  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.
