  We show the skills of a data-driven low-dimensional linear model in
predicting the spatio-temporal evolution of turbulent Rayleigh-B\'enard
convection. The model is based on dynamic mode decomposition with
delay-embedding, which provides a data-driven finite-dimensional approximation
to the system's Koopman operator. The model is built using vector-valued
observables from direct numerical simulations, and can provide accurate
predictions. Similar high prediction skills are found for the
Kuramoto-Sivashinsky equation in the strongly-chaotic regimes.
