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The Koopman Mode Decomposition (KMD) is a data-analysis technique which is often used to extract the spatio-temporal patterns of complex flows.
Bernard O Koopman, “Hamiltonian systems and transformation in hilbert space,” Proceedings of the National Academy of Sciences 17
1931
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1953
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1967
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1971
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1978
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1979
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1980
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1981
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1984
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1985
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1985
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Ralph Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE transactions on antennas and propagation 34
1986
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1988
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Karl E Petersen, Ergodic theory , Vol. 2 (Cambridge University Press, 1989)
1989
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Morteza Gharib and Philip Derango, “A liquid film (soap film) tunnel to study two-dimensional laminar and turbulent shear flows,” Physica D: Nonlinear Phenomena 37
1989
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Gregorio Andria, Mario Savino, and Amerigo Trotta, “Windows and interpolation algorithms to improve electrical measurement accuracy,” IEEE Transactions on Instrumentation and Measurement 38
1989
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Petre Stoica and Arye Nehorai, “Statistical analysis of two nonlinear least-squares estimators of sine-wave parameters in the colored-noise case,” Circuits, Systems and Signal Processing 8
1989
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Richard Roy and Thomas Kailath, “Esprit-estimation of signal parameters via rotational invariance techniques,” IEEE Transactions on acoustics, speech, and signal processing 37
1989
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Jacques Laskar, “The chaotic motion of the solar system: a numerical estimate of the size of the chaotic zones,” Icarus 88
1990
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1991
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1992
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Jacques Laskar, Claude Froeschlé, and Alessandra Celletti, “The measure of chaos by the numerical analysis of the fundamental frequencies. application to the standard mapping,” Physica D: Nonlinear Phenomena 56
1992
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Stéphane G Mallat and Zhifeng Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Transactions on signal processing 41
1993
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Henk Broer and Floris Takens, “Mixed spectra and rotational symmetry,” Archive for rational mechanics and analysis 124
1993
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Gal Berkooz, Philip Holmes, and John L Lumley, “The proper orthogonal decomposition in the analysis of turbulent flows,” Annual review of fluid mechanics 25
1993
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AM Guzmán and CH Amon, “Transition to chaos in converging–diverging channel flows: Ruelle–takens–newhouse scenario,” Physics of Fluids 6
1994
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Maxim Poliashenko and Cyrus K Aidun, “A direct method for computation of simple bifurcations,” Journal of Computational Physics 121
1995
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Jian Li and Petre Stoica, “Efficient mixed-spectrum estimation with applications to target feature extraction,” IEEE transactions on signal processing 44
1996
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Olivier Botella, “On the solution of the navier-stokes equations using chebyshev projection schemes with third-order accuracy in time,” Computers & Fluids 26
1997
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Petre Stoica, Andreas Jakobsson, and Jian Li, “Cisoid parameter estimation in the colored noise case: asymptotic cramer-rao bound, maximum likelihood, and nonlinear least-squares,” IEEE Transactions on Signal Processing 45
1997
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W Cazemier, RWCP Verstappen, and AEP Veldman, “Proper orthogonal decomposition and low-dimensional models for driven cavity flows,” Physics of Fluids (1994-present) 10
1998
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Nathalie Mukolobwiez, Arnaud Chiffaudel, and François Daviaud, “Supercritical eckhaus instability for surface-tension-driven hydrothermal waves,” Physical review letters 80
1998
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Schafer RW Oppenheim, AV and JR Buck, Discrete-time signal processing (Prentice-Hall, NJ, 1999)
1999
Cited alongside, same era.
Yasushi Takeda, “Quasi-periodic state and transition to turbulence in a rotating couette system,” Journal of Fluid Mechanics 389
1999
Cited alongside, same era.
Ananias G Tomboulides and Steven A Orszag, “Numerical investigation of transitional and weak turbulent flow past a sphere,” Journal of Fluid Mechanics 416
2000
Cited alongside, same era.
Lloyd N Trefethen, Spectral methods in MATLAB , Vol. 10 (Siam, 2000)
2000
Cited alongside, same era.
JM Lopez and F Marques, “Dynamics of three-tori in a periodically forced navier-stokes flow,” Physical review letters 85
2000
Cited alongside, same era.
Igor Mezić, “Analysis of fluid flows via spectral properties of the koopman operator,” Annual Review of Fluid Mechanics 45
2013
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Maciej J Balajewicz, Earl H Dowell, and Bernd R Noack, “Low-dimensional modelling of high-reynolds-number shear flows incorporating constraints from the navier–stokes equation,” Journal of Fluid Mechanics 729
2013
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Yoshihiko Susuki and Igor Mezić, “Nonlinear koopman modes and power system stability assessment without models,” Power Systems, IEEE Transactions on 29
2014
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Taraneh Sayadi, Peter J Schmid, Joseph W Nichols, and Parviz Moin, “Reduced-order representation of near-wall structures in the late transitional boundary layer,” Journal of Fluid Mechanics 748
2014
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Yu-heng Tseng and Joel H Ferziger, “Mixing and available potential energy in stratified flows,” Physics of Fluids 13
2001
Cited alongside, same era.
F Auteri, N Parolini, and L Quartapelle, “Numerical investigation on the stability of singular driven cavity flow,” Journal of Computational Physics 183
2002
Cited alongside, same era.
Michael Ghil, MR Allen, MD Dettinger, K Ide, D Kondrashov, ME Mann, Andrew W Robertson, A Saunders, Y Tian, F Varadi, et al. , “Advanced spectral methods for climatic time series,” Reviews of geophysics 40
2002
Cited alongside, same era.
Igor Mezić and Fotis Sotiropoulos, “Ergodic theory and experimental visualization of invariant sets in chaotically advected flows,” Physics of Fluids (1994-present) 14
2002
Cited alongside, same era.
Dusan Agrez, “Weighted multipoint interpolated dft to improve amplitude estimation of multifrequency signal,” IEEE Transactions on Instrumentation and Measurement 51
2002
Cited alongside, same era.
Yih-Ferng Peng, Yuo-Hsien Shiau, and Robert R Hwang, “Transition in a 2-d lid-driven cavity flow,” Computers & Fluids 32
2003
Cited alongside, same era.
Stephen Wiggins, Introduction to applied nonlinear dynamical systems and chaos , Vol. 2 (Springer Science & Business Media, 2003)
2003
Cited alongside, same era.
2014
Later among the works it cites.
Jonathan H Tu, Clarence W Rowley, Dirk M Luchtenburg, Steven L Brunton, and J Nathan Kutz, “On dynamic mode decomposition: theory and applications,” Journal of Computational Dynamics (2014)
2014
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Maziar S Hemati, Matthew O Williams, and Clarence W Rowley, “Dynamic mode decomposition for large and streaming datasets,” Physics of Fluids 26
2014
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Mihailo R Jovanović, Peter J Schmid, and Joseph W Nichols, “Sparsity-promoting dynamic mode decomposition,” Physics of Fluids (1994-present) 26
2014
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Gilles Tissot, Laurent Cordier, Nicolas Benard, and Bernd R Noack, “Model reduction using dynamic mode decomposition,” Comptes Rendus Mécanique 342
2014
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Emmanuel J Candès and Carlos Fernandez-Granda, “Towards a mathematical theory of super-resolution,” Communications on Pure and Applied Mathematics 67
2014
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Dimitrios Giannakis, Joanna Slawinska, and Zhizhen Zhao, “Spatiotemporal feature extraction with data-driven koopman operators,” in Journal of Machine Learning Research, Proceedings of the 1st International Workshop on’Feature Extraction: Modern Questions and Challenges’ and NIPS Conference , Vol. 44 (2015) pp. 103–115
2015
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Michael Georgescu and Igor Mezić, “Building energy modeling: A systematic approach to zoning and model reduction using koopman mode analysis,” Energy and buildings 86
2015
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2015
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Taraneh Sayadi, Peter J Schmid, Franck Richecoeur, and Daniel Durox, “Parametrized data-driven decomposition for bifurcation analysis, with application to thermo-acoustically unstable systems,” Physics of Fluids 27
2015
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2015
Later among the works it cites.
Matthew O Williams, Ioannis G Kevrekidis, and Clarence W Rowley, “A data–driven approximation of the koopman operator: Extending dynamic mode decomposition,” Journal of Nonlinear Science 25
2015
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Florimond Guéniat, Lionel Mathelin, and Luc R Pastur, “A dynamic mode decomposition approach for large and arbitrarily sampled systems,” Physics of Fluids 27
2015
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Yoshihiko Susuki and Igor Mezić, “A prony approximation of koopman mode decomposition,” in Decision and Control (CDC), 2015 IEEE 54th Annual Conference on (IEEE, 2015) pp. 7022–7027
2015
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Bingni W Brunton, Lise A Johnson, Jeffrey G Ojemann, and J Nathan Kutz, “Extracting spatial–temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition,” Journal of neuroscience methods 258
2016
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Jordan Mann and J Nathan Kutz, “Dynamic mode decomposition for financial trading strategies,” Quantitative Finance , 1–13 (2016)
2016
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Jia-Chen Hua, Gemunu H Gunaratne, Douglas G Talley, James R Gord, and Sukesh Roy, “Dynamic-mode decomposition based analysis of shear coaxial jets with and without transverse acoustic driving,” Journal of Fluid Mechanics 790
2016
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2016
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Amit Surana and Andrzej Banaszuk, “Linear observer synthesis for nonlinear systems using koopman operator framework,” IFAC-PapersOnLine 49
2016
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Amit Surana, “Koopman operator based observer synthesis for control-affine nonlinear systems,” in Decision and Control (CDC), 2016 IEEE 55th Conference on (IEEE, 2016) pp. 6492–6499
2016
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J Nathan Kutz, Xing Fu, and Steven L Brunton, “Multiresolution dynamic mode decomposition,” SIAM Journal on Applied Dynamical Systems 15
2016
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Joshua L Proctor, Steven L Brunton, and J Nathan Kutz, “Dynamic mode decomposition with control,” SIAM Journal on Applied Dynamical Systems 15
2016
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Scott TM Dawson, Maziar S Hemati, Matthew O Williams, and Clarence W Rowley, “Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition,” Experiments in Fluids 57
2016
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Carlos Fernandez-Granda, “Super-resolution of point sources via convex programming,” Information and Inference: A Journal of the IMA 5
2016
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Babak Mamandipoor, Dinesh Ramasamy, and Upamanyu Madhow, “Newtonized orthogonal matching pursuit: Frequency estimation over the continuum.” IEEE Trans. Signal Processing 64
2016
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Igor Mezić, “Koopman operator spectrum and data analysis,” arXiv preprint arXiv:1702.07597 (2017)
2017
Closest in time.
Dimitrios Giannakis, “Data-driven spectral decomposition and forecasting of ergodic dynamical systems,” Applied and Computational Harmonic Analysis (2017)
2017
Closest in time.
2017
Closest in time.
2017
Closest in time.
Maziar S Hemati, Clarence W Rowley, Eric A Deem, and Louis N Cattafesta, “De-biasing the dynamic mode decomposition for applied koopman spectral analysis of noisy datasets,” Theoretical and Computational Fluid Dynamics , 1–20 (2017)
2017
Closest in time.
Niothin GOVINDARAJAN, Ryan Mohr, Shiv CHANDRASEKARAN, and Igor Mezić, “A convergent numerical method for computing koopman spectra of volume-preserving maps on the d-torus,” preprint (2017)
2017
Closest in time.