DynAMO: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws

TL;DR

DynAMO introduces a multi-agent reinforcement learning framework for anticipatory mesh refinement in numerical PDE solutions, improving accuracy and efficiency over traditional methods by predicting future solution states.

Contribution

This paper presents a novel reinforcement learning-based approach for adaptive mesh refinement that anticipates future solution states, outperforming traditional threshold-based strategies.

Findings

Outperforms conventional threshold-based mesh refinement methods.

Generalizes across different mesh sizes, remeshing intervals, and initial conditions.

Effective in applications to hyperbolic conservation laws like advection and Euler equations.

Abstract

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.