Study on modal switching and energy efficiency mechanisms of fish schooling in low hydrodynamic pressure environments based on deep reinforcement learning and fluid–structure interaction numerical simulation

Fish schooling, an adaptive strategy shaped by long-term evolution, is closely associated with core biological needs such as survival and reproduction. This study, having adopted a numerical simulation framework built by combining the deep reinforcement learning algorithm with the immersed boundary-lattice Boltzmann fluid–solid interaction simulation method, focused on investigating the effects of modal transitions on energy efficiency and array dynamics during large-scale turning of fish schools under low hydrodynamic pressure environments. Initially, strategic control was applied to two fish utilizing body–caudal fin propulsion, aiming to explore their schooling modes and the intrinsic energy-saving mechanisms inherent to each mode. Subsequently, the school size was expanded non-proportionally, and the influence of modal transitions on energy consumption was analyzed through a leader-guided turning strategy. Results indicated that under low hydrodynamic pressure, carangiform fish exhibited three modes in their modal composition, namely, the vortex action mode, the lateral force action mode, and the combined action mode. Additionally, with an increased number of schooling individuals, the modal transitions of carangiform fish demonstrated greater arbitrariness and flexibility. Notably, exclusive reliance on hydrodynamic information perception via the lateral line could enhance efficiency in small-scale schools. However, as the school expanded, the complex flow field limited the ability of this approach to significantly improve overall schooling performance; meanwhile, in low hydrodynamic pressure environments, the collective movement of fish schools does not depend solely on hydrodynamic information. These findings provide theoretical guidance and strategic foundations for the design of clustered bionic underwater intelligent robots with different undulatory propulsion modes.