A coupled framework for modeling fish schooling.

This paper presents a loosely coupled framework for simulating fish schooling, integrating social interactions through a self-propelled particle (SPP) model and flow dynamics via computational fluid dynamics (CFD). In the SPP model, the fish interact with a finite number of topologically defined neighbors, whereas in the CFD model, the fish follow the positions and orientations prescribed by the SPP model through undulatory motion. The undulatory kinematics are generated using a pre-trained deep reinforcement learning model from prior simulation data. Although the CFD trajectories do not exactly match those of the SPP model, they closely approximate them, providing a useful degree of flexibility that allows for physical realism while preserving computational efficiency. For example, in simulations of a minimal two-fish group, the trailing fish achieves stable locomotion through a slight side-slip, an emergent behavior not explicitly encoded in the SPP input. The model is further extended to large schools, demonstrating that group efficiency increases with the Reynolds number because of more favorable hydrodynamic interactions.