Applications of the dynamic mode decomposition

By Peter J. Schmid, Larry K. B. Li, Matthew P. Juniper, O. Pust. 2011

622 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/52fb8e924e7b6bd5561b1545cc4fe621e8ee2c9f

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In Aerospace Engineering

In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition (2014, background): “This definition is a generalization of preexisting DMD algorithms [4, 35], and does not require the data to be in the form of a single time series.”
On dynamic mode decomposition: Theory and applications (2013, background): “For instance, DMD has been applied in the study of the wake behind a flexible membrane [8], the flow around high-speed trains [9], instabilities in annular liquid sheets [10], shockwave-turbulent boundary layer interactions [11], detonation waves [12], cavity flows [8,13], and various jets [3,8,14,1”
Data-driven discovery of coordinates and governing equations (2019, methodology): “Methods such as dynamic mode decomposition (DMD) [4, 5, 10, 74], extended DMD [75], kernel DMD [76], and time-delay DMD [77, 78] build linear models for dynamics, but these methods rely on a proper set of coordinates for linearization.”
Construction of eigenfunctions for scalar-type operators via Laplace averages with connections to the Koopman operator (2014, methodology): “tion. This is done in the uids literature via the DMD algorithm [29,28] (whose connection to the Koopman operator was given in [25]) and its utility has been born out in a number of studies; e.g. see [25,30,31] or the recent review article [22], and the references therein, for a subset. Other applie”
De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets (2015, background): “, sensor noise), which has led to a host of approaches aimed at mitigating noise-related effects via various forms of rank-reduction, ensemble averaging, cross-validation, and windowing [2, 18, 19, 20, 21, 22, 23, 24, 25].”
Higher Order Dynamic Mode Decomposition (2017, methodology): “Namely, the obtained amplitudes and frequencies strongly depend on the sampled interval because the orbit is chaotic and visits different regions of the attractor S4000[46,50] and using DMD-4000: S 20000 [40,44], and S 20000 [46,50]. in different timespans.”
Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition (2014, methodology): “It has subsequently been used to gain dynamic insight on a wide range of problems arising in ﬂuid mechanics (e.g., Schmid et al., 2011; Schmid, 2011; Jardin and Bury, 2012) and other ﬁelds (e.g., Grosek and Kutz, 2014).”