# Multi-Agent Reinforcement Learning for Adaptive Mesh Refinement

arXiv: https://arxiv.org/abs/2211.00801 · HTML: https://mlsanity.com/paper/2211.00801/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 45 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [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)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [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)
- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [A Survey and Critique of Multiagent Deep Reinforcement Learning](https://mlsanity.com/paper/1810.05587/) (2018)
- [A Generalized Algorithm for Multi-Objective Reinforcement Learning and Policy Adaptation](https://mlsanity.com/paper/1908.08342/) (2019)
- [Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2103.01342/) (2021)
- [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)
- [M2N: Mesh Movement Networks for PDE Solvers](https://mlsanity.com/paper/2204.11188/) (2022)
- [On the Use and Misuse of Absorbing States in Multi-agent Reinforcement Learning](https://mlsanity.com/paper/2111.05992/) (2021)
- [Learning robust marking policies for adaptive mesh refinement](https://mlsanity.com/paper/2207.06339/) (2022)
- [E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation](https://mlsanity.com/paper/2207.11233/) (2022)
- [NUNet: Deep Learning for Non-Uniform Super-Resolution of Turbulent Flows](https://mlsanity.com/paper/2203.14154/) (2022)

## Built on by (most cited first, 5 of 5)

- [Swarm Reinforcement Learning For Adaptive Mesh Refinement](https://mlsanity.com/paper/2304.00818/) (2023)
- [A reinforcement learning strategy for p-adaptation in high order solvers](https://mlsanity.com/paper/2306.08292/) (2023)
- [UGM2N: An Unsupervised and Generalizable Mesh Movement Network via M-Uniform Loss](https://mlsanity.com/paper/2508.08615/) (2025)
- [Iterative Sizing Field Prediction for Adaptive Mesh Generation From Expert Demonstrations](https://mlsanity.com/paper/2406.14161/) (2024)
- [Playing to Par: Reinforcement Learning for Provably Optimal Quadrilateral Block Decompositions](https://mlsanity.com/paper/2609.32146/) (2026)

## Abstract (arXiv)

Adaptive mesh refinement (AMR) is necessary for efficient finite element simulations of complex physical phenomenon, as it allocates limited computational budget based on the need for higher or lower resolution, which varies over space and time. We present a novel formulation of AMR as a fully-cooperative Markov game, in which each element is an independent agent who makes refinement and de-refinement choices based on local information. We design a novel deep multi-agent reinforcement learning (MARL) algorithm called Value Decomposition Graph Network (VDGN), which solves the two core challenges that AMR poses for MARL: posthumous credit assignment due to agent creation and deletion, and unstructured observations due to the diversity of mesh geometries. For the first time, we show that MARL enables anticipatory refinement of regions that will encounter complex features at future times, thereby unlocking entirely new regions of the error-cost objective landscape that are inaccessible by traditional methods based on local error estimators. Comprehensive experiments show that VDGN policies significantly outperform error threshold-based policies in global error and cost metrics. We show that learned policies generalize to test problems with physical features, mesh geometries, and longer simulation times that were not seen in training. We also extend VDGN with multi-objective optimization capabilities to find the Pareto front of the tradeoff between cost and error.