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In recent years there has been a considerable drive towards data-drivenanalysis, discovery and control of dynamical systems. To this end, operatortheoretic methods, namely, Koopman operator methods have gained a lot ofinterest. In general, the Koopman operator is obtained as a solution to aleast-squares problem, and as such, the Koopman operator can be expressed as aclosed-form solution that involves the computation of Moore-Penrose inverse ofa matrix. For high dimensional systems and also if the size of the obtaineddata-set is large, the computation of the Moore-Penrose inverse becomescomputationally challenging. In this paper, we provide an algorithm forcomputing the Koopman operator for high dimensional systems in a time-efficientmanner. We further demonstrate the efficacy of the proposed approach on twodifferent systems, namely a network of coupled oscillators (with state-spacedimension up to 2500) and IEEE 68 bus system (with state-space dimension 204and up to 24,000 time-points).

Computationally Efficient Learning of Large Scale Dynamical Systems: A Koopman Theoretic Approach