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Updated: Jan 24, 2026

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A coupled framework for modeling fish schooling.

Xingyuan Mao1, Zhiqian Xin1, Xuewei Mao1

  • 1State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, People's Republic of China.

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Summary

This study introduces a computational framework combining self-propelled particle (SPP) and computational fluid dynamics (CFD) models to simulate fish schooling behavior. The integrated model captures emergent behaviors and hydrodynamic interactions, enhancing realism and efficiency in fish group dynamics simulations.

Keywords:
collective motiondeep reinforcement learningfish swimmingself-propelled particle model

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Area of Science:

  • Computational Biology
  • Fluid Dynamics
  • Animal Behavior

Background:

  • Simulating collective animal behavior, like fish schooling, requires integrating individual interactions with environmental dynamics.
  • Existing models often face challenges in balancing computational efficiency with physical realism.

Purpose of the Study:

  • To develop and present a loosely coupled simulation framework for fish schooling.
  • To integrate social interactions (SPP model) with fluid dynamics (CFD model).
  • To investigate emergent behaviors and hydrodynamic effects in schooling fish.

Main Methods:

  • Utilized a self-propelled particle (SPP) model for fish social interactions and movement rules.
  • Employed computational fluid dynamics (CFD) to simulate the fluid environment and fish hydrodynamics.
  • Generated fish undulatory kinematics using a pre-trained deep reinforcement learning model.
  • Coupled SPP and CFD models, allowing CFD to follow SPP trajectories with flexibility.

Main Results:

  • The CFD trajectories closely approximated SPP model trajectories, offering a balance of realism and efficiency.
  • Emergent behavior, such as side-slip for stable locomotion in trailing fish, was observed.
  • Simulations of large schools showed increased group efficiency with higher Reynolds numbers due to favorable hydrodynamic interactions.

Conclusions:

  • The loosely coupled SPP-CFD framework effectively simulates fish schooling, capturing complex interactions and emergent phenomena.
  • The model provides a flexible approach for studying fish collective behavior with physical realism and computational efficiency.
  • Hydrodynamic interactions play a significant role in the efficiency of large fish schools.