Data-Driven Prediction of Partially Observed Multiscale Systems

Data-Driven Prediction of Partially Observed Multiscale Systems

Complex systems with dynamics evolving on multiple timescales pose a tremendous challenge for data-driven modeling. For complex systems in oceans and climate exhibiting scale separation, the macroscopic (slow) dynamics are often modeled by treating fast variables as stochastic effects. Motivated by this idea, we use kernel methods in machine learning to approximate the Koopman evolution operator associated with the dynamical system based on only observing the slow variables. This method, called kernel analog forecasting, applies a Gaussian kernel to data points to build a Markov kernel operator and diffusion features from its eigenfunctions. Using these eigenfunctions as a basis, we construct an operator semigroup modeling the slow dynamics, and study its predictive skill on chaotic multiscale examples.

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