Learning to school in dense configurations with multi-agent deep reinforcement learning.

Fish are observed to school in different configurations. However, how and why fish maintain a stable schooling formation still remains unclear. This work presents a numerical study of the dense schooling of two free swimmers by a hybrid method of the multi-agent deep reinforcement learning and the immersed boundary-lattice Boltzmann method. Active control policies are developed by synchronously training the leader to swim at a given speed and orientation and the follower to hold close proximity to the leader. After training, the swimmers could resist the strong hydrodynamic force to remain in stable formations and meantime swim in desired path, only by their tail-beat flapping. The tail movement of the swimmers in the stable formations are irregular and asymmetrical, indicating the swimmers are carefully adjusting their body-kinematics to balance the hydrodynamic force. In addition, a significant decrease in the mean amplitude and the cost of transport is found for the followers, indicating these swimmers could maintain the swimming speed with less efforts. The results also show that the side-by-side formation is hydrodynamically more stable but energetically less efficient than other configurations, while the full-body staggered formation is energetically more efficient as a whole.