Dynamics-based machine learning of transitions in Couette flow

Abstract

We derive low-dimensional, data-driven models for transitions among exact coherent states (ECSs) in one of the most studied canonical shear flows, the plane Couette flow. These one- or two-dimensional nonlinear models represent the leading-order reduced dynamics on attracting spectral submanifolds (SSMs), which we construct using the recently developed SSMLearn algorithm from a small number of simulated transitions. We find that the energy input and output rates provide efficient parametrizations for the most important SSMs. By restricting the dynamics to these SSMs, we obtain reduced-order models that also reliably predict nearby, off-SSM transitions that were not used in their training.