Accelerating PDE Surrogates via RL-Guided Mesh Optimization

2026-03-02

AI Summary

This work proposes RLMesh, a novel framework that introduces reinforcement learning to surrogate modeling for parametric partial differential equations (PDEs) by optimizing mesh generation. Traditional approaches rely on numerous high-resolution simulations, which are computationally expensive. RLMesh addresses this by adaptively allocating mesh points non-uniformly, concentrating resolution in regions most critical to solution accuracy. To enhance training efficiency, the framework employs a lightweight surrogate model to accelerate the reinforcement learning process. Evaluated across multiple PDE benchmarks, RLMesh achieves accuracy comparable to baseline methods while requiring significantly fewer simulation queries, thereby substantially improving surrogate training efficiency and enabling solver-level spatial adaptivity.

Technology Category

• Machine Learning: Reinforcement Learning
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• PDE surrogates
• data efficiency
• simulation budget
• mesh optimization
• computational cost

Innovation

• reinforcement learning
• mesh optimization
• PDE surrogates
• adaptive discretization
• data-efficient training