Data-driven control of spatiotemporal chaos with reduced-order neural ODE-based models and reinforcement learning

Deep reinforcement learning (RL) is a data-driven method capable of discovering complex control strategies for high-dimensional systems, making it promising flow applications. In particular, the present work motivated by goal reducing energy dissipation in turbulent flows, and example considered spatiotemporally chaotic dynamics Kuramoto-Sivashinsky equation (KSE). A major challenge associated with RL that substantial training data must be generated repeatedly interacting target system, costly when system computationally or experimentally expensive. We mitigate this manner combining dimensionality reduction via an autoencoder neural ODE framework to obtain low-dimensional dynamical model from just limited set. substitute reduced-order (ROM) place true during efficiently estimate optimal policy, which can then deployed on system. For KSE actuated localized forcing ("jets") at four locations, we demonstrate are able learn ROM accurately captures as well underlying natural snapshots experiencing random actuations. Using objective minimizing power cost, extract policy using deep RL. show ROM-based strategy translates highlight agent discovers stabilizes forced equilibrium solution captured discovered through related existing known KSE.