De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets

The dynamic mode decomposition (DMD)—a popular method for performing data-driven Koopman spectral analysis—has gained increased popularity for extracting dynamically meaningful spatiotemporal descriptions of fluid flows from snapshot measurements. Often times, DMD descriptions can be used for predic...

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Veröffentlicht in:	Theoretical and computational fluid dynamics Jg. 31; H. 4; S. 349 - 368
Hauptverfasser:	Hemati, Maziar S., Rowley, Clarence W., Deem, Eric A., Cattafesta, Louis N.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2017 Springer Springer Nature B.V
Schlagworte:	Analysis Asymmetry Classical and Continuum Physics Computational fluid dynamics Computational Science and Engineering Decomposition Engineering Engineering Fluid Dynamics Errors Flow (Dynamics) Flow separation Fluid dynamics Fluid flow Fluids Forecasting Frameworks Least squares method Mathematical models Modes Noise Original Article Particle image velocimetry Sensors Spectral analysis Spectral analysis (Signal analysis) Structures Velocity measurement Yields Koopman spectral analysis Sensor noise Data-driven dynamical systems Experimental fluid mechanics Reduced-order model Total least-squares
ISSN:	0935-4964, 1432-2250
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Abstract	The dynamic mode decomposition (DMD)—a popular method for performing data-driven Koopman spectral analysis—has gained increased popularity for extracting dynamically meaningful spatiotemporal descriptions of fluid flows from snapshot measurements. Often times, DMD descriptions can be used for predictive purposes as well, which enables informed decision-making based on DMD model forecasts. Despite its widespread use and utility, DMD can fail to yield accurate dynamical descriptions when the measured snapshot data are imprecise due to, e.g., sensor noise. Here, we express DMD as a two-stage algorithm in order to isolate a source of systematic error. We show that DMD’s first stage, a subspace projection step, systematically introduces bias errors by processing snapshots asymmetrically. To remove this systematic error, we propose utilizing an augmented snapshot matrix in a subspace projection step, as in problems of total least-squares, in order to account for the error present in all snapshots. The resulting unbiased and noise-aware total DMD (TDMD) formulation reduces to standard DMD in the absence of snapshot errors, while the two-stage perspective generalizes the de-biasing framework to other related methods as well. TDMD’s performance is demonstrated in numerical and experimental fluids examples. In particular, in the analysis of time-resolved particle image velocimetry data for a separated flow, TDMD outperforms standard DMD by providing dynamical interpretations that are consistent with alternative analysis techniques. Further, TDMD extracts modes that reveal detailed spatial structures missed by standard DMD.
AbstractList	The dynamic mode decomposition (DMD)--a popular method for performing data-driven Koopman spectral analysis--has gained increased popularity for extracting dynamically meaningful spatiotemporal descriptions of fluid flows from snapshot measurements. Often times, DMD descriptions can be used for predictive purposes as well, which enables informed decision-making based on DMD model forecasts. Despite its widespread use and utility, DMD can fail to yield accurate dynamical descriptions when the measured snapshot data are imprecise due to, e.g., sensor noise. Here, we express DMD as a two-stage algorithm in order to isolate a source of systematic error. We show that DMD's first stage, a subspace projection step, systematically introduces bias errors by processing snapshots asymmetrically. To remove this systematic error, we propose utilizing an augmented snapshot matrix in a subspace projection step, as in problems of total least-squares, in order to account for the error present in all snapshots. The resulting unbiased and noise-aware total DMD (TDMD) formulation reduces to standard DMD in the absence of snapshot errors, while the two-stage perspective generalizes the de-biasing framework to other related methods as well. TDMD's performance is demonstrated in numerical and experimental fluids examples. In particular, in the analysis of time-resolved particle image velocimetry data for a separated flow, TDMD outperforms standard DMD by providing dynamical interpretations that are consistent with alternative analysis techniques. Further, TDMD extracts modes that reveal detailed spatial structures missed by standard DMD.
Audience	Academic
Author	Rowley, Clarence W. Cattafesta, Louis N. Hemati, Maziar S. Deem, Eric A.
Author_xml	– sequence: 1 givenname: Maziar S. surname: Hemati fullname: Hemati, Maziar S. email: mhemati@umn.edu organization: Aerospace Engineering and Mechanics, University of Minnesota – sequence: 2 givenname: Clarence W. surname: Rowley fullname: Rowley, Clarence W. organization: Mechanical and Aerospace Engineering, Princeton University – sequence: 3 givenname: Eric A. surname: Deem fullname: Deem, Eric A. organization: Florida Center for Advanced Aero-Propulsion, Florida State University – sequence: 4 givenname: Louis N. surname: Cattafesta fullname: Cattafesta, Louis N. organization: Florida Center for Advanced Aero-Propulsion, Florida State University
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Cites_doi	10.1137/0717073 10.1073/pnas.18.3.255 10.1007/s00348-011-1235-7 10.1016/0024-3795(94)00209-6 10.1073/pnas.17.5.315 10.1007/978-1-4612-5280-1 10.3934/jcd.2014.1.391 10.1109/TAC.1966.1098264 10.1029/JD093iD09p11015 10.1088/0957-0233/24/3/035302 10.1017/jfm.2013.426 10.1017/jfm.2011.516 10.1146/annurev-fluid-011212-140652 10.1007/s00332-012-9130-9 10.1007/s00348-010-0911-3 10.1063/1.4772195 10.1017/S0022112003006694 10.1016/j.csda.2007.05.015 10.1073/pnas.18.1.70 10.1016/j.sigpro.2007.04.004 10.1109/TAC.1974.1100705 10.2514/3.20031 10.1007/s00332-015-9258-5 10.1080/00401706.1979.10489751 10.1088/0957-0233/26/7/074002 10.1063/1.4901016 10.1007/s00348-012-1354-9 10.1016/0005-1098(89)90033-2 10.1017/S0022112010001217 10.1214/aos/1176345330 10.1007/s00348-012-1341-1 10.1063/1.4908073 10.1093/inthealth/ihv009 10.1063/1.4863670 10.1080/01691864.2014.981292 10.1118/1.4870976 10.1063/1.4895898 10.1017/CBO9780511919701 10.1002/nla.1680020206 10.1007/s00162-010-0203-9 10.1017/S0022112009992059 10.1016/j.acha.2010.02.003 10.1137/S1064827594263837 10.1117/12.948493 10.1137/1034115 10.1007/s11071-005-2824-x 10.3934/jcd.2015005 10.1109/CDC.2012.6426995 10.1016/j.jneumeth.2015. 10.1137/1.9781611971002 10.1007/s00348-016-2127-7
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Keywords	Koopman spectral analysis Sensor noise Data-driven dynamical systems Experimental fluid mechanics Reduced-order model Total least-squares
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PublicationYear	2017
Publisher	Springer Berlin Heidelberg Springer Springer Nature B.V
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References	von Neumann (CR53) 1932; 18 Duke, Honnery, Soria (CR12) 2012; 691 Bagheri (CR2) 2014; 26 Semeraro, Bellani, Lundell (CR47) 2012; 53 Fierro, Golub, Hansen, O’Leary (CR16) 1997; 18 CR33 Hansen (CR24) 1992; 32 Wynn, Pearson, Ganapathisubramani, Goulart (CR58) 2013; 733 Morozov (CR39) 1984 Jovanović, Schmid, Nichols (CR29) 2014; 26 Rowley, Mezić, Bagheri, Schlatter, Henningson (CR42) 2009; 641 Guéniat, Mathelin, Pastur (CR23) 2015; 27 Hasselmann (CR25) 1988; 93 Sima, Van Huffel (CR48) 2007; 52 Noack, Afanasiev, Morzynski, Tadmor, Thiele (CR40) 2003; 497 Ho, Kalman (CR27) 1966; 14 Davison (CR10) 1966; 11 CR7 Markovsky, Van Huffel (CR35) 2007; 87 Koopman, von Neumann (CR32) 1932; 18 Fierro, Bunch (CR14) 1995; 2 Golub, Van Loan (CR19) 1980; 17 Schmid (CR44) 2011; 50 Bendat, Piersol (CR3) 2011 CR46 Berger, Sastuba, Vogt, Jung, Ben Amor (CR4) 2015; 29 Duke, Soria, Honnery (CR13) 2012; 52 Wieneke (CR54) 2015; 26 Golub, Heath, Wahba (CR18) 1979; 21 Lanczos (CR34) 1988 Bourantas, Ghommem, Kagadis, Katsanos, Loukopoulos, Burganos, Nikiforidis (CR5) 2014; 41 Timmins, Wilson, Smith, Vlachos (CR49) 2012; 53 Mezić (CR38) 2013; 45 Williams, Rowley, Kevrekidis (CR56) 2015; 2 Golub, Van Loan (CR20) 1996 CR11 Martinsson, Rokhlin, Tygert (CR36) 2011; 30 Wilson, Smith (CR57) 2013; 24 CR52 Juang, Pappa (CR30) 1985; 8 Koopman (CR31) 1931; 17 Schmid (CR43) 2010; 656 Proctor, Eckhoff (CR41) 2015; 7 Box, Jenkins, Reinsel (CR6) 1994 Hemati, Williams, Rowley (CR26) 2014; 26 Gleser (CR17) 1981; 9 Tu, Rowley, Luchtenburg, Brunton, Kutz (CR50) 2014; 1 Holmes, Lumley, Berkooz, Rowley (CR28) 2012 Schmid, Li, Juniper, Pust (CR45) 2011; 25 Mezić (CR37) 2005; 41 Akaike (CR1) 1974; 19 Zoltowski (CR59) 1988; 975 CR22 Chen, Tu, Rowley (CR9) 2012; 22 CR21 Fierro, Bunch (CR15) 1996; 234 Budis̆ić, Mohr, Mezić (CR8) 2012; 22 Van Huffel, Vandewalle (CR51) 1989; 25 Williams, Kevrekidis, Rowley (CR55) 2015; 25 LJ Gleser (432_CR17) 1981; 9 BM Wilson (432_CR57) 2013; 24 PG Martinsson (432_CR36) 2011; 30 O Semeraro (432_CR47) 2012; 53 H Akaike (432_CR1) 1974; 19 BL Ho (432_CR27) 1966; 14 F Guéniat (432_CR23) 2015; 27 P Holmes (432_CR28) 2012 BO Koopman (432_CR31) 1931; 17 I Markovsky (432_CR35) 2007; 87 I Mezić (432_CR38) 2013; 45 432_CR46 D Duke (432_CR12) 2012; 691 JH Tu (432_CR50) 2014; 1 M Budis̆ić (432_CR8) 2012; 22 C Lanczos (432_CR34) 1988 S Van Huffel (432_CR51) 1989; 25 GC Bourantas (432_CR5) 2014; 41 MO Williams (432_CR56) 2015; 2 MS Hemati (432_CR26) 2014; 26 JL Proctor (432_CR41) 2015; 7 BR Noack (432_CR40) 2003; 497 K Hasselmann (432_CR25) 1988; 93 GH Golub (432_CR20) 1996 RD Fierro (432_CR14) 1995; 2 A Wynn (432_CR58) 2013; 733 432_CR11 EJ Davison (432_CR10) 1966; 11 432_CR52 MO Williams (432_CR55) 2015; 25 E Berger (432_CR4) 2015; 29 JN Juang (432_CR30) 1985; 8 P Schmid (432_CR45) 2011; 25 BO Koopman (432_CR32) 1932; 18 K Chen (432_CR9) 2012; 22 P Schmid (432_CR44) 2011; 50 CW Rowley (432_CR42) 2009; 641 432_CR7 GH Golub (432_CR18) 1979; 21 BH Timmins (432_CR49) 2012; 53 RD Fierro (432_CR15) 1996; 234 D Duke (432_CR13) 2012; 52 GH Golub (432_CR19) 1980; 17 432_CR22 432_CR21 GE Box (432_CR6) 1994 B Wieneke (432_CR54) 2015; 26 VA Morozov (432_CR39) 1984 JS Bendat (432_CR3) 2011 DM Sima (432_CR48) 2007; 52 J von Neumann (432_CR53) 1932; 18 PC Hansen (432_CR24) 1992; 32 RD Fierro (432_CR16) 1997; 18 P Schmid (432_CR43) 2010; 656 I Mezić (432_CR37) 2005; 41 S Bagheri (432_CR2) 2014; 26 432_CR33 MD Zoltowski (432_CR59) 1988; 975 MR Jovanović (432_CR29) 2014; 26
References_xml	– volume: 17 start-page: 883 issue: 6 year: 1980 end-page: 893 ident: CR19 article-title: An analysis of the total least squares problem publication-title: SIAM J. Numer. Anal. doi: 10.1137/0717073 – volume: 18 start-page: 255 issue: 3 year: 1932 end-page: 263 ident: CR32 article-title: Dynamical systems of continuous spectra publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.18.3.255 – volume: 52 start-page: 529 issue: 2 year: 2012 end-page: 542 ident: CR13 article-title: An error analysis of the dynamic mode decomposition publication-title: Exp. Fluids doi: 10.1007/s00348-011-1235-7 – ident: CR22 – volume: 234 start-page: 71 year: 1996 end-page: 96 ident: CR15 article-title: Perturbation theory and orthogonal projection methods with applications to least squares and total least squares publication-title: Linear Algebra Its Appl. doi: 10.1016/0024-3795(94)00209-6 – volume: 17 start-page: 315 issue: 5 year: 1931 end-page: 318 ident: CR31 article-title: Hamiltonian systems and transformation in Hilbert space publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.17.5.315 – year: 1984 ident: CR39 publication-title: Methods for Solving Incorrectly Posed Problems doi: 10.1007/978-1-4612-5280-1 – volume: 1 start-page: 391 issue: 2 year: 2014 end-page: 421 ident: CR50 article-title: On dynamic mode decomposition: theory and applications publication-title: J. Comput. Dyn. doi: 10.3934/jcd.2014.1.391 – volume: 11 start-page: 93 issue: 1 year: 1966 end-page: 101 ident: CR10 article-title: A method for simplifying linear dynamic systems publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.1966.1098264 – volume: 93 start-page: 11015 issue: D9 year: 1988 end-page: 11021 ident: CR25 article-title: PIPs and POPs: the reduction of complex dynamical systems using principal interaction and oscillation patterns publication-title: J. Geophys. Res. doi: 10.1029/JD093iD09p11015 – volume: 14 start-page: 545 issue: 12 year: 1966 end-page: 548 ident: CR27 article-title: Effective construction of linear, state-variable models from input/output functions publication-title: Regelungstechnik – volume: 24 start-page: 035,302 issue: 3 year: 2013 ident: CR57 article-title: Uncertainty on piv mean and fluctuating velocity due to bias and random errors publication-title: Meas. Sci. Technol. doi: 10.1088/0957-0233/24/3/035302 – volume: 733 start-page: 473 year: 2013 end-page: 503 ident: CR58 article-title: Optimal mode decomposition for unsteady flows publication-title: J. Fluid Mech. doi: 10.1017/jfm.2013.426 – volume: 691 start-page: 594 year: 2012 end-page: 604 ident: CR12 article-title: Experimental investigation of nonlinear instabilities in annular liquid sheets publication-title: J. Fluid Mech. doi: 10.1017/jfm.2011.516 – volume: 45 start-page: 357 year: 2013 end-page: 378 ident: CR38 article-title: Analysis of fluid flows via spectral properties of the Koopman operator publication-title: Ann. Rev. Fluid Mech. doi: 10.1146/annurev-fluid-011212-140652 – ident: CR21 – ident: CR46 – volume: 22 start-page: 887 issue: 6 year: 2012 end-page: 915 ident: CR9 article-title: Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analysis publication-title: J. Nonlinear Sci. doi: 10.1007/s00332-012-9130-9 – volume: 50 start-page: 1123 year: 2011 end-page: 1130 ident: CR44 article-title: Application of the dynamic mode decomposition to experimental data publication-title: Exp. Fluids doi: 10.1007/s00348-010-0911-3 – volume: 22 start-page: 047510 year: 2012 ident: CR8 article-title: Applied Koopmanism publication-title: Chaos doi: 10.1063/1.4772195 – ident: CR11 – volume: 2 start-page: 247 issue: 2 year: 2015 end-page: 265 ident: CR56 article-title: A kernel-based method for data-driven Koopman spectral analysis publication-title: J. Comput. Dyn. – volume: 497 start-page: 335 year: 2003 end-page: 363 ident: CR40 article-title: A hierarchy of low-dimensional models for the transient and post-transient cylinder wake publication-title: J. Fluid Mech. doi: 10.1017/S0022112003006694 – volume: 52 start-page: 1103 issue: 2 year: 2007 end-page: 1118 ident: CR48 article-title: Level choice in truncated total least squares publication-title: Comput. Stat. Data Anal. doi: 10.1016/j.csda.2007.05.015 – volume: 18 start-page: 70 year: 1932 end-page: 82 ident: CR53 article-title: Proof of the quasi-ergodic hypothesis publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.18.1.70 – year: 1996 ident: CR20 publication-title: Matrix Computations – volume: 87 start-page: 2283 issue: 10 year: 2007 end-page: 2302 ident: CR35 article-title: Overview of total least squares methods publication-title: Signal Process. doi: 10.1016/j.sigpro.2007.04.004 – volume: 19 start-page: 716 issue: 6 year: 1974 end-page: 723 ident: CR1 article-title: A new look at the statistical model identification publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.1974.1100705 – volume: 8 start-page: 620 issue: 5 year: 1985 end-page: 627 ident: CR30 article-title: An eigensystem realization algorithm for modal parameter-identification and model-reduction publication-title: J. Guid. Control Dyn. doi: 10.2514/3.20031 – volume: 25 start-page: 1307 issue: 6 year: 2015 end-page: 1346 ident: CR55 article-title: A data-driven approximation of the Koopman operator: extending dynamic mode decomposition publication-title: J. Nonlinear. Sci. doi: 10.1007/s00332-015-9258-5 – volume: 21 start-page: 215 year: 1979 end-page: 223 ident: CR18 article-title: Generalized cross-validation as a method for choosing a good ridge parameter publication-title: Technometrics doi: 10.1080/00401706.1979.10489751 – volume: 26 start-page: 074002 year: 2015 ident: CR54 article-title: PIV uncertainty quantification from correlation statistics publication-title: Meas. Sci. Technol. doi: 10.1088/0957-0233/26/7/074002 – volume: 26 start-page: 111701 year: 2014 ident: CR26 article-title: Dynamic mode decomposition for large and streaming datasets publication-title: Phys. Fluids doi: 10.1063/1.4901016 – year: 1988 ident: CR34 publication-title: Applied Analysis – volume: 53 start-page: 1203 year: 2012 end-page: 1220 ident: CR47 article-title: Analysis of time-resolved PIV masurements of a confined turbulent jet using POD and Koopman modes publication-title: Exp. Fluids doi: 10.1007/s00348-012-1354-9 – volume: 41 start-page: 309 issue: 1–3 year: 2005 end-page: 325 ident: CR37 article-title: Spectral properties of dynamical systems, model reduction and decompositions publication-title: Nonlinear Dyn. – volume: 25 start-page: 765 issue: 5 year: 1989 end-page: 769 ident: CR51 article-title: On the accuracy of total least squares and least squares techniques in the presence of errors on all data publication-title: Automatica doi: 10.1016/0005-1098(89)90033-2 – volume: 656 start-page: 5 year: 2010 end-page: 28 ident: CR43 article-title: Dynamic mode decomposition of numerical and experimental data publication-title: J. Fluid Mech. doi: 10.1017/S0022112010001217 – volume: 9 start-page: 24 issue: 1 year: 1981 end-page: 44 ident: CR17 article-title: Estimation in a multivariate “error-in-variables” regression model: large sample results publication-title: Ann. Stat. doi: 10.1214/aos/1176345330 – ident: CR33 – volume: 53 start-page: 1133 issue: 4 year: 2012 end-page: 1147 ident: CR49 article-title: A method for automatic estimation of instantaneous local uncertainty in particle image velocimetry measurements publication-title: Exp. Fluids doi: 10.1007/s00348-012-1341-1 – volume: 27 start-page: 025113 year: 2015 ident: CR23 article-title: A dynamic mode decomposition approach for large and arbitrarily sampled systems publication-title: Phys. Fluids doi: 10.1063/1.4908073 – volume: 7 start-page: 139 issue: 2 year: 2015 end-page: 145 ident: CR41 article-title: Discovering dynamic patterns from infectious disease data using dynamic mode decomposition publication-title: Int. Health doi: 10.1093/inthealth/ihv009 – volume: 26 start-page: 024103 year: 2014 ident: CR29 article-title: Sparsity promoting dynamic mode decomposition publication-title: Phys. Fluids doi: 10.1063/1.4863670 – volume: 29 start-page: 331 issue: 5 year: 2015 end-page: 343 ident: CR4 article-title: Estimation of perturbations in robotic behavior using dynamic mode decomposition publication-title: Adv. Robot. doi: 10.1080/01691864.2014.981292 – volume: 41 start-page: 053301 year: 2014 ident: CR5 article-title: Real-time tumor ablation simulation based on dynamic mode decomposition method publication-title: Med. Phys. doi: 10.1118/1.4870976 – volume: 26 start-page: 094104 year: 2014 ident: CR2 article-title: Effects of weak noise on oscillating flows: linking quality factor, floquet modes, and Koopman spectrum publication-title: Phys. Fluids doi: 10.1063/1.4895898 – year: 2012 ident: CR28 publication-title: Turbulence, Coherent Structures, Dynamical Systems and Symmetry doi: 10.1017/CBO9780511919701 – volume: 2 start-page: 135 issue: 2 year: 1995 end-page: 153 ident: CR14 article-title: Orthogonal projection and total least squares publication-title: Numer. Linear Algebra Appl. doi: 10.1002/nla.1680020206 – year: 2011 ident: CR3 publication-title: Random Data: Analysis and Measurement Procedures – volume: 25 start-page: 249 year: 2011 end-page: 259 ident: CR45 article-title: Applications of the dynamic mode decomposition publication-title: Theor. Comput. Fluid Dyn. doi: 10.1007/s00162-010-0203-9 – volume: 641 start-page: 115 year: 2009 end-page: 127 ident: CR42 article-title: Spectral analysis of nonlinear flows publication-title: J. Fluid Mech. doi: 10.1017/S0022112009992059 – ident: CR52 – volume: 30 start-page: 47 issue: 1 year: 2011 end-page: 68 ident: CR36 article-title: A randomized algorithm for the decomposition of matrices publication-title: Appl. Comput. Harmonic Anal. doi: 10.1016/j.acha.2010.02.003 – volume: 18 start-page: 1223 issue: 4 year: 1997 end-page: 1241 ident: CR16 article-title: Regularization by truncated total least squares publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827594263837 – volume: 975 start-page: 78 year: 1988 end-page: 85 ident: CR59 article-title: Generalized minimum norm and constrained total least squares with applications to array signal processing publication-title: Proc. SPIE doi: 10.1117/12.948493 – ident: CR7 – year: 1994 ident: CR6 publication-title: Time Series Analysis – volume: 32 start-page: 561 year: 1992 end-page: 580 ident: CR24 article-title: Analysis of discrete ill-posed problems by means of the L-curve publication-title: SIAM Rev. doi: 10.1137/1034115 – volume: 41 start-page: 309 issue: 1–3 year: 2005 ident: 432_CR37 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-005-2824-x – volume: 27 start-page: 025113 year: 2015 ident: 432_CR23 publication-title: Phys. Fluids doi: 10.1063/1.4908073 – volume: 25 start-page: 249 year: 2011 ident: 432_CR45 publication-title: Theor. Comput. Fluid Dyn. doi: 10.1007/s00162-010-0203-9 – volume: 26 start-page: 094104 year: 2014 ident: 432_CR2 publication-title: Phys. Fluids doi: 10.1063/1.4895898 – volume: 24 start-page: 035,302 issue: 3 year: 2013 ident: 432_CR57 publication-title: Meas. Sci. Technol. doi: 10.1088/0957-0233/24/3/035302 – volume: 2 start-page: 247 issue: 2 year: 2015 ident: 432_CR56 publication-title: J. Comput. Dyn. doi: 10.3934/jcd.2015005 – volume: 234 start-page: 71 year: 1996 ident: 432_CR15 publication-title: Linear Algebra Its Appl. doi: 10.1016/0024-3795(94)00209-6 – volume-title: Time Series Analysis year: 1994 ident: 432_CR6 – volume: 18 start-page: 255 issue: 3 year: 1932 ident: 432_CR32 publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.18.3.255 – ident: 432_CR21 doi: 10.1109/CDC.2012.6426995 – volume: 8 start-page: 620 issue: 5 year: 1985 ident: 432_CR30 publication-title: J. Guid. Control Dyn. doi: 10.2514/3.20031 – volume: 52 start-page: 1103 issue: 2 year: 2007 ident: 432_CR48 publication-title: Comput. Stat. Data Anal. doi: 10.1016/j.csda.2007.05.015 – volume: 26 start-page: 024103 year: 2014 ident: 432_CR29 publication-title: Phys. Fluids doi: 10.1063/1.4863670 – volume: 93 start-page: 11015 issue: D9 year: 1988 ident: 432_CR25 publication-title: J. Geophys. Res. doi: 10.1029/JD093iD09p11015 – volume: 21 start-page: 215 year: 1979 ident: 432_CR18 publication-title: Technometrics doi: 10.1080/00401706.1979.10489751 – volume: 7 start-page: 139 issue: 2 year: 2015 ident: 432_CR41 publication-title: Int. Health doi: 10.1093/inthealth/ihv009 – volume: 22 start-page: 887 issue: 6 year: 2012 ident: 432_CR9 publication-title: J. Nonlinear Sci. doi: 10.1007/s00332-012-9130-9 – volume-title: Turbulence, Coherent Structures, Dynamical Systems and Symmetry year: 2012 ident: 432_CR28 doi: 10.1017/CBO9780511919701 – volume: 17 start-page: 883 issue: 6 year: 1980 ident: 432_CR19 publication-title: SIAM J. Numer. Anal. doi: 10.1137/0717073 – volume: 25 start-page: 765 issue: 5 year: 1989 ident: 432_CR51 publication-title: Automatica doi: 10.1016/0005-1098(89)90033-2 – volume: 26 start-page: 111701 year: 2014 ident: 432_CR26 publication-title: Phys. Fluids doi: 10.1063/1.4901016 – volume: 25 start-page: 1307 issue: 6 year: 2015 ident: 432_CR55 publication-title: J. Nonlinear. Sci. doi: 10.1007/s00332-015-9258-5 – volume: 19 start-page: 716 issue: 6 year: 1974 ident: 432_CR1 publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.1974.1100705 – volume: 41 start-page: 053301 year: 2014 ident: 432_CR5 publication-title: Med. Phys. doi: 10.1118/1.4870976 – volume: 2 start-page: 135 issue: 2 year: 1995 ident: 432_CR14 publication-title: Numer. Linear Algebra Appl. doi: 10.1002/nla.1680020206 – volume: 733 start-page: 473 year: 2013 ident: 432_CR58 publication-title: J. Fluid Mech. doi: 10.1017/jfm.2013.426 – volume: 641 start-page: 115 year: 2009 ident: 432_CR42 publication-title: J. Fluid Mech. doi: 10.1017/S0022112009992059 – volume-title: Methods for Solving Incorrectly Posed Problems year: 1984 ident: 432_CR39 doi: 10.1007/978-1-4612-5280-1 – volume: 53 start-page: 1203 year: 2012 ident: 432_CR47 publication-title: Exp. Fluids doi: 10.1007/s00348-012-1354-9 – volume: 29 start-page: 331 issue: 5 year: 2015 ident: 432_CR4 publication-title: Adv. Robot. doi: 10.1080/01691864.2014.981292 – volume: 18 start-page: 70 year: 1932 ident: 432_CR53 publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.18.1.70 – ident: 432_CR7 doi: 10.1016/j.jneumeth.2015. – volume: 32 start-page: 561 year: 1992 ident: 432_CR24 publication-title: SIAM Rev. doi: 10.1137/1034115 – ident: 432_CR46 – volume: 497 start-page: 335 year: 2003 ident: 432_CR40 publication-title: J. Fluid Mech. doi: 10.1017/S0022112003006694 – volume: 9 start-page: 24 issue: 1 year: 1981 ident: 432_CR17 publication-title: Ann. Stat. doi: 10.1214/aos/1176345330 – volume: 691 start-page: 594 year: 2012 ident: 432_CR12 publication-title: J. Fluid Mech. doi: 10.1017/jfm.2011.516 – volume: 14 start-page: 545 issue: 12 year: 1966 ident: 432_CR27 publication-title: Regelungstechnik – volume: 18 start-page: 1223 issue: 4 year: 1997 ident: 432_CR16 publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827594263837 – volume-title: Matrix Computations year: 1996 ident: 432_CR20 – volume: 22 start-page: 047510 year: 2012 ident: 432_CR8 publication-title: Chaos doi: 10.1063/1.4772195 – volume: 1 start-page: 391 issue: 2 year: 2014 ident: 432_CR50 publication-title: J. Comput. Dyn. doi: 10.3934/jcd.2014.1.391 – volume: 53 start-page: 1133 issue: 4 year: 2012 ident: 432_CR49 publication-title: Exp. Fluids doi: 10.1007/s00348-012-1341-1 – volume: 17 start-page: 315 issue: 5 year: 1931 ident: 432_CR31 publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.17.5.315 – volume: 11 start-page: 93 issue: 1 year: 1966 ident: 432_CR10 publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.1966.1098264 – volume: 656 start-page: 5 year: 2010 ident: 432_CR43 publication-title: J. Fluid Mech. doi: 10.1017/S0022112010001217 – volume: 30 start-page: 47 issue: 1 year: 2011 ident: 432_CR36 publication-title: Appl. Comput. Harmonic Anal. doi: 10.1016/j.acha.2010.02.003 – ident: 432_CR22 – volume: 26 start-page: 074002 year: 2015 ident: 432_CR54 publication-title: Meas. Sci. Technol. doi: 10.1088/0957-0233/26/7/074002 – volume-title: Applied Analysis year: 1988 ident: 432_CR34 – volume: 87 start-page: 2283 issue: 10 year: 2007 ident: 432_CR35 publication-title: Signal Process. doi: 10.1016/j.sigpro.2007.04.004 – volume: 45 start-page: 357 year: 2013 ident: 432_CR38 publication-title: Ann. Rev. Fluid Mech. doi: 10.1146/annurev-fluid-011212-140652 – volume-title: Random Data: Analysis and Measurement Procedures year: 2011 ident: 432_CR3 – ident: 432_CR33 – ident: 432_CR52 doi: 10.1137/1.9781611971002 – volume: 975 start-page: 78 year: 1988 ident: 432_CR59 publication-title: Proc. SPIE doi: 10.1117/12.948493 – volume: 50 start-page: 1123 year: 2011 ident: 432_CR44 publication-title: Exp. Fluids doi: 10.1007/s00348-010-0911-3 – ident: 432_CR11 doi: 10.1007/s00348-016-2127-7 – volume: 52 start-page: 529 issue: 2 year: 2012 ident: 432_CR13 publication-title: Exp. Fluids doi: 10.1007/s00348-011-1235-7
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Snippet	The dynamic mode decomposition (DMD)—a popular method for performing data-driven Koopman spectral analysis—has gained increased popularity for extracting... The dynamic mode decomposition (DMD)-a popular method for performing data-driven Koopman spectral analysis-has gained increased popularity for extracting... The dynamic mode decomposition (DMD)--a popular method for performing data-driven Koopman spectral analysis--has gained increased popularity for extracting...
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SubjectTerms	Analysis Asymmetry Classical and Continuum Physics Computational fluid dynamics Computational Science and Engineering Decomposition Engineering Engineering Fluid Dynamics Errors Flow (Dynamics) Flow separation Fluid dynamics Fluid flow Fluids Forecasting Frameworks Least squares method Mathematical models Modes Noise Original Article Particle image velocimetry Sensors Spectral analysis Spectral analysis (Signal analysis) Structures Velocity measurement Yields
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Title	De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets
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