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

arXiv: https://arxiv.org/abs/2507.19787 · HTML: https://mlsanity.com/paper/2507.19787/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 52 references that are in the map.
- First posted on arXiv 26 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition](https://mlsanity.com/paper/1409.5496/) (2014)
- [A unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [A Unified Framework for Sparse Relaxed Regularized Regression: SR3](https://mlsanity.com/paper/1807.05411/) (2018)
- [Active Learning of Dynamics for Data-Driven Control Using Koopman Operators](https://mlsanity.com/paper/1906.05194/) (2019)
- [Sparsity-promoting dynamic mode decomposition](https://mlsanity.com/paper/1309.4165/) (2013)
- [Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification](https://mlsanity.com/paper/2107.10878/) (2021)
- [Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Control](https://mlsanity.com/paper/1902.02827/) (2019)
- [Compressed Dynamic Mode Decomposition for Background Modeling](https://mlsanity.com/paper/1512.04205/) (2015)
- [Sparse Principal Component Analysis via Variable Projection](https://mlsanity.com/paper/1804.00341/) (2018)
- [An Incremental Approach to Online Dynamic Mode Decomposition for Time-Varying Systems with Applications to EEG Data Modeling](https://mlsanity.com/paper/1908.01047/) (2019)
- [Robust and scalable methods for the dynamic mode decomposition](https://mlsanity.com/paper/1712.01883/) (2017)

## Abstract (arXiv)

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.