Data-driven Spatio-temporal Prediction of High-dimensional Geophysical Turbulence using Koopman Operator Approximation

Abstract

We show the skills of a data-driven low-dimensional linear model in predicting the spatio-temporal evolution of turbulent Rayleigh-Bénard 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.

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