mlsanityData to 7 Oct 2026

Multi-Agent Reinforcement Learning for Adaptive Mesh Refinement

arXiv 2211.00801 ↗First posted 2 Nov 2022cs.LG cs.AI cs.NAcited by 5

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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.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 21 of its 45 references that are in the map. First posted on arXiv 2 Nov 2022.

Builds on

21 of 45 references.

References · 21

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9 more
  1. 2019A Generalized Algorithm for Multi-Objective Reinforcement Learning and Policy Adaptationcited by 166
  2. 2021Reinforcement Learning for Adaptive Mesh Refinementcited by 37
  3. 2022Deep Reinforcement Learning for Adaptive Mesh Refinementcited by 19
  4. 2022Reinforcement learning for automatic quadrilateral mesh generation: a soft actor-critic approachcited by 16
  5. 2022M2N: Mesh Movement Networks for PDE Solverscited by 16
  6. 2021On the Use and Misuse of Absorbing States in Multi-agent Reinforcement Learningcited by 10
  7. 2022Learning robust marking policies for adaptive mesh refinementcited by 9
  8. 2022E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptationcited by 7
  9. 2022NUNet: Deep Learning for Non-Uniform Super-Resolution of Turbulent Flowscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 1; 2026: 1.

5 papers.

  1. 2023Swarm Reinforcement Learning For Adaptive Mesh Refinementcited by 16
  2. 2023A reinforcement learning strategy for p-adaptation in high order solverscited by 4
  3. 2025UGM2N: An Unsupervised and Generalizable Mesh Movement Network via M-Uniform Losscited by 2
  4. 2024Iterative Sizing Field Prediction for Adaptive Mesh Generation From Expert Demonstrationscited by 1
  5. 2026Playing to Par: Reinforcement Learning for Provably Optimal Quadrilateral Block Decompositionscited by 0