Emergence of odd elasticity in a microswimmer using deep reinforcement learning

We use the Deep Q-Network with reinforcement learning to investigate the emergence of odd elasticity in an elastic microswimmer model. For an elastic microswimmer, it is challenging to obtain the optimized dynamics due to the intricate elastohydrodynamic interactions. However, our machine-trained model adopts a transition strategy (the waiting behavior) to optimize the locomotion. For the trained microswimmers, we evaluate the performance of the cycles by the product of the loop area (called nonreciprocality) and the loop frequency and show that the average swimming velocity is proportional to the performance. By calculating the force-displacement correlations, we obtain the effective odd elasticity of the microswimmer to characterize its nonreciprocal dynamics. This emergent odd elasticity is shown to be closely related to the loop frequency of the cyclic deformation. Our work demonstrates the utility of machine learning in achieving optimal dynamics for elastic microswimmers and introduces postanalysis methods to extract crucial physical quantities such as nonreciprocality and odd elasticity.