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Modal decomposition techniques are showing a fast growth in popularity for their good properties as data-driven tools. There are several modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode…

A theoretical framework which unifies the conventional Mori-Zwanzig formalism and the approximate Koopman learning is presented. In this framework, the Mori-Zwanzig formalism, developed in statistical mechanics to tackle the hard problem of…

Statistical Mechanics · Physics 2021-07-27 Yen Ting Lin , Yifeng Tian , Marian Anghel , Daniel Livescu

Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD)…

Signal Processing · Electrical Eng. & Systems 2020-12-16 Mohammad N. Murshed , M. Monir Uddin

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…

Machine Learning · Statistics 2025-07-29 Sara M. Ichinaga , Steven L. Brunton , Aleksandr Y. Aravkin , J. Nathan Kutz

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory…

Numerical Analysis · Mathematics 2023-03-14 Alessandro Alla , Angela Monti , Ivonne Sgura

The Dynamic Mode Decomposition (DMD) is a tool of trade in computational data driven analysis of fluid flows. More generally, it is a computational device for Koopman spectral analysis of nonlinear dynamical systems, with a plethora of…

Numerical Analysis · Mathematics 2017-08-10 Zlatko Drmač , Igor Mezić , Ryan Mohr

The DMD (Dynamic Mode Decomposition) method has attracted widespread attention as a representative modal-decomposition method and can build a predictive model. However, the DMD may give predicted results that deviate from physical reality…

Computational Physics · Physics 2023-11-29 Yuhui Yin , Chenhui Kou , Shengkun Jia , Lu Lu , Xigang Yuan , Yiqing Luo

The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…

Optimization and Control · Mathematics 2017-12-07 Travis Askham , Peng Zheng , Aleksandr Aravkin , J. Nathan Kutz

Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…

Numerical Analysis · Mathematics 2024-01-17 Francesco Andreuzzi , Nicola Demo , Gianluigi Rozza

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

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

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…

Numerical Analysis · Mathematics 2023-01-25 Quincy A. Huhn , Mauricio E. Tano , Jean C. Ragusa , Youngsoo Choi

Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the…

Optimization and Control · Mathematics 2017-09-12 Byron Heersink , Michael A. Warren , Heiko Hoffmann

We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…

Numerical Analysis · Mathematics 2016-02-17 Alessandro Alla , J. Nathan Kutz

The Dynamic Mode Decomposition (DMD) extracted dynamic modes are the non-orthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamical system analysis,…

Statistics Theory · Mathematics 2020-03-09 Arvind Prasadan , Raj Rao Nadakuditi

There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to…

Neurons and Cognition · Quantitative Biology 2015-11-24 Bingni W. Brunton , Lise A. Johnson , Jeffrey G. Ojemann , J. Nathan Kutz

The characterization of intermittent, multiscale and transient dynamics using data-driven analysis remains an open challenge. We demonstrate an application of the Dynamic Mode Decomposition (DMD) with sparse sampling for the diagnostic…

Dynamical Systems · Mathematics 2020-05-18 Krithika Manohar , Eurika Kaiser , Steven L. Brunton , J. Nathan Kutz

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

Numerical Analysis · Mathematics 2019-08-14 Stefan Klus , Patrick Gelß , Sebastian Peitz , Christof Schütte

The increasing penetration of renewable energy sources, characterised by low inertia and intermittent disturbances, presents substantial challenges to power system stability. As critical indicators of system stability, frequency dynamics…

Systems and Control · Electrical Eng. & Systems 2025-02-19 Xiao Li , Xinyi Wen , Benjamin Schäfer

In this two-part article, we evaluate the utility and the generalizability of the Dynamic Mode Decomposition (DMD) algorithm for data-driven analysis and reduced-order modelling of plasma dynamics in cross-field ExB configurations. The DMD…

Plasma Physics · Physics 2023-08-29 Farbod Faraji , Maryam Reza , Aaron Knoll , J. Nathan Kutz