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A central challenge in data-driven model discovery is the presence of hidden, or latent, variables that are not directly measured but are dynamically important.
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J Nathan Kutz, Steven L Brunton, Bingni W Brunton, and Joshua L Proctor · 2016
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Extracting spatial–temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition
Bingni W Brunton, Lise A Johnson, Jeffrey G Ojemann, and J Nathan Kutz · 2016
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Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
Julia Ling, Andrew Kurzawski, and Jeremy Templeton · 2016
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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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Chaos as an intermittently forced linear system
Steven L Brunton, Bingni W Brunton, Joshua L Proctor, Eurika Kaiser, and J Nathan Kutz · 2017
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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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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Naoya Takeishi, Yoshinobu Kawahara, and Takehisa Yairi · 2017
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Learning deep neural network representations for koopman operators of nonlinear dynamical systems
Enoch Yeung, Soumya Kundu, and Nathan Hodas · 2017
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Reconstruction of normal forms by learning informed observation geometries from data
Or Yair, Ronen Talmon, Ronald R Coifman, and Ioannis G Kevrekidis · 2017
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Learning partial differential equations via data discovery and sparse optimization
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Sparse reduced-order modeling: sensor-based dynamics to full-state estimation
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Data-driven discovery of closure models
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Steven Atkinson · 2020
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On the structure of time-delay embedding in linear models of non-linear dynamical systems
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Delay-coordinate maps, coherence, and approximate spectra of evolution operators
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Time-delay observables for Koopman: Theory and applications
M. Kamb, E. Kaiser, S. L. Brunton, and J. N. Kutz · 2020
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Deep learning to discover and predict dynamics on an inertial manifold
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Deep learning of dynamical attractors from time series measurements
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Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
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Deep learning markov and koopman models with physical constraints
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Machine learning for fluid mechanics
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Formulating turbulence closures using sparse regression with embedded form invariance
S Beetham and J Capecelatro · 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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Discovery of algebraic reynolds-stress models using sparse symbolic regression
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Capturing turbulent dynamics and statistics in experiments with unstable periodic orbits
Balachandra Suri, Logan Kageorge, Roman O Grigoriev, and Michael F Schatz · 2020
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Chaotic waterwheel, 2020
Harvard Natural Sciences Lecture Demonstrations · 2020
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Pysindy: a python package for the sparse identification of nonlinear dynamics from data
Brian M de Silva, Kathleen Champion, Markus Quade, Jean-Christophe Loiseau, J Nathan Kutz, and Steven L Brunton · 2020
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Model selection of chaotic systems from data with hidden variables using sparse data assimilation
H Ribera, S Shirman, AV Nguyen, and NM Mangan · 2021
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Structured time-delay models for dynamical systems with connections to frenet-serret frame
Seth M Hirsh, Sara M Ichinaga, Steven L Brunton, J Nathan Kutz, and Bingni W Brunton · 2021
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Manu Kalia, Steven L Brunton, Hil GE Meijer, Christoph Brune, and J Nathan Kutz · 2021
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Sparse identification of multiphase turbulence closures for coupled fluid–particle flows
Sarah Beetham, Rodney O Fox, and Jesse Capecelatro · 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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Data-driven discovery of coarse-grained equations
Joseph Bakarji and Daniel M Tartakovsky · 2021
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Pysindy: A comprehensive python package for robust sparse system identification
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Urban Fasel, J Nathan Kutz, Bingni W Brunton, and Steven L Brunton · 2021
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