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We introduce a data-driven method and shows its skills for spatiotemporalprediction of high-dimensional chaotic dynamics and turbulence. The method isbased on a finite-dimensional approximation of the Koopman operator where theobservables are vector-valued and delay-embedded, and the nonlinearities aretreated as external forcings. The predictive capabilities of the method aredemonstrated for well-known prototypes of chaos such as theKuramoto-Sivashinsky equation and Lorenz-96 system, for which the data-drivenpredictions are accurate for several Lyapunov timescales. Similar performanceis seen for two-dimensional lid-driven cavity flows at high Reynolds numbers.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings