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The high dimensionality and complex dynamics of turbulent flows remain anobstacle to the discovery and implementation of control strategies. Deepreinforcement learning (RL) is a promising avenue for overcoming theseobstacles, but requires a training phase in which the RL agent iterativelyinteracts with the flow environment to learn a control policy, which can beprohibitively expensive when the environment involves slow experiments orlarge-scale simulations. We overcome this challenge using a framework we call"DManD-RL" (data-driven manifold dynamics-RL), which generates a data-drivenlow-dimensional model of our system that we use for RL training. With thisapproach, we seek to minimize drag in a direct numerical simulation (DNS) of aturbulent minimal flow unit of plane Couette flow at Re=400 using two slot jetson one wall. We obtain, from DNS data with $\mathcal{O}(10^5)$ degrees offreedom, a 25-dimensional DManD model of the dynamics by combining anautoencoder and neural ordinary differential equation. Using this model as theenvironment, we train an RL control agent, yielding a 440-fold speedup overtraining on the DNS, with equivalent control performance. The agent learns apolicy that laminarizes 84% of unseen DNS test trajectories within 900 timeunits, significantly outperforming classical opposition control (58%), despitethe actuation authority being much more restricted. The agent often achieveslaminarization through a counterintuitive strategy that drives the formation oftwo low-speed streaks, with a spanwise wavelength that is too small to beself-sustaining. The agent demonstrates the same performance when we limitobservations to wall shear rate.

Turbulence control in plane Couette flow using low-dimensional neural ODE-based models and deep reinforcement learning