# Adaptive Swarm Mesh Refinement using Deep Reinforcement Learning with Local Rewards

arXiv: https://arxiv.org/abs/2406.08440 · HTML: https://mlsanity.com/paper/2406.08440/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 11 of its 45 references that are in the map.
- First posted on arXiv 12 Jun 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 11 of 11)

- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Rainbow: Combining Improvements in Deep Reinforcement Learning](https://mlsanity.com/paper/1710.02298/) (2017)
- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [Bigger, Regularized, Optimistic: scaling for compute and sample-efficient continuous control](https://mlsanity.com/paper/2405.16158/) (2024)
- [Deep Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2209.12351/) (2022)
- [Reinforcement learning for automatic quadrilateral mesh generation: a soft actor-critic approach](https://mlsanity.com/paper/2203.11203/) (2022)
- [Swarm Reinforcement Learning For Adaptive Mesh Refinement](https://mlsanity.com/paper/2304.00818/) (2023)
- [Liquid Splash Modeling with Neural Networks](https://mlsanity.com/paper/1704.04456/) (2017)
- [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)
- [Quasi-optimal hp-finite element refinements towards singularities via deep neural network prediction](https://mlsanity.com/paper/2209.05844/) (2022)
- [A reinforcement learning strategy for p-adaptation in high order solvers](https://mlsanity.com/paper/2306.08292/) (2023)

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

- [AMBER: Adaptive Mesh Generation by Iterative Mesh Resolution Prediction](https://mlsanity.com/paper/2505.23663/) (2025)
- [UGM2N: An Unsupervised and Generalizable Mesh Movement Network via M-Uniform Loss](https://mlsanity.com/paper/2508.08615/) (2025)

## Abstract (arXiv)

Simulating physical systems is essential in engineering, but analytical solutions are limited to straightforward problems. Consequently, numerical methods like the Finite Element Method (FEM) are widely used. However, the FEM becomes computationally expensive as problem complexity and accuracy demands increase. Adaptive Mesh Refinement (AMR) improves the FEM by dynamically placing mesh elements on the domain, balancing computational speed and accuracy. Classical AMR depends on heuristics or expensive error estimators, which may lead to suboptimal performance for complex simulations. While AMR methods based on machine learning are promising, they currently only scale to simple problems. In this work, we formulate AMR as a system of collaborating, homogeneous agents that iteratively split into multiple new agents. This agent-wise perspective enables a spatial reward formulation focused on reducing the maximum mesh element error. Our approach, Adaptive Swarm Mesh Refinement++ (ASMR++), offers efficient, stable optimization and generates highly adaptive meshes at user-defined resolution at inference time. Extensive experiments demonstrate that ASMR++ outperforms heuristic approaches and learned baselines, matching the performance of expensive error-based oracle AMR strategies. ASMR additionally generalizes to different domains during inference, and produces meshes that simulate up to 2 orders of magnitude faster than uniform refinements in more demanding settings.