Accelerating PDE Surrogates via RL-Guided Mesh Optimization

TL;DR

RLMesh uses reinforcement learning to adaptively optimize mesh grids in PDE simulations, significantly reducing the number of simulations needed for high-accuracy surrogate models.

Contribution

The paper introduces RLMesh, a novel RL-based framework for mesh optimization that enhances PDE surrogate training efficiency with limited simulation data.

Findings

Achieves comparable accuracy with fewer simulation queries

Utilizes a lightweight proxy model for faster RL training

Demonstrates effectiveness across multiple PDE benchmarks

Abstract

Deep surrogate models for parametric partial differential equations (PDEs) can deliver high-fidelity approximations but remain prohibitively data-hungry: training often requires thousands of fine-grid simulations, each incurring substantial computational cost. To address this challenge, we introduce RLMesh, an end-to-end framework for efficient surrogate training under limited simulation budget. The key idea is to use reinforcement learning (RL) to adaptively allocate mesh grid points non-uniformly within each simulation domain, focusing numerical resolution in regions most critical for accurate PDE solutions. A lightweight proxy model further accelerates RL training by providing efficient reward estimates without full surrogate retraining. Experiments on PDE benchmarks demonstrate that RLMesh achieves competitive accuracy to baselines but with substantially fewer simulation queries. These results show that solver-level spatial adaptivity can dramatically improve the efficiency of surrogate training pipelines, enabling practical deployment of learning-based PDE surrogates across a wide range of problems.