  A comparative assessment of machine learning (ML) methods for active flow
control is performed. The chosen benchmark problem is the drag reduction of a
two-dimensional K\'arm\'an vortex street past a circular cylinder at a low
Reynolds number ($Re=100$). The flow is manipulated with two blowing/suction
actuators on the upper and lower side of a cylinder. The feedback employs
several velocity sensors. Two probe configurations are evaluated: 5 and 11
velocity probes located at different points around the cylinder and in the
wake. The control laws are optimized with Deep Reinforcement Learning (DRL) and
Linear Genetic Programming Control (LGPC). By interacting with the unsteady
wake, both methods successfully stabilize the vortex alley and effectively
reduce drag while using small mass flow rates for the actuation. DRL has shown
higher robustness with respect to variable initial conditions and to noise
contamination of the sensor data; on the other hand, LGPC is able to identify
compact and interpretable control laws, which only use a subset of sensors,
thus allowing reducing the system complexity with reasonably good results. Our
study points at directions of future machine learning control combining
desirable features of different approaches.
