Linot Lab

The high dimensionality and complex dynamics of turbulent flows remain an obstacle to the discovery and implementation of control strategies. Deep reinforcement learning (RL) is a promising avenue for overcoming these obstacles, but requires a training phase in which the RL agent iteratively interacts with the flow environment to learn a control policy, which can be prohibitively expensive when the environment involves slow experiments or large-scale simulations. We overcome this challenge using a framework we call “DManD-RL” (data-driven manifold dynamics-RL), which generates a data-driven low-dimensional model of our system that we use for RL training. With this approach, we seek to minimize drag in a direct numerical simulation (DNS) of a turbulent minimal flow unit of plane Couette flow at Re=400 using two slot jets on one wall. We obtain, from DNS data with O(105) degrees of freedom, a 25-dimensional DManD model of the dynamics by combining an autoencoder and neural ordinary differential equation. Using this model as the environment, we train an RL control agent, yielding a 440-fold speedup over training on the DNS, with equivalent control performance. The agent learns a policy that laminarizes 84% of unseen DNS test trajectories within 900 time units, significantly outperforming classical opposition control (58%), despite the actuation authority being much more restricted. The agent often achieves laminarization through a counterintuitive strategy that drives the formation of two low-speed streaks, with a spanwise wavelength that is too small to be self-sustaining. The agent demonstrates the same performance when we limit observations to wall shear rate.

In data-driven modeling of spatiotemporal phenomena careful consideration is needed in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or chaotic dynamics. We present a data-driven modeling method that accurately captures shocks and chaotic dynamics by proposing a new architecture, stabilized neural ordinary differential equation (ODE). In our proposed architecture, we learn the right-hand-side (RHS) of an ODE by adding the outputs of two NN together where one learns a linear term and the other a nonlinear term. Specifically, we implement this by training a sparse linear convolutional NN to learn the linear term and a dense fully-connected nonlinear NN to learn the nonlinear term. This contrasts with the standard neural ODE which involves training a single NN for the RHS. We apply this setup to the viscous Burgers equation, which exhibits shocked behavior, and show stabilized neural ODEs provide better short-time tracking, prediction of the energy spectrum, and robustness to noisy initial conditions than standard neural ODEs. We also apply this method to chaotic trajectories of the Kuramoto-Sivashinsky equation. In this case, stabilized neural ODEs keep long-time trajectories on the attractor, and are highly robust to noisy initial conditions, while standard neural ODEs fail at achieving either of these results. We conclude by demonstrating how stabilizing neural ODEs provide a natural extension for use in reduced-order modeling by projecting the dynamics onto the eigenvectors of the learned linear term.