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Scientific multi-agent reinforcement learning for wall-models of turbulent flows

arXiv 2106.11144 ↗First posted 21 Jun 2021physics.flu-dyn cs.LG physics.comp-phcited by 52

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Abstract (arXiv)

The predictive capabilities of turbulent flow simulations, critical for aerodynamic design and weather prediction, hinge on the choice of turbulence models. The abundance of data from experiments and simulations and the advent of machine learning have provided a boost to turbulence modeling efforts. However, simulations of turbulent flows remain hindered by the inability of heuristics and supervised learning to model the near-wall dynamics. We address this challenge by introducing scientific multi-agent reinforcement learning (SciMARL) for the discovery of wall models for large-eddy simulations (LES). In SciMARL, discretization points act also as cooperating agents that learn to supply the LES closure model. The agents self-learn using limited data and generalize to extreme Reynolds numbers and previously unseen geometries. The present simulations reduce by several orders of magnitude the computational cost over fully-resolved simulations while reproducing key flow quantities. We believe that SciMARL creates unprecedented capabilities for the simulation of turbulent flows.

Key facts. Cited by 52 papers in the map (data through 7 Oct 2026). Builds on 8 of its 76 references that are in the map. First posted on arXiv 21 Jun 2021.

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8 of 76 references.

References · 8

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  3. 2016Safe and Efficient Off-Policy Reinforcement Learningcited by 260
  4. 2018Efficient collective swimming by harnessing vortices through deep reinforcement learningcited by 73
  5. 2018Remember and Forget for Experience Replaycited by 42
  6. 2018Deep Neural Networks for Data-Driven Turbulence Modelscited by 35
  7. 2019Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using Reinforcement Learningcited by 21
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 11; 2023: 12; 2024: 9; 2025: 13; 2026: 6.

52 papers.

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  1. 2021Enhancing Computational Fluid Dynamics with Machine Learningcited by 137
  2. 2025Towards Scientific Intelligence: A Survey of LLM-based Scientific Agentscited by 96
  3. 2023Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flowscited by 30
  4. 2023The transformative potential of machine learning for experiments in fluid mechanicscited by 26
  5. 2024SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learningcited by 24
  6. 2023Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learningcited by 21
  7. 2022Improving aircraft performance using machine learning: a reviewcited by 19
  8. 2022Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulationscited by 16
  9. 2022Deep Learning Closure Models for Large-Eddy Simulation of Flows around Bluff Bodiescited by 11
  10. 2024Koopman-Assisted Reinforcement Learningcited by 11
  11. 2024Multi-agent reinforcement learning for the control of three-dimensional Rayleigh-B'enard convectioncited by 8
  12. 2022Emerging trends in machine learning for computational fluid dynamicscited by 7
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  3. 2022Deep Reinforcement Learning for Computational Fluid Dynamics on HPC Systemscited by 6
  4. 2022Neural modal ordinary differential equations: Integrating physics-based modeling with neural ordinary differential equations for modeling high-dimensional monitored structurescited by 5
  5. 2023Multi-Agent Reinforcement Learning: Methods, Applications, Visionary Prospects, and Challengescited by 5
  6. 2023Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learningcited by 5
  7. 2023Gradient-free online learning of subgrid-scale dynamics with neural emulatorscited by 5
  8. 2024Data Assimilation in Chaotic Systems Using Deep Reinforcement Learningcited by 5
  9. 2025PICT -- A Differentiable, GPU-Accelerated Multi-Block PISO Solver for Simulation-Coupled Learning Tasks in Fluid Dynamicscited by 5
  10. 2023Physics-Preserving AI-Accelerated Simulations of Plasma Turbulencecited by 4
  11. 2024Mean flow data assimilation using physics-constrained Graph Neural Networkscited by 3
  12. 2022Remember and Forget Experience Replay for Multi-Agent Reinforcement Learningcited by 2
  13. 2022Multi-agent reinforcement learning for wall modeling in LES of flow over periodic hillscited by 2
  14. 2023Predicting the wall-shear stress and wall pressure through convolutional neural networkscited by 2
  15. 2023Discovering Individual Rewards in Collective Behavior through Inverse Multi-Agent Reinforcement Learningcited by 2
  16. 2023In Situ Framework for Coupling Simulation and Machine Learning with Application to CFDcited by 2
  17. 2023Uncovering wall-shear stress dynamics from neural-network enhanced fluid flow measurementscited by 2
  18. 2023Extreme Event Prediction with Multi-agent Reinforcement Learning-based Parametrization of Atmospheric and Oceanic Turbulencecited by 2
  19. 2024Closure Discovery for Coarse-Grained Partial Differential Equations Using Grid-based Reinforcement Learningcited by 2
  20. 2024Physics-Guided Actor-Critic Reinforcement Learning for Swimming in Turbulencecited by 2
  21. 2025Multi-fidelity Reinforcement Learning Control for Complex Dynamical Systemscited by 2
  22. 2025Optimal Lattice Boltzmann Closures through Multi-Agent Reinforcement Learningcited by 2
  23. 2025Multi-Agent Reinforcement Learning in Intelligent Transportation Systems: A Comprehensive Surveycited by 2
  24. 2026Plug-and-Play Benchmarking of Reinforcement Learning Algorithms for Large-Scale Flow Controlcited by 2
  25. 2022Backpropagation through Time and Space: Learning Numerical Methods with Multi-Agent Reinforcement Learningcited by 1
  26. 2022Ad Hoc Teamwork in the Presence of Adversariescited by 1
  27. 2024Deep reinforcement learning for tracking a moving target in jellyfish-like swimmingcited by 1
  28. 2025An Analytical and AI-discovered Stable, Accurate, and Generalizable Subgrid-scale Closure for Geophysical Turbulencecited by 1
  29. 2025oRANS: Online optimisation of RANS machine learning models with embedded DNS data generationcited by 1
  30. 2025Empirical Study on Robustness and Resilience in Cooperative Multi-Agent Reinforcement Learningcited by 1
  31. 2026Reward hacking in physical reinforcement learning revealed by turbulent drag reductioncited by 1
  32. 2022Multi-Agent Learning of Numerical Methods for Hyperbolic PDEs with Factored Dec-MDPcited by 0
  33. 2025Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Datacited by 0
  34. 2025OGF: An Online Gradient Flow Method for Optimizing the Statistical Steady-State Time Averages of Unsteady Turbulent Flowscited by 0
  35. 2025Fast-Forward Lattice Boltzmann: Learning Kinetic Behaviour with Physics-Informed Neural Operatorscited by 0
  36. 2025Addressing A Posteriori Performance Degradation in Neural Network Subgrid Stress Modelscited by 0
  37. 2026Deep Learning-based Algebraic Reynolds Stress Closures for RANS Simulations of Turbulent Flowscited by 0
  38. 2026Offline Reinforcement Learning for Fluid Controls: Data-based Multi-observational Policy Extractioncited by 0

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