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We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs).
Turbulence and the dynamics of coherent structures, parts I-III
L. Sirovich · 1987
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Reconstructing phase space from PDE simulations
Michael Kirby and Dieter Armbruster · 1992
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The proper orthogonal decomposition in the analysis of turbulent flows
Gal Berkooz, Philip Holmes, and John L Lumley · 1993
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Regression shrinkage and selection via the lasso
Robert Tibshirani · 1996
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Reconstruction equations and the Karhunen–Loève expansion for systems with symmetry
Clarence W Rowley and Jerrold E Marsden · 2000
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Reduced order modeling for a one-dimensional nozzle flow with moving shocks
David Lucia, Paul King, Mark Oxley, and Philip Beran · 2001
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Neural network modeling for near wall turbulent flow
Michele Milano and Petros Koumoutsakos · 2002
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On spectral clustering: Analysis and an algorithm
Andrew Y Ng, Michael I Jordan, and Yair Weiss · 2002
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A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
B. R. Noack, K. Afanasiev, M. Morzynski, G. Tadmor, and F. Thiele · 2003
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Model reduction for compressible flows using POD and Galerkin projection
Clarence W Rowley, Tim Colonius, and Richard M Murray · 2004
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Approximation of large-scale dynamical systems
Athanasios C Antoulas · 2005
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Fourth-order time-stepping for stiff PDEs
Aly-Khan Kassam and Lloyd N Trefethen · 2005
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Continuous mode interpolation for control-oriented models of fluid flow
Marek Morzyński, Witold Stankiewicz, Bernd R Noack, Rudibert King, Frank Thiele, and Gilead Tadmor · 2007
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Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow
Chris C. T. Pringle and Rich R. Kerswell · 2007
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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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Input-output analysis and control design applied to a linear model of spatially developing flows
Shervin Bagheri, DS Henningson, J Hoepffner, and PJ Schmid · 2009
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Dynamic mode decomposition of numerical and experimental data
P. J. Schmid · 2010
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Reduced-order modelling for flow control
Bernd R Noack, Marek Morzynski, and Gilead Tadmor · 2011
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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
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Reduced-order models for closed-loop wake control
Gilead Tadmor, Oliver Lehmann, Bernd R Noack, Laurent Cordier, Joël Delville, Jean-Paul Bonnet, and Marek Morzyński · 2011
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Nonlinear dispersive waves: asymptotic analysis and solitons
Mark J Ablowitz · 2011
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Robust principal component analysis?
E. J. Candès, X. Li, Y. Ma, and J. Wright · 2011
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Turbulence, coherent structures, dynamical systems and symmetry
P. J. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley · 2012
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Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data
Data Mining: Practical machine learning tools and techniques
Ian H Witten, Eibe Frank, Mark A Hall, and Christopher J Pal · 2016
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Modal analysis of fluid flows: An overview
Kunihiko Taira, Steven L Brunton, Scott Dawson, Clarence W Rowley, Tim Colonius, Beverley J McKeon, Oliver T Schmidt, Stanislav Gordeyev, Vassilios Theofilis, and Lawrence S Ukeiley · 2017
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A neural network approach for the blind deconvolution of turbulent flows
Romit Maulik and Omer San · 2017
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Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction
Kevin Carlberg, Matthew Barone, and Harbir Antil · 2017
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Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows
Rambod Mojgani and Maciej Balajewicz · 2017
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J. N. Kutz · 2013
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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
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On dynamic mode decomposition: theory and applications
J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz · 2014
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Advection modes by optimal mass transfer
Angelo Iollo and Damiano Lombardi · 2014
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Approximated Lax pairs for the reduced order integration of nonlinear evolution equations
Jean-Frédéric Gerbeau and Damiano Lombardi · 2014
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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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Reduced basis methods for partial differential equations: an introduction
Alfio Quarteroni, Andrea Manzoni, and Federico Negri · 2015
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Rapid contour detection for image classification
Christoph Rasche · 2017
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Sparse reduced-order modeling: sensor-based dynamics to full-state estimation
J.-C. Loiseau, B. R. Noack, and S. L. Brunton · 2018
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Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
Aaron Towne, Oliver T Schmidt, and Tim Colonius · 2018
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The shifted proper orthogonal decomposition: A mode decomposition for multiple transport phenomena
Julius Reiss, Philipp Schulze, Jörn Sesterhenn, and Volker Mehrmann · 2018
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Transport reversal for model reduction of hyperbolic partial differential equations
Donsub Rim, Scott Moe, and Randall J LeVeque · 2018
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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 · 2018
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Turbulence modeling in the age of data
Karthik Duraisamy, Gianluca Iaccarino, and Heng Xiao · 2019
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Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control
S. L. Brunton and J. N. Kutz · 2019
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Modal analysis of fluid flows: Applications and outlook
Kunihiko Taira, Maziar S Hemati, Steven L Brunton, Yiyang Sun, Karthik Duraisamy, Shervin Bagheri, Scott Dawson, and Chi-An Yeh · 2019
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Perspective on machine learning for advancing fluid mechanics
MP Brenner, JD Eldredge, and JB Freund · 2019
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Model order reduction for problems with large convection effects
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