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Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of reduced-order models for a variety of scientific and engineering tasks.
Hamiltonian systems and transformation in Hilbert space
B. O. Koopman · 1931
Earlier work this paper cites.
A mathematical model illustrating the theory of turbulence
J. M. Burgers · 1948
Earlier work this paper cites.
A mathematical example displaying features of turbulence
E. Hopf · 1948
Earlier work this paper cites.
Deterministic nonperiodic flow
Edward N Lorenz · 1963
Earlier work this paper cites.
A First Course in Turbulence
H. Tennekes and J. L. Lumley · 1972
Earlier work this paper cites.
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
Philip Holmes and John Guckenheimer · 1983
Earlier work this paper cites.
On minimizing the maximum eigenvalue of a symmetric matrix
Michael L Overton · 1988
Earlier work this paper cites.
Is there a statistical mechanics of turbulence?
R. H. Kraichnan and S. Chen · 1989
Earlier work this paper cites.
Neural networks and principal component analysis: Learning from examples without local minima
Pierre Baldi and Kurt Hornik · 1989
Earlier work this paper cites.
The physics of fluid turbulence
William D McComb · 1990
Earlier work this paper cites.
Low-dimensional models for complex geometry flows: application to grooved channels and circular cylinders
AE Deane, IG Kevrekidis, G Em Karniadakis, and SA Orszag · 1991
Earlier work this paper cites.
Relaxation processes in magnetohydrodynamics-a triad-interaction model
V Carbone and P Veltri · 1992
Earlier work this paper cites.
A Gauss—Newton method for convex composite optimization
James V Burke and Michael C Ferris · 1995
Earlier work this paper cites.
Direct Galerkin approximation of plane-parallel-Couette and channel flows by Stokes eigenfunctions
Bernd Rummler and Andreas Noske · 1998
Earlier work this paper cites.
Remarkable statistical behavior for truncated Burgers–Hopf dynamics
Andrew J Majda and Ilya Timofeyev · 2000
Earlier work this paper cites.
Balanced model reduction via the proper orthogonal decomposition
Karen Willcox and Jaime Peraire · 2002
Earlier work this paper cites.
Neural network modeling for near wall turbulent flow
Michele Milano and Petros Koumoutsakos · 2002
Earlier work this paper cites.
A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
Bernd R Noack, Konstantin Afanasiev, Marek Morzyński, Gilead Tadmor, and Frank Thiele · 2003
Earlier work this paper cites.
Intermodal energy transfers in a proper orthogonal decomposition-Galerkin representation of a turbulent separated flow
M Couplet, P Sagaut, and C Basdevant · 2003
Earlier work this paper cites.
Model reduction for fluids, using balanced proper orthogonal decomposition
Clarence W Rowley · 2005
Earlier work this paper cites.
Chaos in a coupled oscillators system with widely spaced frequencies and energy-preserving non-linearity
JM Tuwankotta · 2006
Earlier work this paper cites.
Steady solutions of the Navier-Stokes equations by selective frequency damping
Espen Åkervik, Luca Brandt, Dan S Henningson, Jérôme Hœpffner, Olaf Marxen, and Philipp Schlatter · 2006
Earlier work this paper cites.
Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows
D. Sipp and A. Lebedev · 2007
Earlier work this paper cites.
A finite-time thermodynamics of unsteady fluid flows
Bernd R Noack, Michael Schlegel, Boye Ahlborn, Gerd Mutschke, Marek Morzyński, Pierre Comte, and Gilead Tadmor · 2008
Earlier work this paper cites.
Nek5000 web pages
P. F. Fischer, J. W. Lottes, and S. G. Kerkemeir · 2008
Earlier work this paper cites.
Spectral analysis of nonlinear flows
C. W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D.S. Henningson · 2009
Earlier work this paper cites.
A fast iterative shrinkage-thresholding algorithm for linear inverse problems
Amir Beck and Marc Teboulle · 2009
Earlier work this paper cites.
Dynamic mode decomposition of numerical and experimental data
Peter J. Schmid · 2010
Earlier work this paper cites.
A critical-layer framework for turbulent pipe flow
Beverley J McKeon and Ati S Sharma · 2010
Earlier work this paper cites.
Reduced-order modelling for flow control
Bernd R Noack, Marek Morzynski, and Gilead Tadmor · 2011
Earlier work this paper cites.
Efficient non-linear model reduction via a least-squares Petrov–Galerkin projection and compressive tensor approximations
Kevin Carlberg, Charbel Bou-Mosleh, and Charbel Farhat · 2011
Earlier work this paper cites.
Local POD plus Galerkin projection in the unsteady lid-driven cavity problem
Filippo Terragni, Eusebio Valero, and José M Vega · 2011
Earlier work this paper cites.
Turbulence, coherent structures, dynamical systems and symmetry
Philip Holmes, John L Lumley, Gahl Berkooz, and Clarence W Rowley · 2012
Earlier work this paper cites.
Physics constrained nonlinear regression models for time series
Andrew J Majda and John Harlim · 2012
Earlier work this paper cites.
Stabilization of projection-based reduced order models of the Navier–Stokes
Maciej Balajewicz and Earl H Dowell · 2012
Earlier work this paper cites.
N-widths in Approximation Theory
Allan Pinkus · 2012
Earlier work this paper cites.
The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
Kevin Carlberg, Charbel Farhat, Julien Cortial, and David Amsallem · 2013
Earlier work this paper cites.
Analysis of fluid flows via spectral properties of the Koopman operator
Igor Mezic · 2013
Earlier work this paper cites.
Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier-Stokes equation
Maciej J Balajewicz, Earl H Dowell, and Bernd R Noack · 2013
Earlier work this paper cites.
Lyapunov stable Galerkin models of post-transient incompressible flows
Maciej Balajewicz · 2013
Earlier work this paper cites.
Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods
Hedy Attouch, Jérôme Bolte, and Benar Fux Svaiter · 2013
Earlier work this paper cites.
Gradient methods for minimizing composite functions
Yu Nesterov · 2013
Earlier work this paper cites.
Neural learning of stable dynamical systems based on data-driven Lyapunov candidates
Klaus Neumann, Andre Lemme, and Jochen J Steil · 2013
Earlier work this paper cites.
Cluster-based reduced-order modelling of a mixing layer
E. Kaiser, B. R. Noack, L. Cordier, A. Spohn, M. Segond, M. Abel, G. Daviller, J. Osth, S. Krajnovic, and R. K. Niven · 2014
Earlier work this paper cites.
Ideal MHD
Jeffrey P Freidberg · 2014
Earlier work this paper cites.
Opposition control within the resolvent analysis framework
Mitul Luhar, Ati S Sharma, and Beverley J McKeon · 2014
Earlier work this paper cites.
Learning control Lyapunov function to ensure stability of dynamical system-based robot reaching motions
S Mohammad Khansari-Zadeh and Aude Billard · 2014
Earlier work this paper cites.
On long-term boundedness of Galerkin models
Michael Schlegel and Bernd R Noack · 2015
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A survey of projection-based model reduction methods for parametric dynamical systems
Peter Benner, Serkan Gugercin, and Karen Willcox · 2015
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Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations
Francesco Ballarin, Andrea Manzoni, Alfio Quarteroni, and Gianluigi Rozza · 2015
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Preserving Lagrangian structure in nonlinear model reduction with application to structural dynamics
Kevin Carlberg, Ray Tuminaro, and Paul Boggs · 2015
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
S. L. Brunton, J. L. Proctor, and J. N. Kutz · 2016
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A unified framework for sparse relaxed regularized regression: SR3
Peng Zheng, Travis Askham, Steven L Brunton, J Nathan Kutz, and Aleksandr Y Aravkin · 2019
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Efficiency of minimizing compositions of convex functions and smooth maps
Dmitriy Drusvyatskiy and Courtney Paquette · 2019
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From the POD-Galerkin method to sparse manifold models
Jean-Christophe Loiseau, Steven L Brunton, and Bernd R Noack · 2019
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Learning deep neural network representations for Koopman operators of nonlinear dynamical systems
Enoch Yeung, Soumya Kundu, and Nathan Hodas · 2019
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Linearly recurrent autoencoder networks for learning dynamics
Samuel E Otto and Clarence W Rowley · 2019
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Modal analysis of fluid flows: Applications and outlook
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Symplectic model reduction of Hamiltonian systems
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Sum-of-squares approach to feedback control of laminar wake flows
Davide Lasagna, Deqing Huang, Owen R Tutty, and Sergei Chernyshenko · 2016
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Boundary-layer theory
Hermann Schlichting and Klaus Gersten · 2016
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Introduction to modern magnetohydrodynamics
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Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems
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