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Updated: Feb 10, 2026

04:35
Preparation of Free-Surface Hyperbolic Water Vortices
Published on: July 28, 2023
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Efficient collective swimming by harnessing vortices through deep reinforcement learning
Siddhartha Verma1, Guido Novati1, Petros Koumoutsakos2
1Computational Science and Engineering Laboratory, ETH Zürich, CH-8092 Zürich, Switzerland.
Summary
Fish schooling behavior offers energy savings by strategically navigating vortex wakes. Smart swimmers position themselves off-center to harness energy from vortices, enhancing efficiency without burdening leaders.
Area of Science:
- Fluid dynamics
- Biomechanics
- Robotics
Background:
- Fish schooling is observed to provide evolutionary advantages, including energy conservation.
- The precise physical mechanisms behind energy savings in fish schools remain largely unknown.
- Understanding these mechanisms could inform bio-inspired robotic systems.
Purpose of the Study:
- To investigate the physical mechanisms by which fish achieve energy savings while schooling.
- To determine optimal strategies for fish to exploit the vortical wakes of conspecifics.
- To explore the application of deep reinforcement learning in simulating and understanding fluid-structure interactions.
Main Methods:
- High-fidelity computational fluid dynamics (CFD) simulations were employed.
- A deep reinforcement learning (RL) algorithm, utilizing recurrent neural networks with long-short-term memory (LSTM) cells, was developed.
- The RL agent learned navigation policies within complex, unsteady, vortical flow fields.
Main Results:
- Fish can enhance propulsive efficiency by positioning themselves optimally within the vortex wakes of other swimmers.
- Off-center positioning relative to leaders, not in-line swimming, yields energetic benefits for followers.
- Fish synchronize body deformation with oncoming vortices to harvest energy, improving efficiency without increasing the leader's energetic cost.
Conclusions:
- Fish actively harvest energy from vortices shed by conspecifics, confirming the energetic advantages of schooling.
- This study demonstrates the potential of deep RL for developing navigation strategies in complex fluid environments.
- Findings have implications for improving energy efficiency in autonomous robotic swarms operating in fluid dynamics.
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