Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses

By Kevin K. Chen, Jonathan H. Tu, Clarence W. Rowley. Journal of nonlinear science, 2012

748 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/82e19123c7fdf1c047531eec5bce6f925dcc5ad5

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Citations in the corpus

On dynamic mode decomposition: Theory and applications (2013, methodology): “) The relationship between Koopman modes and DMD modes is similar to that established in [3] (and discussed further in [22]), but the present result differs in some”
Dynamic Mode Decomposition with Control (2014, methodology): “First, it is based upon the DMD algorithm which is a data-driven, equation-free architecture that reconstructs the underlying dynamics of the system from snapshot measurements alone [34], [30], [8], [38].”
Multi-scale proper orthogonal decomposition of complex fluid flows (2018, methodology): “More robust variants of this method are the optimized DMD by Chen et al. (2012) or the sparsity promoting DMD by Jovanović et al. (2014) in which the L2 minimization problem is extended to the entire dataset and not just on the last realization.”
Optimal mode decomposition for unsteady flows (2013, methodology): “Optimized Dynamic Mode Decomposition Koopman modes also provide the motivation for the recently proposed Optimized Dynamic Mode Decomposition (opt-DMD) algorithm in Chen et al. (2012). To calculate opt-DMD, the following optimization problem is solved:”
Recursive dynamic mode decomposition of transient and post-transient wake flows (2016, methodology): “Already in the early literature (Rowley et al. 2009; Schmid 2010; Chen et al. 2012), DMD has been shown to accurately capture the onset of fluctuations in the linear regime or the post-transient behaviour on the attractor.”
Model Reduction for Flow Analysis and Control (2017, background): “Integration of non-time-resolved PIV and time-resolved velocity point sensors for dynamic estimation of velocity fields.”
Colour of turbulence (2016, neutral): “In general, model reduction techniques (Sirovich 1987; Berkoo et al. 1993; Rowley 2005; Mezić 2005, 2013; Lumley 2007; Rowley et al. 2009; Schmid 2010; Chen et al. 2012; Jovanović et al. 2014) can also be used for this purpose.”
Chaos as an intermittently forced linear system (2016, background): “• Dynamics discovery [19] • Sugihara and time series [21, 26].”
Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition (2017, background): “Preprocessing One must not subtract the mean from the original data because subtracting something from the data may change the spectra of the underlying dynamical systems (see, e.g., [48]).”
Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis (2017, methodology): “…a nonzero mean, but in practice the physically-relevant DMD modes tend to have have nearly zero growth/decay rates for stationary flows (e.g., Rowley et al., 2009; Chen et al., 2012; Schmid et al., 2012; Semeraro et al., 2012), which is logical since stationary flows are persistent by definition.”