mlsanityData to 7 Oct 2026

Efficient collective swimming by harnessing vortices through deep reinforcement learning

arXiv 1802.02674 ↗First posted 7 Feb 2018physics.flu-dyn cs.AI physics.comp-phcited by 73

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Abstract (arXiv)

Fish in schooling formations navigate complex flow-fields replete with mechanical energy in the vortex wakes of their companions. Their schooling behaviour has been associated with evolutionary advantages including collective energy savings. How fish harvest energy from their complex fluid environment and the underlying physical mechanisms governing energy-extraction during collective swimming, is still unknown. Here we show that fish can improve their sustained propulsive efficiency by actively following, and judiciously intercepting, vortices in the wake of other swimmers. This swimming strategy leads to collective energy-savings and is revealed through the first ever combination of deep reinforcement learning with high-fidelity flow simulations. We find that a `smart-swimmer' can adapt its position and body deformation to synchronise with the momentum of the oncoming vortices, improving its average swimming-efficiency at no cost to the leader. The results show that fish may harvest energy deposited in vortices produced by their peers, and support the conjecture that swimming in formation is energetically advantageous. Moreover, this study demonstrates that deep reinforcement learning can produce navigation algorithms for complex flow-fields, with promising implications for energy savings in autonomous robotic swarms.

Key facts. Cited by 73 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Feb 2018.

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Citing papers per year: 2021: 13; 2022: 11; 2023: 11; 2024: 17; 2025: 15; 2026: 6.

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  1. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulationcited by 65
  2. 2021Scientific multi-agent reinforcement learning for wall-models of turbulent flowscited by 52
  3. 2024Wavelet Diffusion Neural Operatorcited by 28
  4. 2021Learning Efficient Navigation in Vortical Flow Fieldscited by 26
  5. 2023The transformative potential of machine learning for experiments in fluid mechanicscited by 26
  6. 2024SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learningcited by 24
  7. 2025Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networkscited by 24
  8. 2021Physics-informed Dyna-Style Model-Based Deep Reinforcement Learning for Dynamic Controlcited by 22
  9. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  10. 2021Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolutioncited by 14
  11. 2021Applying Machine Learning to Study Fluid Mechanicscited by 13
  12. 2021Thermal Control of Laser Powder Bed Fusion Using Deep Reinforcement Learningcited by 11
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  1. 2024Koopman-Assisted Reinforcement Learningcited by 11
  2. 2021Symmetry reduction for deep reinforcement learning active control of chaotic spatiotemporal dynamicscited by 10
  3. 2022A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluidscited by 9
  4. 2022Multi-fidelity reinforcement learning framework for shape optimizationcited by 8
  5. 2024Multi-agent reinforcement learning for the control of three-dimensional Rayleigh-B'enard convectioncited by 8
  6. 2024CL-DiffPhyCon: Closed-loop Diffusion Control of Complex Physical Systemscited by 8
  7. 2021Reinforcement learning for pursuit and evasion of microswimmers at low Reynolds numbercited by 7
  8. 2023Dynamic Feature-based Deep Reinforcement Learning for Flow Control of Circular Cylinder with Sparse Surface Pressure Sensingcited by 7
  9. 2022Comparative analysis of machine learning methods for active flow controlcited by 6
  10. 2023Turbulence control in plane Couette flow using low-dimensional neural ODE-based models and deep reinforcement learningcited by 5
  11. 2022ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Biascited by 4
  12. 2022Machine Learning to Predict Aerodynamic Stallcited by 4
  13. 2023Adaptive learning of effective dynamics: Adaptive real-time, online modeling for complex systemscited by 4
  14. 2024Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order modelscited by 4
  15. 2025Reinforcement Learning for Active Mattercited by 4
  16. 2025CBIL: Collective Behavior Imitation Learning for Fish from Real Videoscited by 4
  17. 2026Explainable AI: Learning from the Learnerscited by 4
  18. 2026Self-Evolving Scientific Agent Designs Physically Reasoned White-Box Fluid Controlcited by 4
  19. 2021Learning swimming escape patterns for larval fish under energy constraintscited by 3
  20. 2021Emergent behavior and neural dynamics in artificial agents tracking turbulent plumescited by 2
  21. 2022Remember and Forget Experience Replay for Multi-Agent Reinforcement Learningcited by 2
  22. 2022Optimizing Airborne Wind Energy with Reinforcement Learningcited by 2
  23. 2022Taming Lagrangian Chaos with Multi-Objective Reinforcement Learningcited by 2
  24. 2022Data-driven control of COVID-19 in buildings: a reinforcement-learning approachcited by 2
  25. 2024Training microrobots to swim by a large language modelcited by 2
  26. 2024Model-Based Reinforcement Learning for Control of Strongly-Disturbed Unsteady Aerodynamic Flowscited by 2
  27. 2025Optimal Lattice Boltzmann Closures through Multi-Agent Reinforcement Learningcited by 2
  28. 2022Control of Two-way Coupled Fluid Systems with Differentiable Solverscited by 1
  29. 2022Chemotaxis of sea urchin sperm cells through deep reinforcement learningcited by 1
  30. 2023Active Control of Flow over Rotating Cylinder by Multiple Jets using Deep Reinforcement Learningcited by 1
  31. 2024Asynchronous Parallel Reinforcement Learning for Optimizing Propulsive Performance in Fin Ray Controlcited by 1
  32. 2024Real-World Fluid Directed Rigid Body Control via Deep Reinforcement Learningcited by 1
  33. 2024Optimal Parallelization Strategies for Active Flow Control in Deep Reinforcement Learning-Based Computational Fluid Dynamicscited by 1
  34. 2024Optimal navigation of magnetic artificial microswimmers in blood capillaries with deep reinforcement learningcited by 1
  35. 2024Deep Dive into Model-free Reinforcement Learning for Biological and Robotic Systems: Theory and Practicecited by 1
  36. 2024Deep reinforcement learning for tracking a moving target in jellyfish-like swimmingcited by 1
  37. 2024Multi-modal Policies with Physics-informed Representations in Complex Fluid Environmentscited by 1
  38. 2025Understanding the role of autoencoders for stiff dynamical systems using information theorycited by 1

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