# Accelerating PDE Surrogates via RL-Guided Mesh Optimization

arXiv: https://arxiv.org/abs/2603.02066 · HTML: https://mlsanity.com/paper/2603.02066/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 2 Mar 2026.

## Builds on (most cited first, 18 of 18)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2103.01342/) (2021)
- [Wavelet Diffusion Neural Operator](https://mlsanity.com/paper/2412.04833/) (2024)
- [MAgNet: Mesh Agnostic Neural PDE Solver](https://mlsanity.com/paper/2210.05495/) (2022)
- [Multi-Resolution Active Learning of Fourier Neural Operators](https://mlsanity.com/paper/2309.16971/) (2023)
- [Active Learning for Neural PDE Solvers](https://mlsanity.com/paper/2408.01536/) (2024)
- [Deep Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2209.12351/) (2022)
- [Disentangled Multi-Fidelity Deep Bayesian Active Learning](https://mlsanity.com/paper/2305.04392/) (2023)
- [Hierarchical Implicit Neural Emulators](https://mlsanity.com/paper/2506.04528/) (2025)
- [SwarmRL: Building the Future of Smart Active Systems](https://mlsanity.com/paper/2404.16388/) (2024)
- [G-Adaptivity: optimised graph-based mesh relocation for finite element methods](https://mlsanity.com/paper/2407.04516/) (2024)

## Built on by (most cited first, 2 of 2)

- [Rethinking Transfer in Continual Learning: A Replay-Based Realisation](https://mlsanity.com/paper/2607.15587/) (2026)
- [Learning When to Refine: Long-Horizon Reinforcement Learning for Budgeted Neural-Operator PDE Solvers](https://mlsanity.com/paper/2610.06883/) (2026)

## Abstract (arXiv)

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.