Bayesian Machine Learning for Experimental Optimization of Fish Schooling Kinematics*

A Bayesian machine learning algorithm is used to find the position and kinematics that maximize the propulsive efficiency of the follower in a tandem heaving hydrofoil system. The propulsive efficiency of the trailing hydrofoil is affected by wake interactions that depend on foil spacing, phase offset, and heave frequency/amplitude. As the number of experimental variables increases, grid search methods become impractical due to the exponentially growing test permutations. Therefore, we integrate a Bayesian optimization routine with the hydrofoil actuation system to find the global efficiency maximum with fewer trials. For each iteration, the algorithm builds a Gaussian Process surrogate model from observed data and evaluates the conditions with the highest likelihood of improving the current estimate. Preliminary results indicate that the Bayesian method's estimates deviate only 1.5% from the maximum efficiency found with a direct grid search while sampling nearly 80% fewer conditions. Our work demonstrates the potential benefits of machine learning for revealing the optimal kinematics for fish schooling.