Accelerating PDE Surrogates via RL-Guided Mesh Optimization

Yang Meng, Ruoxi Jiang, Zhuokai Zhao, Chong Liu, Rebecca Willett, Yuxin Chen

Abstract: Deep learning–based 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 standard PDE benchmarks, including 1D Burgers’ equation and 2D Darcy flow, 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.

Submission Number: 1438