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We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator.
Hamiltonian systems and transformation in Hilbert space
B. O. Koopman · 1931
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Dynamical systems of continuous spectra
B. O. Koopman and J. von Neumann · 1932
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Lectures on ergodic theory
Paul Richard Halmos · 1956
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Deterministic nonperiodic flow
Edward N Lorenz · 1963
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Detecting strange attractors in turbulence
F. Takens · 1981
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Ergodic theory of chaos and strange attractors
J-P Eckmann and David Ruelle · 1985
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An eigensystem realization algorithm for modal parameter identification and model reduction
J-N Juang and Richard S Pappa · 1985
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Ergodic theorems
Ulrich Krengel and Antoine Brunel · 1985
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Turbulence and the dynamics of coherent structures part i: coherent structures
Lawrence Sirovich · 1987
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Embedology
Tim Sauer, James A Yorke, and Martin Casdagli · 1991
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Composition operators on function spaces
RK Singh and JS Manhas · 1993
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Ergodic Theory
K. Petersen · 1995
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Numerical linear algebra
Lloyd N Trefethen and David Bau III · 1997
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Advanced spectral methods for climatic time series
Michael Ghil, MR Allen, MD Dettinger, K Ide, D Kondrashov, ME Mann, Andrew W Robertson, A Saunders, Y Tian, F Varadi, et al · 2002
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Ergodic theory and experimental visualization of invariant sets in chaotically advected flows
Igor Mezić and Fotis Sotiropoulos · 2002
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What are SRB measures, and which dynamical systems have them?
L.S. Young · 2002
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Comparison of systems with complex behavior
Igor Mezić and Andrzej Banaszuk · 2004
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The lorenz attractor is mixing
Stefano Luzzatto, Ian Melbourne, and Frederic Paccaut · 2005
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Spectral properties of dynamical systems, model reduction and decompositions
Igor Mezić · 2005
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Elementary functional analysis
Barbara MacCluer · 2008
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Dynamic mode decomposition of numerical and experimental data
P. Schmid and J. Sesterhenn · 2008
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Sensitivity measures for oscillating systems: Application to mammalian circadian gene network
Stephanie R Taylor, Rudiyanto Gunawan, Linda R Petzold, and Francis J Doyle III · 2008
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Event-based minimum-time control of oscillatory neuron models
Per Danzl, João Hespanha, and Jeff Moehlis · 2009
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Compressive sampling and dynamic mode decomposition
Steven L Brunton, Joshua L Proctor, and J Nathan Kutz · 2013
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Global stability analysis using the eigenfunctions of the koopman operator
Alexandre Mauroy and Igor Mezić · 2014
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On dynamic mode decomposition: theory and applications
Jonathan H Tu, Clarence W Rowley, Dirk M Luchtenburg, Steven L Brunton, and J Nathan Kutz · 2014
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Building energy modeling: A systematic approach to zoning and model reduction using koopman mode analysis
Michael Georgescu and Igor Mezić · 2015
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Data-driven spectral decomposition and forecasting of ergodic dynamical systems
Dimitrios Giannakis · 2015
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Spectral analysis of nonlinear flows
C.W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D.S. Henningson · 2009
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Infinite-dimensional numerical linear algebra: theory and applications
Anders C Hansen · 2010
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Dynamic mode decomposition of numerical and experimental data
Peter J Schmid · 2010
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Numerical Methods for Large Eigenvalue Problems: Revised Edition
Yousef Saad · 2011
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Nonlinear koopman modes and coherency identification of coupled swing dynamics
Yoshihiko Susuki and Igor Mezić · 2011
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Applied koopmanism a)
Marko Budi v · 2012
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Stefan Klus, Péter Koltai, and Christof Schütte · 2015
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On applications of the spectral theory of the koopman operator in dynamical systems and control theory
Igor Mezić · 2015
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A prony approximation of koopman mode decomposition
Yoshihiko Susuki and Igor Mezić · 2015
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A data-driven approximation of the koopman operator: Extending dynamic mode decomposition
Matthew O Williams, Ioannis G Kevrekidis, and Clarence W Rowley · 2015
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Extracting spatial–temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition
Bingni W Brunton, Lise A Johnson, Jeffrey G Ojemann, and J Nathan Kutz · 2016
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Chaos as an intermittently forced linear system
Steven L Brunton, Bingni W Brunton, Joshua L Proctor, Eurika Kaiser, and J Nathan Kutz · 2016
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Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control
Steven L Brunton, Bingni W Brunton, Joshua L Proctor, and J Nathan Kutz · 2016
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Multiresolution dynamic mode decomposition
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Dynamic mode decomposition with control
Joshua L Proctor, Steven L Brunton, and J Nathan Kutz · 2016
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Study of dynamics in unsteady flows using koopman mode decomposition
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Koopman operator spectrum and data analysis
Igor Mezić · 2017
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