In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In general, the Koopman operator is obtained as a solution to a least-squares problem, and as such, the Koopman operator can be expressed as a closed-form solution that involves the computation of Moore-Penrose inverse of a matrix. For high dimensional systems and also if the size of the obtained data-set is large, the computation of the Moore-Penrose inverse becomes computationally challenging. In this paper, we provide an algorithm for computing the Koopman operator for high dimensional systems in a time-efficient manner. We further demonstrate the efficacy of the proposed approach on two different systems, namely a network of coupled oscillators (with state-space dimension up to 2500) and IEEE 68 bus system (with state-space dimension 204 and up to 24,000 time-points).

中文翻译：

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大规模动力系统的计算高效学习：Koopman 理论方法

近年来，在动力系统的数据驱动分析、发现和控制方面出现了相当大的推动力。为此，算子理论方法，即 Koopman 算子方法获得了很多关注。通常，Koopman 算子是作为最小二乘问题的解而获得的，因此，Koopman 算子可以表示为涉及矩阵的 Moore-Penrose 逆计算的封闭形式的解。对于高维系统以及如果获得的数据集的大小很大，Moore-Penrose 逆的计算在计算上变得具有挑战性。在本文中，我们提供了一种算法，用于以高效的方式计算高维系统的 Koopman 算子。我们进一步证明了所提出的方法在两个不同系统上的有效性，