Reduced-order models for coupled dynamical systems: Data-driven methods and the Koopman operator

Providing efficient and accurate parameterizations for model reduction is a key goal in many areas of science technology. Here, we present strong link between data-driven theoretical approaches to achieving this goal. Formal perturbation expansions the Koopman operator allow us derive general stochastic weakly coupled dynamical systems. Such yield set integrodifferential equations with explicit noise memory kernel formulas describe effects unresolved variables. We show that involved need not be truncated when coupling additive. The unwieldy can recast as simpler multilevel Markovian model, establish an intuitive connection generalized Langevin equation. This helps setting up parallelism top-down, equation-based methodology herein well-established empirical (EMR) has been shown provide closures partially observed Hence, our findings, on one hand, support physical basis robustness EMR and, other illustrate practical relevance perturbative expansion used deriving parameterizations.