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Non-Stationary Dynamic Mode Decomposition [PDF]
IEEE Access, 2023 Many physical processes display complex high-dimensional time-varying behavior, from global weather patterns to brain activity. An outstanding challenge is to express high dimensional data in terms of a dynamical model that reveals their spatiotemporal ...
John Ferre +4 more
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Consistent Dynamic Mode Decomposition [PDF]
SIAM Journal on Applied Dynamical Systems, 2019 We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of data alignment
Azencot, Omri +2 more
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Challenges in dynamic mode decomposition. [PDF]
J R Soc Interface, 2021 Dynamic mode decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics and neuroscience. Two of the main challenges remaining in DMD research are noise sensitivity and issues related to Krylov ...
Wu Z, Brunton SL, Revzen S.
europepmc +5 more sources
Robust Dynamic Mode Decomposition
IEEE Access, 2022 This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions, including heavy ...
Amir Hossein Abolmasoumi +2 more
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Randomized Dynamic Mode Decomposition [PDF]
SIAM Journal on Applied Dynamical Systems, 2019 This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of deterministic ...
Brunton, Steven L. +3 more
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Towards an Adaptive Dynamic Mode Decomposition
Results in Control and Optimization, 2022 Dynamic Mode Decomposition (DMD) is a tool that creates an approximate model from spatio-temporal data. We have developed an architecture of this tool that will adapt to the data from a given problem by leveraging time delay coordinates, projections, and
Mohammad N. Murshed, M. Monir Uddin
doaj +4 more sources
Swarm Modeling With Dynamic Mode Decomposition
IEEE Access, 2022 Modelling biological or engineering swarms is challenging due to the inherently high dimension of the system, despite the often low-dimensional emergent dynamics.
Emma Hansen +2 more
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Dynamic mode decomposition with control [PDF]
SIAM Journal on Applied Dynamical Systems, 2014 We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems.
Brunton, Steven L. +2 more
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Tensor-based dynamic mode decomposition [PDF]
Nonlinearity, 2017 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 high-dimensional ...
Gelß, Patrick +3 more
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Real-time motion detection using dynamic mode decomposition [PDF]
EURASIP Journal on Image and Video ProcessingDynamic mode decomposition (DMD) is a numerical method that seeks to fit time-series data to a linear dynamical system. In doing so, DMD decomposes dynamic data into spatially coherent modes that evolve in time according to exponential growth/decay or ...
Marco Mignacca +2 more
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