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Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community.
Numerical differentiation of experimental data: local versus global methods
Karsten Ahnert and Markus Abel · 2007
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Automated reverse engineering of nonlinear dynamical systems
J. Bongard and H. Lipson · 2007
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Distilling free-form natural laws from experimental data
Michael Schmidt and Hod Lipson · 2009
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Dynamic mode decomposition of numerical and experimental data
Peter J Schmid · 2010
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Numerical differentiation of noisy, nonsmooth data
Rick Chartrand · 2011
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The solution path of the generalized lasso
Ryan J Tibshirani and Jonathan Taylor · 2011
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Nonlinear system identification: NARMAX methods in the time, frequency, and spatio-temporal domains
Stephen A Billings · 2013
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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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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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Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems
J. N. Kutz, S. L. Brunton, B. W. Brunton, and J. L. Proctor · 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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Data-driven operator inference for nonintrusive projection-based model reduction
Benjamin Peherstorfer and Karen Willcox · 2016
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Machine learning of linear differential equations using Gaussian processes
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 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
Cited alongside, same era.
Learning partial differential equations via data discovery and sparse optimization
Hayden Schaeffer · 2017
Cited alongside, same era.
Sparse model selection via integral terms
Hayden Schaeffer and Scott G McCalla · 2017
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Sparse learning of stochastic dynamical equations
Lorenzo Boninsegna, Feliks Nüske, and Cecilia Clementi · 2018
Cited alongside, same era.
Sparse identification of nonlinear dynamics for model predictive control in the low-data limit
Eurika Kaiser, J Nathan Kutz, and Steven L Brunton · 2018
Cited alongside, same era.
Constrained sparse Galerkin regression
J.-C. Loiseau and Steven L. Brunton · 2018
Cited alongside, same era.
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics
Kadierdan Kaheman, J Nathan Kutz, and Steven L Brunton · 2020
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Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
Elizabeth Qian, Boris Kramer, Benjamin Peherstorfer, and Karen Willcox · 2020
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Using noisy or incomplete data to discover models of spatiotemporal dynamics
Patrick AK Reinbold, Daniel R Gurevich, and Roman O Grigoriev · 2020
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Modern Koopman theory for dynamical systems
Steven L Brunton, Marko Budišić, Eurika Kaiser, and J Nathan Kutz · 2021
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On the role of nonlinear correlations in reduced-order modeling
Jared L Callaham, Steven L Brunton, and Jean-Christophe Loiseau · 2021
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Model-free prediction of large spatiotemporally chaotic systems from data: a reservoir computing approach
Jaideep Pathak, Brian Hunt, Michelle Girvan, Zhixin Lu, and Edward Ott · 2018
Cited alongside, same era.
sparsereg - collection of modern sparse regression algorithms, February 2018
Markus Quade · 2018
Cited alongside, same era.
Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks
Pantelis R Vlachas, Wonmin Byeon, Zhong Y Wan, Themistoklis P Sapsis, and Petros Koumoutsakos · 2018
Cited alongside, same era.
Suryanarayana Maddu, Bevan L Cheeseman, Ivo F Sbalzarini, and Christian L Müller · 2019
Cited alongside, same era.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M Raissi, P Perdikaris, and GE Karniadakis · 2019
Cited alongside, same era.
A unified sparse optimization framework to learn parsimonious physics-informed models from data
Kathleen Champion, Peng Zheng, Aleksandr Y Aravkin, Steven L Brunton, and J Nathan Kutz · 2020
Cited alongside, same era.
A toolkit for data-driven discovery of governing equations in high-noise regimes
Charles B Delahunt and J Nathan Kutz · 2021
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SINDy with control: A tutorial
Urban Fasel, Eurika Kaiser, J Nathan Kutz, Bingni W Brunton, and Steven L Brunton · 2021
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Urban Fasel, J Nathan Kutz, Bingni W Brunton, and Steven L Brunton · 2021
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Promoting global stability in data-driven models of quadratic nonlinear dynamics
Alan A. Kaptanoglu, Jared L. Callaham, Aleksandr Aravkin, Christopher J. Hansen, and Steven L. Brunton · 2021
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Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches
Alan A. Kaptanoglu, Kyle D. Morgan, Chris J. Hansen, and Steven L. Brunton · 2021
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Weak SINDy for partial differential equations
Daniel A Messenger and David M Bortz · 2021
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Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression
Patrick AK Reinbold, Logan M Kageorge, Michael F Schatz, and Roman O Grigoriev · 2021
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