Adaptive Swarm Mesh Refinement using Deep Reinforcement Learning with Local Rewards

TL;DR

This paper introduces ASMR++, a deep reinforcement learning-based method for adaptive mesh refinement that outperforms traditional heuristics and learned models, achieving faster and more accurate simulations in complex physical systems.

Contribution

It formulates AMR as a multi-agent system with local rewards, enabling scalable, efficient, and domain-general mesh refinement using deep RL.

Findings

ASMR++ outperforms heuristic and baseline methods.

It matches the performance of error-based oracle strategies.

Meshes are generated up to 100 times faster than uniform refinements.

Abstract

Simulating physical systems is essential in engineering, but analytical solutions are limited to straightforward problems. Consequently, numerical methods like the Finite Element Method (FEM) are widely used. However, the FEM becomes computationally expensive as problem complexity and accuracy demands increase. Adaptive Mesh Refinement (AMR) improves the FEM by dynamically placing mesh elements on the domain, balancing computational speed and accuracy. Classical AMR depends on heuristics or expensive error estimators, which may lead to suboptimal performance for complex simulations. While AMR methods based on machine learning are promising, they currently only scale to simple problems. In this work, we formulate AMR as a system of collaborating, homogeneous agents that iteratively split into multiple new agents. This agent-wise perspective enables a spatial reward formulation focused on reducing the maximum mesh element error. Our approach, Adaptive Swarm Mesh Refinement++ (ASMR++), offers efficient, stable optimization and generates highly adaptive meshes at user-defined resolution at inference time. Extensive experiments demonstrate that ASMR++ outperforms heuristic approaches and learned baselines, matching the performance of expensive error-based oracle AMR strategies. ASMR additionally generalizes to different domains during inference, and produces meshes that simulate up to 2 orders of magnitude faster than uniform refinements in more demanding settings.