Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures

TL;DR

This paper introduces sparse-mode DMD, a novel variant of dynamic mode decomposition that uses sparsity regularization to distinguish between local and global spatial structures in spatiotemporal data, improving interpretability.

Contribution

The paper presents sparse-mode DMD, which enhances optimized DMD by promoting sparsity to better identify localized modes and separate spectral components in an unsupervised manner.

Findings

Successfully disambiguates local and global modes in synthetic data.

Effectively analyzes real-world systems like optical waveguides and sea surface temperatures.

Maintains noise robustness while distinguishing spectral features.

Abstract

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.