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Dynamic mode decomposition (DMD), which the family of singular-value decompositions (SVD), is a popular tool of data-driven regression.
Hamiltonian systems and transformation in Hilbert space
B. O. Koopman · 1931
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Galerkin finite element methods for parabolic problems
Vidar Thomée · 1984
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Conditional stochastic averaging of steady state unsaturated flow by means of Kirchhoff transformation
Daniel M Tartakovsky, Shlomo P Neuman, and Zhiming Lu · 1999
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Reconstruction equations and the Karhunen-Loève expansion for systems with symmetry
C. W. Rowley and J. E. Marsden · 2000
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Equation-free, coarse-grained multiscale computation: Enabling mocroscopic simulators to perform system-level analysis
I. G. Kevrekidis, C. W. Gear, J. M. Hyman, P. G. Kevrekidid, O. Runborg, C. Theodoropoulos, et al · 2003
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Stochastic averaging of nonlinear flows in heterogeneous porous media
D. M. Tartakovsky, A. Guadagnini, and M. Riva · 2003
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An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations
M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera · 2004
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The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview
G. Kerschen, J.-C. Golinval, A. F. Vakakis, and L. A. Bergman · 2005
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Model reduction for fluids, using balanced proper orthogonal decomposition
C. W. Rowley · 2005
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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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Distilling free-form natural laws from experimental data
M. Schmidt and H. Lipson · 2009
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Nonlinear model reduction via discrete empirical interpolation
Saifon Chaturantabut and Danny C Sorensen · 2010
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Dynamic mode decomposition of numerical and experimental data
P. J. Schmid · 2010
Cited alongside, same era.
Predicting catastrophes in nonlinear dynamical systems by compressive sensing
W.-X. Wang, R. Yang, Y.-C. Lai, V. Kovanis, and C. Grebogi · 2011
Cited alongside, same era.
An error analysis of the dynamic mode decomposition
D. Duke, J. Soria, and D. Honnery · 2012
Cited alongside, same era.
Analysis of fluid flows via spectral properties of the Koopman operator
I. Mezić · 2013
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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 · 2013
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Hybrid reduced-order integration with proper orthogonal decomposition and dynamic mode decomposition
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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Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
S. T. M. Dawson, M. S. Hemati, M. O. Williams, and C. W. Rowley · 2016
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Dynamic mode decomposition: data-driven modeling of complex systems
J. N. Kutz, S. L. Brunton, B. W. Brunton, and J. L. Proctor · 2016
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Multiresolution dynamic mode decomposition
J. N. Kutz, X. Fu, and S. L. Brunton · 2016
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Dynamic mode decomposition for robust pca with applications to foreground/background subtraction in video streams and multi-resolution analysis
J. N. Kutz, J. Grosek, and S. L. Brunton · 2016
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Matthew O Williams, Peter J Schmid, and J Nathan Kutz · 2013
Cited alongside, same era.
Spectral analysis of fluid flows using sub-Nyquist-rate PIV data
J. H. Tu, C. W. Rowley, J. N. Kutz, and J. K. Shang · 2014
Cited alongside, same era.
Compressed sensing and dynamic mode decomposition
S. L. Brunton, J. L. Proctor, J. H. Tu, and J. N. Kutz · 2015
Cited alongside, same era.
Discovering dynamic patterns from infectious disease data using dynamic mode decomposition
J. L. Proctor and P. A. Eckhoff · 2015
Cited alongside, same era.
A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition
M. O. Williams, I. G. Kevrekidis, and C. W. Rowley · 2015
Cited alongside, same era.
Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition
B. W. Brunton, L. A. Johnson, J. G. Ojemann, and J. N. Kutz · 2016
Cited alongside, same era.
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
S. L. Brunton, J. L. Proctor, and J. N. Kutz · 2016
Cited alongside, same era.
Dynamic mode decomposition for financial trading strategies
J. Mann and J. N. Kutz · 2016
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Dynamic mode decomposition with control
J. L. Proctor, S. L. Brunton, and J. N. Kutz · 2016
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Nonlinear model order reduction via dynamic mode decomposition
Alessandro Alla and J Nathan Kutz · 2017
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Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator
Q. Li, F. Dietrich, E. M. Bollt, and I. G. Kevrekidis · 2017
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Data-driven discovery of partial differential equations
S. H. Rudy, S. L. Brunton, J. L. Proctor, and J. N. Kutz · 2017
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Data driven modal decompositions: analysis and enhancements
Z. Drmac, I. Mezić, and R. Mohr · 2018
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On convergence of extended dynamic mode decomposition to the Koopman operator
M. Korda and I. Mezić · 2018
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