Finding Low-Dimensional Dynamical Structure Through Variational Auto-Encoding Dynamic Mode Decomposition

Abstract

Dynamic mode decomposition (DMD) is a modal decomposition method. DMD decomposes time-series data into multiple spatial modes each of which is associated with fixed frequency (damping) oscillator. DMD has been attracting attention in many science and engineering fields since they can be used to analyze a wide range of dynamical systems. In many high-dimensional dynamical systems, it can be assumed that there exists a low-dimensional latent variable and a observed value is generated from it. Therefore, it is important to find not only the spatiotemporal modes but also the low-dimensional latent variables in case of high-dimensional time-series data. By introducing variational inference procedure to the existing method, DMD based latent variable estimation is proposed in this study. By applying the proposed method to a synthetic dynamical system and comparing with the existing method, it is shown that the proposed method can decompose data precisely and can estimate latent variables.