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One way to understand time-series data is to identify the underlying dynamical system which generates it.
Regression shrinkage and selection via the lasso
Robert Tibshirani · 1996
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Iterative hard thresholding and ℓ 0 \ell^{0} regularisation
Thomas Blumensath, Mehrdad Yaghoobi, and Mike E. Davies · 2007
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Automated reverse engineering of nonlinear dynamical systems
Josh Bongard and Hod Lipson · 2007
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Iterative thresholding for sparse approximations
Thomas Blumensath and Mike E. Davies · 2008
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Iterative hard thresholding for compressed sensing
Thomas Blumensath and Mike E. Davies · 2009
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Distilling free-form natural laws from experimental data
Michael Schmidt and Hod Lipson · 2009
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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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Sparse identification of nonlinear dynamics with control (SINDYc)
Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz · 2016
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Inferring biological networks by sparse identification of nonlinear dynamics
Niall M. Mangan, Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz · 2016
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Sparse identification for nonlinear optical communication systems: SINO method
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Sparse identification of a predator-prey system from simulation data of a convection model
Magnus Dam, Morten Brøns, Jens Juul Rasmussen, Volker Naulin, and Jan S. Hesthaven · 2017
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Sparse identification of nonlinear dynamics for model predictive control in the low-data limit
Eurika Kaiser, J. Nathan Kutz, and Steven L. Brunton · 2017
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Data-driven discovery of partial differential equations
Samuel H. Rudy, Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz · 2017
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Sparse model selection via integral terms
Hayden Schaeffer and Scott G. McCalla · 2017
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Extracting sparse high-dimensional dynamics from limited data
Hayden Schaeffer, Giang Tran, and Rachel Ward · 2017
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Learning dynamical systems and bifurcation via group sparsity
Hayden Schaeffer, Giang Tran, and Rachel Ward · 2017
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Constrained sparse Galerki regression
Jean-Christophe Loiseau and Steven L. Brunton · 2018
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Sparse identification of nonlinear dynamics for rapid model recovery
Markus Quade, Markus Abel, J. Nathan Kutz, and Steven L. Brunton · 2018
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Zichao Long, Yiping Lu, Xianzhong Ma, and Bin Dong · 2017
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Model selection for dynamical systems via sparse regression and information criteria
Niall M. Mangan, J. Nathan Kutz, Steven L. Brunton, and Joshua L. Proctor · 2017
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A unified approach for sparse dynamical system inference from temporal measurements
Yannis Pantazis and Ioannis Tsamardinos · 2017
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Learning partial differential equations via data discovery and sparse optimization
Hayden Schaeffer
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Exact recovery of chaotic systems from highly corrupted data
Giang Tran and Rachel Ward
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Just relax: convex programming methods for identifying sparse signals in noise
Joel A. Tropp
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Hidden physics models: Machine learning of nonlinear partial differential equations
Maziar Raissi and George Em Karniadakis · 2018
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Extracting structured dynamical systems using sparse optimization with very few samples
Hayden Schaeffer, Giang Tran, Rachel Ward, and Linan Zhang · 2018
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