Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures
This work addresses the challenge of disambiguating local versus global modes in data analysis for fields such as physics and climate science, representing an incremental improvement to existing DMD methods.
The paper tackles the problem of distinguishing between local and global structures in spatiotemporal data by introducing sparse-mode DMD, a variant of optimized DMD that uses sparsity-promoting regularization to approximate modes with localized spatial features, and demonstrates its application on synthetic and real-world systems like optical waveguides and sea surface temperature data.
The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically leverages sparsity-promoting regularization in order to approximate DMD modes which have localized spatial structure. The algorithm maintains the noise-robust properties of optimized DMD while disambiguating between modes which are spatially local versus global in nature. In many applications, such modes are associated with discrete and continuous spectra respectively, thus allowing the algorithm to explicitly construct, in an unsupervised manner, the distinct portions of the spectrum. We demonstrate this by analyzing synthetic and real-world systems, including examples from optical waveguides, quantum mechanics, and sea surface temperature data.