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Recent deep learning extensions in Koopman theory have enabled compact,interpretable representations of nonlinear dynamical systems which are amenableto linear analysis. Deep Koopman networks attempt to learn the Koopmaneigenfunctions which capture the coordinate transformation to globallylinearize system dynamics. These eigenfunctions can be linked to underlyingsystem modes which govern the dynamical behavior of the system. While manyrelated techniques have demonstrated their efficacy on canonical systems andtheir associated state variables, in this work the system dynamics are observedoptically (i.e. in video format). We demonstrate the ability of a deepconvolutional Koopman network (CKN) in automatically identifying independentmodes for dynamical systems with discrete spectra. Practically, this affordsflexibility in system data collection as the data are easily obtainableobservable variables. The learned models are able to successfully and robustlyidentify the underlying modes governing the system, even with a redundantlylarge embedding space. Modal disaggregation is encouraged using a simplemasking procedure. All of the systems analyzed in this work use an identicalnetwork architecture.

Extraction of Discrete Spectra Modes from Video Data Using a Deep Convolutional Koopman Network