  We present a deep reinforcement learning approach to a classical problem in
fluid dynamics, i.e., the reduction of the drag of a bluff body. We cast the
problem as a discrete-time control with continuous action space: at each time
step, an autonomous agent can set the flow rate of two jets of fluid,
positioned at the back of the body. The agent, trained with Proximal Policy
Optimization, learns an effective strategy to make the jets interact with the
vortexes of the wake, thus reducing the drag. To tackle the computational
complexity of the fluid dynamics simulations, which would make the training
procedure prohibitively expensive, we train the agent on a coarse
discretization of the domain. We provide numerical evidence that a policy
trained in this approximate environment still retains good performance when
carried over to a denser mesh. Our simulations show a considerable drag
reduction with a consequent saving of total power, defined as the sum of the
power spent by the control system and of the power of the drag force, amounting
to 40% when compared to simulations with the reference bluff body without any
jet. Finally, we qualitatively investigate the control policy learnt by the
neural network. We can observe that it achieves the drag reduction by learning
the frequency of formation of the vortexes and activating the jets accordingly,
thus blowing them away off the rear body surface.
