A reinforcement learning strategy to automate and accelerate h/p-multigrid solvers

• URL: http://arxiv.org/abs/2407.15872v1
• Date: Thu, 18 Jul 2024 21:26:28 GMT
• Title: A reinforcement learning strategy to automate and accelerate h/p-multigrid solvers
• Authors: David Huergo, Laura Alonso, Saumitra Joshi, Adrian Juanicoteca, Gonzalo Rubio, Esteban Ferrer,
• Abstract summary: Multigrid methods are very efficient but require fine-tuning of numerical parameters, such as the number of smoothing sweeps per level. This paper is to use a proximal policy optimization algorithm to automatically tune the multigrid parameters. Our findings reveal that the proposed reinforcement learning h/p-multigrid approach significantly accelerates and improves the robustness of steady-state simulations.
• Score: 0.37109226820205005
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We explore a reinforcement learning strategy to automate and accelerate h/p-multigrid methods in high-order solvers. Multigrid methods are very efficient but require fine-tuning of numerical parameters, such as the number of smoothing sweeps per level and the correction fraction (i.e., proportion of the corrected solution that is transferred from a coarser grid to a finer grid). The objective of this paper is to use a proximal policy optimization algorithm to automatically tune the multigrid parameters and, by doing so, improve stability and efficiency of the h/p-multigrid strategy. Our findings reveal that the proposed reinforcement learning h/p-multigrid approach significantly accelerates and improves the robustness of steady-state simulations for one dimensional advection-diffusion and nonlinear Burgers' equations, when discretized using high-order h/p methods, on uniform and nonuniform grids.

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