Stable Schooling Formations Emerge from the Combined Effect of the Active Control and Passive Self-Organization

Abstract

This work presents a numerical study of the collective motion of two freely-swimming swimmers by a hybrid method of the deep reinforcement learning method (DRL) and the immersed boundary-lattice Boltzmann method (IB-LBM). An active control policy is developed by training a fish-like swimmer to swim at an average speed of 0.4 L/T and an average orientation angle of 0∘. After training, the swimmer is able to restore the desired swimming speed and orientation from moderate external perturbation. Then the control policy is adopted by two identical swimmers in the collective swimming. Stable side-by-side, in-line and staggered formations are achieved according to the initial positions. The stable side-by-side swimming area of the follower is concentrated to a small area left or right to the leader with an average distance of 1.35 L. The stable in-line area is concentrated to a small area about 0.25 L behind the leader. A detailed analysis shows that both the active control and passive self-organization play an important role in the emergence of the stable schooling formations, while the active control works for maintaining the speed and orientation in case the swimmers collide or depart from each other and the passive self-organization works for emerging a stable schooling configuration. The result supports the Lighthill conjecture and also highlights the importance of the active control.

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

“…In the second case, both swimmers take the same control strategy to maximize their efficiency. Under this strategy, the side-by-side and compact configuration are emerged, as in [35,45]. We note that similar configurations are emerged, even though one is due to the self-organization and the other is due to the pursuit of highest swimming efficiency.…”

“…The kinematic model used here is the same as that in our previous works [45,46]. Here we briefly describe it for completeness.…”

“…Recently, a novel control method based on deep reinforcement learning (DRL) is adopted by several works [28,42,44,45] to investigate the 3-DoF fish schooling, considering yawing and moving in both longitudinal and lateral directions. Novati et al [42] and Verma et al [44] trained two selfpropelled swimmers to swim in a leader-follower configuration with deep reinforcement learning.…”

“…Both formations lead to the reduction in the energy expenditure of the follower. Zhu et al [45] applied a shared control policy to two identical swimmers in a schooling, in which the swimmers are trained to swim at the same speed and orientation. A competition exists between the active control and the passive hydrodynamic force, while the active control maintains the speed and orientation and the passive force derives the swimmers from the desired speed and orientation.…”

Fast prediction of blood flow in stenosed arteries using machine learning and immersed boundary-lattice Boltzmann method

“…Sekar et al (2019) presented a data-driven approach by using the combination of CNN and multilayer perceptron for the prediction of laminar flow around NACA airfoil, which achieves the flow prediction of various airfoils. ML has also been combined with CFD tools to study fish swimming (Zhu et al, 2021(Zhu et al, , 2022. Moreover, ML has been studied in the field of biomedicine, such as prediction of malaria (Lee et al, 2020) and patient quality-of-life after prostate radiation therapy (Yang et al, 2020).…”