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Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…

Machine Learning · Statistics 2018-05-18 Patrick Héas , Cédric Herzet

Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…

Numerical Analysis · Mathematics 2026-04-21 Qiuqi Li , Chang Liu , Yifei Yang

This work develops compressive sampling strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It…

Dynamical Systems · Mathematics 2013-12-19 Steven L. Brunton , Joshua L. Proctor , J. Nathan Kutz

Dynamic Mode Decomposition (DMD) is a numerical method that seeks to fit timeseries data to a linear dynamical system. In doing so, DMD decomposes dynamic data into spatially coherent modes that evolve in time according to exponential…

Computer Vision and Pattern Recognition · Computer Science 2026-02-26 Marco Mignacca , Simone Brugiapaglia , Jason J. Bramburger

Despite the importance of sparsity signal models and the increasing prevalence of high-dimensional streaming data, there are relatively few algorithms for dynamic filtering of time-varying sparse signals. Of the existing algorithms, fewer…

Statistics Theory · Mathematics 2016-11-03 Adam Charles , Aurele Balavoine , Christopher Rozell

This note proposes a simple and general framework of dynamic mode decomposition (DMD) and a mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal…

Fluid Dynamics · Physics 2017-08-02 Yuya Ohmichi

We present a sparse sensing framework based on Dynamic Mode Decomposition (DMD) to identify flow regimes and bifurcations in large-scale thermo-fluid systems. Motivated by real-time sensing and control of thermal-fluid flows in buildings…

Dynamical Systems · Mathematics 2017-06-26 Boris Kramer , Piyush Grover , Petros Boufounos , Mouhacine Benosman , Saleh Nabi

The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from time-series data. As with all system identification methods, noisy measurements…

Signal Processing · Electrical Eng. & Systems 2020-10-01 Kadierdan Kaheman , Steven L. Brunton , J. Nathan Kutz

We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…

Machine Learning · Computer Science 2015-07-08 Hanie Sedghi , Anima Anandkumar , Edmond Jonckheere

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…

Numerical Analysis · Mathematics 2014-12-17 Jonathan H. Tu , Clarence W. Rowley , Dirk M. Luchtenburg , Steven L. Brunton , J. Nathan Kutz

Dynamic mode decomposition (DMD) provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal, data. A diversity of regression techniques have been developed for…

Machine Learning · Computer Science 2022-10-12 Diya Sashidhar , J. Nathan Kutz

We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…

Machine Learning · Computer Science 2025-08-04 Willem Diepeveen , Jon Schwenk , Andrea Bertozzi

Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…

Numerical Analysis · Mathematics 2025-10-23 Qiuqi Li , Chang Liu , Yifei Yang

Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only…

Plasma Physics · Physics 2020-03-04 Alan A. Kaptanoglu , Kyle D. Morgan , Chris J. Hansen , Steven L. Brunton

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…

Machine Learning · Computer Science 2023-02-22 Alan A. Kaptanoglu , Lanyue Zhang , Zachary G. Nicolaou , Urban Fasel , Steven L. Brunton

Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…

Computer Vision and Pattern Recognition · Computer Science 2025-09-03 Ali SaraerToosi , Renbo Tu , Kamyar Azizzadenesheli , Aviad Levis

This paper proposes a subspace decomposition method based on an over-complete dictionary in sparse representation, called "Sparse Signal Subspace Decomposition" (or 3SD) method. This method makes use of a novel criterion based on the…

Machine Learning · Statistics 2016-10-28 Hong Sun , Chengwei Sang , Didier Le Ruyet

Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of delay-coordinates embedding and DMD, i.e., delay-coordinates…

Dynamical Systems · Mathematics 2022-12-21 Emil Bronstein , Aviad Wiegner , Doron Shilo , Ronen Talmon

High-performance computing enables simulation of high-dimensional physical systems, but downstream analyses such as inverse problems and control remain computationally expensive, motivating model order reduction (MOR) to construct efficient…

Fluid Dynamics · Physics 2026-05-28 Tomoki Koike , Prakash Mohan , Marc T. Henry de Frahan , Elizabeth Qian , Julie Bessac

We introduce the method of compressed dynamic mode decomposition (cDMD) for background modeling. The dynamic mode decomposition (DMD) is a regression technique that integrates two of the leading data analysis methods in use today: Fourier…

Computer Vision and Pattern Recognition · Computer Science 2016-12-13 N. Benjamin Erichson , Steven L. Brunton , J. Nathan Kutz