用强化学习动态优化网格，减少训练微分方程代理模型所需的仿真次数。
Accelerating PDE Surrogates via RL-Guided Mesh Optimization
- 用强化学习自适应调整网格密度，聚焦关键区域提高精度。
- 仅需少量仿真即可达到与基线相当的准确率，减少90%以上查询次数。
- 适合需要高效训练微分方程代理模型的研究者和工程应用。
参数化偏微分方程（PDE）的深度代理模型可提供高保真近似，但训练数据需求量大：通常需数千次细网格仿真，计算成本高昂。为应对这一挑战，我们提出RLMesh，一种在有限仿真预算下高效训练代理模型的端到端框架。核心思想是利用强化学习（RL）在每个仿真域内非均匀分配网格点，将数值分辨率集中在对准确解至关重要的区域。一个轻量级代理模型进一步加速了RL训练，通过无需重新训练完整代理模型即可提供高效的奖励估计。在多个PDE基准测试中，RLMesh实现了与基线相当的竞争力精度，但显著减少了仿真查询次数。结果表明，求解器级别的空间自适应可大幅提高代理训练效率，使基于学习的PDE代理模型在广泛问题中实现实际部署。
原文摘要 · Abstract (English)
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.
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