover new local refinement policies that can anticipate and respond to future solution states by producing meshes that deliver more accurate solutions for longer time intervals. By applying DynAMO to discontinuous Galerkin methods for the linear advection and compressible Euler equations in two dimensions, we demonstrate that this new mesh refinement paradigm can outperform conventional threshold-based strategies while also generalizing to different mesh sizes, remeshing and simulation times, and initial conditions.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2335990

Report Number(s):: LLNL--JRNL-855285; 1083857

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: no. 1 Vol. 506; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Related Subjects

97 MATHEMATICS AND COMPUTING
adaptive mesh refinement
finite element methods
hyperbolic conservation laws
reinforcement learning
scientific machine learning

Title: Dyn$$\mathrm{AMO}$$: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws

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