Koopman-mode decomposition of the cylinder wake

By Shervin Bagheri. Journal of Fluid Mechanics, 2013

303 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fbcfa0cfd253e38c9394730df38819821c8fd2e3

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In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

Sparsity-promoting dynamic mode decomposition (2012, methodology): “For an in-depth discussion of the connection between DMD and other data decomposition methods, we refer the reader to [8, 9, 13].”
Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition (2014, methodology): “in Bagheri (2014) to be a parabolic decay in the growth rate of identified eigenvalues with increasing frequency. It turns out that a similar effect is observed here for the case of measurement noise. Isolating sensor noise from process noise (especially with limited prior information about the stat”
Optimal mode decomposition for unsteady flows (2013, methodology): “2009) as a method of approximating the Koopman modes of the underlying fluid system (see Bagheri (2013) for a discussion of when this interpretation is appropriate).”
A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition (2014, background): “For example, basis functions defined in polar coordinates are useful when limit cycles or other periodic orbits are present as theymimic the form of the Koopman eigenfunctions for simple limit cycles (Bagheri 2013).”
Model Reduction for Flow Analysis and Control (2017, methodology): “Integration of non-time-resolved PIV and time-resolved velocity point sensors for dynamic estimation of velocity fields.”
Chaos as an intermittently forced linear system (2016, background): “old with measles data [22] • Donoho hard threshold [8] • Predicting chaotic time series [7] • Equations from data series [6] • Extracting dynamics from chaotic data [17] • Chaos from random[24]”
Data-driven discovery of Koopman eigenfunctions for control (2017, unknown): “DMD was originally introduced in the fluid dynamics community [36], [48], [58], [70]–[72] to decompose large data sets into dominant spatialtemporal coherent structures, and a connection with Koopman theory was soon established [59].”
Cluster-based reduced-order modelling of a mixing layer (2013, background): “More recently, Bagheri (2013) studied the conditions under which the DMD algorithm approximates the Koopman modes.”
Constrained sparse Galerkin regression (2016, background): “In the fluid dynamics community, a large body of literature exists in which this particular set-up has been chosen to illustrate modal decomposition (Bagheri 2013; Noack et al. 2016) and model identification techniques (Noack et al. 2003; Sengupta et al. 2015; Brunton et al. 2016a; Rowley & Dawson…”
On dynamic mode decomposition: Theory and applications (2013, methodology): “For instance, in some systems DMD modes and eigenvalues closely approximate those of the Koopman operator near an attractor, but not far from it [26].”
Data-driven prediction of unsteady flow over a circular cylinder using deep learning (2018, methodology): “This differs from the aim of ROMs, which is to discover and understand low-dimensional representation of flow fields at certain Reynolds numbers by learning them (Liberge & Hamdouni 2010; Bagheri 2013).”