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

• URL: http://arxiv.org/abs/2507.19787v1
• Date: Sat, 26 Jul 2025 04:24:40 GMT
• Title: Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures
• Authors: Sara M. Ichinaga, Steven L. Brunton, Aleksandr Y. Aravkin, J. Nathan Kutz,
• Abstract summary: We introduce sparse-mode DMD, a new variant of the optimized DMD framework that leverages sparsity-temporal regularization.<n>The algorithm maintains the noise-robust of optimized modes while disambiguating between modes which are local versus global in nature.<n>We demonstrate this by analyzing synthetic and real-world systems, including examples from optical waveguides, quantum mechanics, and surface temperature data.
• Score: 48.407500521383646
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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