  This study presents novel active-flow-control (AFC) strategies aimed at
achieving drag reduction for a three-dimensional cylinder immersed in a flow at
a Reynolds number based on freestream velocity and cylinder diameter of
(Re_D=3900). The cylinder in this subcritical flow regime has been extensively
studied in the literature and is considered a classic case of turbulent flow
arising from a bluff body. The strategies presented are explored through the
use of deep reinforcement learning. The cylinder is equipped with 10
independent zero-net-mass-flux jet pairs, distributed on the top and bottom
surfaces, which define the AFC setup. The method is based on the coupling
between a computational-fluid-dynamics solver and a multi-agent
reinforcement-learning (MARL) framework using the proximal-policy-optimization
algorithm. Thanks to the acceleration in training facilitated by exploiting the
local invariants with MARL, a drag reduction of (8\%) was achieved, with a mass
cost efficiency two orders of magnitude lower than those of the existing
classical controls in the literature. This development represents a significant
advancement in active flow control, particularly in turbulent regimes critical
to industrial applications.
