Accelerating PDE Surrogates via RL-Guided Mesh Optimization

Yang Meng, Ruoxi Jiang, Zhuokai Zhao, Chong Liu, Rebecca Willett, Yuxin Chen
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3286-3294, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-meng26a, title = { Accelerating PDE Surrogates via RL-Guided Mesh Optimization }, author = {Meng, Yang and Jiang, Ruoxi and Zhao, Zhuokai and Liu, Chong and Willett, Rebecca and Chen, Yuxin}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3286--3294}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/meng26a/meng26a.pdf}, url = {https://proceedings.mlr.press/v300/meng26a.html}, 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. } }
Endnote
%0 Conference Paper %T Accelerating PDE Surrogates via RL-Guided Mesh Optimization %A Yang Meng %A Ruoxi Jiang %A Zhuokai Zhao %A Chong Liu %A Rebecca Willett %A Yuxin Chen %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-meng26a %I PMLR %P 3286--3294 %U https://proceedings.mlr.press/v300/meng26a.html %V 300 %X 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.
APA
Meng, Y., Jiang, R., Zhao, Z., Liu, C., Willett, R. & Chen, Y.. (2026). Accelerating PDE Surrogates via RL-Guided Mesh Optimization . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3286-3294 Available from https://proceedings.mlr.press/v300/meng26a.html.

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