Complex systems with multiple timescales of dynamics pose a tremendous challenge for data analysis and modeling. For complex systems in oceans and climate exhibiting scale separation, the macroscopic (slow) evolution is often modeled by treating fast variables as stochastic effects. This work uses an entirely data-driven method called kernel analog forecasting for prediction, using observations of only slow variables. We apply a smooth kernel function to data from two chaotic multiscale dynamical systems to numerically approximate eigenfunctions of an associated diffusion operator. Using these eigenfunctions as a basis, we construct an operator semigroup modeling the slow dynamics, and study its predictive skill.
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