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Learning the governing equations in dynamical systems from time-varying measurements is of great interest across different scientific fields.
Deterministic nonperiodic flow
Edward N Lorenz · 1963
Earlier work this paper cites.
Chemical turbulence: chaos in a simple reaction-diffusion system
Otto E Rössler · 1976
Earlier work this paper cites.
An equation for hyperchaos
OE Rossler · 1979
Earlier work this paper cites.
Geometry from a time series
Norman H Packard, James P Crutchfield, J Doyne Farmer, and Robert S Shaw · 1980
Earlier work this paper cites.
Detecting strange attractors in turbulence
Floris Takens · 1981
Earlier work this paper cites.
Equations of motion from a data series
James P Crutchfield and Bruce S McNamara · 1987
Earlier work this paper cites.
State space reconstruction in the presence of noise
Martin Casdagli, Stephen Eubank, J Doyne Farmer, and John Gibson · 1991
Earlier work this paper cites.
Determining embedding dimension for phase-space reconstruction using a geometrical construction
Matthew B Kennel, Reggie Brown, and Henry DI Abarbanel · 1992
Earlier work this paper cites.
Extraction of dynamical equations from chaotic data
G Rowlands and JC Sprott · 1992
Earlier work this paper cites.
Some simple chaotic flows
J Clint Sprott · 1994
Earlier work this paper cites.
Nonlinear black-box modeling in system identification: a unified overview
Jonas Sjöberg, Qinghua Zhang, Lennart Ljung, Albert Benveniste, Bernard Delyon, Pierre-Yves Glorennec, Håkan Hjalmarsson, and Anatoli Juditsky · 1995
Earlier work this paper cites.
State space reconstruction parameters in the analysis of chaotic time series – the role of the time window length
Dimitris Kugiumtzis · 1996
Earlier work this paper cites.
System identification
Lennart Ljung · 1998
Earlier work this paper cites.
The Lorenz attractor exists
Warwick Tucker · 1999
Earlier work this paper cites.
Nonlinear dimensionality reduction by locally linear embedding
Sam T Roweis and Lawrence K Saul · 2000
Earlier work this paper cites.
Algebraically simple chaotic flows
Julien Clinton Sprott and Stefan J Linz · 2000
Earlier work this paper cites.
A new chaotic system and beyond: the generalized Lorenz-like system
Jinhu Lü, Guanrong Chen, and Daizhan Cheng · 2004
Earlier work this paper cites.
The fractal property of the Lorenz attractor
Divakar Viswanath · 2004
Earlier work this paper cites.
Stable signal recovery from incomplete and inaccurate measurements
Emmanuel J Candes, Justin K Romberg, and Terence Tao · 2006
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Compressed sensing
D.L. Donoho · 2006
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Recovery algorithms for vector-valued data with joint sparsity constraints
Massimo Fornasier and Holger Rauhut · 2008
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Modeling nonlinear dynamics and chaos: a review
Luis A Aguirre and Christophe Letellier · 2009
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Compressed sensing and best k k -term approximation
Albert Cohen, Wolfgang Dahmen, and Ronald DeVore · 2009
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Sparse regression using mixed norms
Matthieu Kowalski · 2009
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A mathematical introduction to compressive sensing
Simon Foucart and Holger Rauhut · 2013
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Compressed modes for variational problems in mathematics and physics
Vidvuds Ozoliņš, Rongjie Lai, Russel Caflisch, and Stanley Osher · 2013
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Numerical data fitting in dynamical systems: a practical introduction with applications and software
Klaus Schittkowski · 2013
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Sparse dynamics for partial differential equations
Hayden Schaeffer, Russel Caflisch, Cory D Hauck, and Stanley Osher · 2013
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The nature of statistical learning theory
Vladimir Vapnik · 2013
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Statistical properties of Lorenz-like flows, recent developments and perspectives
Vitor Araujo, Stefano Galatolo, and Maria José Pacifico · 2014
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Michael Schmidt and Hod Lipson · 2009
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Perspectives on system identification
Lennart Ljung · 2010
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On partial sparse recovery
Afonso S Bandeira, Katya Scheinberg, and Luis Nunes Vicente · 2011
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Extracting dynamical equations from experimental data is NP hard
Toby S Cubitt, Jens Eisert, and Michael M Wolf · 2012
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Learning functions of few arbitrary linear parameters in high dimensions
Massimo Fornasier, Karin Schnass, and Jan Vybiral · 2012
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A class of lorenz-like systems
Claudia Lainscsek · 2012
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Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems
Steven L Brunton, Jonathan H Tu, Ido Bright, and J Nathan Kutz · 2014
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On the compressive spectral method
Alan Mackey, Hayden Schaeffer, and Stanley Osher · 2014
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Compressed plane waves yield a compactly supported multiresolution basis for the Laplace operator
Vidvuds Ozoliņš, Rongjie Lai, Russel Caflisch, and Stanley Osher · 2014
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Exploiting sparsity and equation-free architectures in complex systems
JL Proctor, SL Brunton, BW Brunton, and JN Kutz · 2014
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Exponential decay of correlations for nonuniformly hyperbolic flows with a C 1 + α {C}^{1+\alpha} stable foliation, including the classical Lorenz attractor
Vitor Araújo and Ian Melbourne · 2015
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Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps
V Araujo, I Melbourne, and P Varandas · 2015
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PDEs with compressed solutions
Russel E Caflisch, Stanley J Osher, Hayden Schaeffer, and Giang Tran · 2015
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Statistical learning with sparsity: the lasso and generalizations
Trevor Hastie, Robert Tibshirani, and Martin Wainwright · 2015
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Machine learning: Trends, perspectives, and prospects
MI Jordan and TM Mitchell · 2015
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An l 1 l^{1} penalty method for general obstacle problems
Giang Tran, Hayden Schaeffer, William M Feldman, and Stanley J Osher · 2015
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Steven L Brunton, Joshua L Proctor, and J Nathan Kutz · 2016
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