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The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data.
Smoothing and differentiation of data by simplified least squares procedures
Abraham Savitzky and Marcel JE Golay · 1964
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Regression shrinkage and selection via the lasso
Robert Tibshirani · 1996
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Random forests
Leo Breiman · 2001
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Algorithmic learning in a random world
Vladimir Vovk, Alexander Gammerman, and Glenn Shafer · 2005
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Conditional variable importance for random forests
Carolin Strobl, Anne-Laure Boulesteix, Thomas Kneib, Thomas Augustin, and Achim Zeileis · 2008
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Time series analysis by state space methods
James Durbin and Siem Jan Koopman · 2012
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Valid post-selection inference
Richard Berk, Lawrence Brown, Andreas Buja, Kai Zhang, and Linda Zhao · 2013
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Confidence intervals for low dimensional parameters in high dimensional linear models
Cun-Hui Zhang and Stephanie S Zhang · 2014
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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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Data assimilation: methods, algorithms, and applications
Mark Asch, Marc Bocquet, and Maëlle Nodet · 2016
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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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Robust data-driven discovery of governing physical laws with error bars
Sheng Zhang and Guang Lin · 2018
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Distribution-free predictive inference for regression
Jing Lei, Max G’Sell, Alessandro Rinaldo, Ryan J Tibshirani, and Larry Wasserman · 2018
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Constrained sparse galerkin regression
Jean-Christophe Loiseau and Steven L Brunton · 2018
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Double/debiased machine learning for treatment and structural parameters, 2018
Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whitney Newey, and James Robins · 2018
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Smoothing and parameter estimation by soft-adherence to governing equations
Samuel H Rudy, Steven L Brunton, and J Nathan Kutz · 2019
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Algorithmic discovery of dynamic models from infectious disease data
Jonathan Horrocks and Chris T Bauch · 2020
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Bayesian differential programming for robust systems identification under uncertainty
Yibo Yang, Mohamed Aziz Bhouri, and Paris Perdikaris · 2020
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Bayesian system ID: optimal management of parameter, model, and measurement uncertainty
Nicholas Galioto and Alex Arkady Gorodetsky · 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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Predictive inference is free with the jackknife+-after-bootstrap
Byol Kim, Chen Xu, and Rina Barber · 2020
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Sparse identification of nonlinear dynamics with low-dimensionalized flow representations
Kai Fukami, Takaaki Murata, Kai Zhang, and Koji Fukagata · 2021
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Conformal prediction interval for dynamic time-series
Chen Xu and Yao Xie · 2021
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Weak sindy: Galerkin-based data-driven model selection
Daniel A Messenger and David M Bortz · 2021
Inference for sparse linear regression based on the leave-one-covariate-out solution path
Xiangyang Cao, Karl Gregory, and Dewei Wang · 2023
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Conformal prediction for time series with modern hopfield networks
Andreas Auer, Martin Gauch, Daniel Klotz, and Sepp Hochreiter · 2023
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Direct estimation of parameters in ode models using wendy: Weak-form estimation of nonlinear dynamics
David M Bortz, Daniel A Messenger, and Vanja Dukic · 2023
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Benchmarking sparse system identification with low-dimensional chaos
Alan A Kaptanoglu, Lanyue Zhang, Zachary G Nicolaou, Urban Fasel, and Steven L Brunton · 2023
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Improved online conformal prediction via strongly adaptive online learning
Aadyot Bhatnagar, Huan Wang, Caiming Xiong, and Yu Bai · 2023
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Predictive inference with the jackknife+
Rina Foygel Barber, Emmanuel J Candes, Aaditya Ramdas, and Ryan J Tibshirani · 2021
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Adaptive conformal inference under distribution shift
Isaac Gibbs and Emmanuel Candes · 2021
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Chaos as an interpretable benchmark for forecasting and data-driven modelling
William Gilpin · 2021
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Sparsifying priors for bayesian uncertainty quantification in model discovery
Seth M Hirsh, David A Barajas-Solano, and J Nathan Kutz · 2022
Cited alongside, same era.
A bayesian approach for data-driven dynamic equation discovery
Joshua S North, Christopher K Wikle, and Erin M Schliep · 2022
Cited alongside, same era.
Ensemble-sindy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control
Urban Fasel, J. Nathan Kutz, Bingni W. Brunton, and Steven L. Brunton · 2022
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Dynamical system identification, model selection, and model uncertainty quantification by bayesian inference
Robert K Niven, Laurent Cordier, Ali Mohammad-Djafari, Markus Abel, and Markus Quade · 2024
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Statistical mechanics of dynamical system identification
Andrei A Klishin, Joseph Bakarji, J Nathan Kutz, and Krithika Manohar · 2024
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Ekf–sindy: Empowering the extended kalman filter with sparse identification of nonlinear dynamics
Luca Rosafalco, Paolo Conti, Andrea Manzoni, Stefano Mariani, and Attilio Frangi · 2024
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Veni, vindy, vici: a variational reduced-order modeling framework with uncertainty quantification
Paolo Conti, Jonas Kneifl, Andrea Manzoni, Attilio Frangi, Jörg Fehr, Steven L Brunton, and J Nathan Kutz · 2024
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Theoretical foundations of conformal prediction
Anastasios N Angelopoulos, Rina Foygel Barber, and Stephen Bates · 2024
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Conformalized time series with semantic features
Baiting Chen, Zhimei Ren, and Lu Cheng · 2024
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Conformal prediction after efficiency-oriented model selection
Ruiting Liang, Wanrong Zhu, and Rina Foygel Barber · 2024
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Conformal inference for online prediction with arbitrary distribution shifts
Isaac Gibbs and Emmanuel J Candès · 2024
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Hypergraph reconstruction from dynamics
Robin Delabays, Giulia De Pasquale, Florian Dörfler, and Yuanzhao Zhang · 2025
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Safe physics-informed machine learning for dynamics and control
Jan Drgona, Truong X Nghiem, Thomas Beckers, Mahyar Fazlyab, Enrique Mallada, Colin Jones, Draguna Vrabie, Steven L Brunton, and Rolf Findeisen · 2025
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Rapid bayesian identification of sparse nonlinear dynamics from scarce and noisy data
Lloyd Fung, Urban Fasel, and Matthew Juniper · 2025
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Online learning in bifurcating dynamic systems via sindy and kalman filtering
Luca Rosafalco, Paolo Conti, Andrea Manzoni, Stefano Mariani, and Attilio Frangi · 2025
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Multi-objective sindy for parameterized model discovery from single transient trajectory data
Javier Lemus and Benjamin Herrmann · 2025
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