Modal extraction of spatiotemporal atomization data using a deep convolutional Koopman network

Abstract

Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems that are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions that capture the coordinate transformation to globally linearize system dynamics. These eigenfunctions can be linked to underlying system modes that govern the dynamical behavior of the system. While many related techniques have demonstrated their efficacy on low-dimensional systems and their associated state variables, in this work the system dynamics are observed optically (i.e., spatiotemporal data from video or simulation). We demonstrate the ability of a deep convolutional Koopman network (CKN) in automatically identifying independent modes of simple simulated and atomization systems. Practically, the CKN allows for flexibility in system data collection as the data can be easily obtainable observable variables. The learned models are able to successfully and robustly identify the underlying modes governing the system, even with a redundantly large embedding space. Modal disaggregation is encouraged using a simple masking procedure. All of the systems analyzed in this work use an identical network architecture and results are more compact and interpretable compared to dynamic mode decomposition.