# Swarm Reinforcement Learning For Adaptive Mesh Refinement

arXiv: https://arxiv.org/abs/2304.00818 · HTML: https://mlsanity.com/paper/2304.00818/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 109 references that are in the map.
- First posted on arXiv 3 Apr 2023.

## Builds on (most cited first, 30 of 47)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Rainbow: Combining Improvements in Deep Reinforcement Learning](https://mlsanity.com/paper/1710.02298/) (2017)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [Value-Decomposition Networks For Cooperative Multi-Agent Learning](https://mlsanity.com/paper/1706.05296/) (2017)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow](https://mlsanity.com/paper/1802.10123/) (2018)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Deep Reinforcement Learning for Swarm Systems](https://mlsanity.com/paper/1807.06613/) (2018)
- [tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow](https://mlsanity.com/paper/1801.09710/) (2018)
- [Learning rigid dynamics with face interaction graph networks](https://mlsanity.com/paper/2212.03574/) (2022)
- [Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2103.01342/) (2021)

## Built on by (most cited first, 17 of 17)

- [Physics-informed MeshGraphNets (PI-MGNs): Neural finite element solvers for non-stationary and nonlinear simulations on arbitrary meshes](https://mlsanity.com/paper/2402.10681/) (2024)
- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)
- [Geometry-aware RL for Manipulation of Varying Shapes and Deformable Objects](https://mlsanity.com/paper/2502.07005/) (2025)
- [A reinforcement learning strategy for p-adaptation in high order solvers](https://mlsanity.com/paper/2306.08292/) (2023)
- [AMBER: Adaptive Mesh Generation by Iterative Mesh Resolution Prediction](https://mlsanity.com/paper/2505.23663/) (2025)
- [G-Adaptivity: optimised graph-based mesh relocation for finite element methods](https://mlsanity.com/paper/2407.04516/) (2024)
- [A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling](https://mlsanity.com/paper/2506.07969/) (2025)
- [Adaptive Swarm Mesh Refinement using Deep Reinforcement Learning with Local Rewards](https://mlsanity.com/paper/2406.08440/) (2024)
- [Learning Sub-Second Routing Optimization in Computer Networks requires Packet-Level Dynamics](https://mlsanity.com/paper/2410.10377/) (2024)
- [Iterative Sizing Field Prediction for Adaptive Mesh Generation From Expert Demonstrations](https://mlsanity.com/paper/2406.14161/) (2024)
- [Context-aware Learned Mesh-based Simulation via Trajectory-Level Meta-Learning](https://mlsanity.com/paper/2511.05234/) (2025)
- [Latent Task-Specific Graph Network Simulators](https://mlsanity.com/paper/2311.05256/) (2023)
- [Loop2Net: Data-Driven Generation and Optimization of Airfoil CFD Meshes from Sparse Boundary Coordinates](https://mlsanity.com/paper/2507.01057/) (2025)
- [Autonomous Adaptive Solver Selection for Chemistry Integration via Reinforcement Learning](https://mlsanity.com/paper/2604.00264/) (2026)
- [MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers](https://mlsanity.com/paper/2606.04366/) (2026)
- [Mesh-RL: Coupled subgrid reinforcement learning](https://mlsanity.com/paper/2606.26333/) (2026)
- [Learned Adaptive Multiresolution Diffusion Imaging](https://mlsanity.com/paper/2610.07884/) (2026)

## Abstract (arXiv)

Adaptive Mesh Refinement (AMR) enhances the Finite Element Method, an important technique for simulating complex problems in engineering, by dynamically refining mesh regions, enabling a favorable trade-off between computational speed and simulation accuracy. Classical methods for AMR depend on heuristics or expensive error estimators, hindering their use for complex simulations. Recent learning-based AMR methods tackle these issues, but so far scale only to simple toy examples. We formulate AMR as a novel Adaptive Swarm Markov Decision Process in which a mesh is modeled as a system of simple collaborating agents that may split into multiple new agents. This framework allows for a spatial reward formulation that simplifies the credit assignment problem, which we combine with Message Passing Networks to propagate information between neighboring mesh elements. We experimentally validate our approach, Adaptive Swarm Mesh Refinement (ASMR), on challenging refinement tasks. Our approach learns reliable and efficient refinement strategies that can robustly generalize to different domains during inference. Additionally, it achieves a speedup of up to 2 orders of magnitude compared to uniform refinements in more demanding simulations. We outperform learned baselines and heuristics, achieving a refinement quality that is on par with costly error-based oracle AMR strategies.