Fetching the paper…
Reading the bibliography…
The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions.
On lines and planes of closest fit to systems of points in space
K. Pearson · 1901
Earlier work this paper cites.
Hamiltonian systems and transformation in Hilbert space
B. O. Koopman · 1931
Earlier work this paper cites.
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
Philip Holmes and John Guckenheimer · 1983
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.
Neural networks and principal component analysis: Learning from examples without local minima
Pierre Baldi and Kurt Hornik · 1989
Earlier work this paper cites.
Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, and Halbert White · 1989
Earlier work this paper cites.
Long short-term memory
Sepp Hochreiter and Jürgen Schmidhuber · 1997
Earlier work this paper cites.
LSTM can solve hard long time lag problems
Sepp Hochreiter and Jürgen Schmidhuber · 1997
Earlier work this paper cites.
Identification of distributed parameter systems: A neural net based approach
R Gonzalez-Garcia, R Rico-Martinez, and IG Kevrekidis · 1998
Earlier work this paper cites.
Neural network modeling for near wall turbulent flow
Michele Milano and Petros Koumoutsakos · 2002
Earlier work this paper cites.
Equation-free, coarse-grained multiscale computation: Enabling mocroscopic simulators to perform system-level analysis
Ioannis G Kevrekidis, C William Gear, James M Hyman, Panagiotis G Kevrekidid, Olof Runborg, Constantinos Theodoropoulos, and others · 2003
Earlier work this paper cites.
Spectral properties of dynamical systems, model reduction and decompositions
Igor Mezic · 2005
Earlier work this paper cites.
Automated reverse engineering of nonlinear dynamical systems
Josh Bongard and Hod Lipson · 2007
Earlier work this paper cites.
Modeling and nonlinear parameter estimation with Kronecker product representation for coupled oscillators and spatiotemporal systems
Chen Yao and Erik M Bollt · 2007
Earlier work this paper cites.
Distilling free-form natural laws from experimental data
Michael Schmidt and Hod Lipson · 2009
Earlier work this paper cites.
Spectral analysis of nonlinear flows
C. W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D.S. Henningson · 2009
Earlier work this paper cites.
Dynamic mode decomposition of numerical and experimental data
Peter J. Schmid · 2010
Earlier work this paper cites.
Understanding the difficulty of training deep feedforward neural networks
Xavier Glorot and Yoshua Bengio · 2010
Earlier work this paper cites.
Predicting catastrophes in nonlinear dynamical systems by compressive sensing
W. X. Wang, R. Yang, Y. C. Lai, V. Kovanis, and C. Grebogi · 2011
Earlier work this paper cites.
Automated refinement and inference of analytical models for metabolic networks
Michael D Schmidt, Ravishankar R Vallabhajosyula, Jerry W Jenkins, Jonathan E Hood, Abhishek S Soni, John P Wikswo, and Hod Lipson · 2011
Earlier work this paper cites.
Applications of the dynamic mode decomposition
PJ Schmid, L Li, MP Juniper, and O Pust · 2011
Earlier work this paper cites.
Numerical differentiation of noisy, nonsmooth data
Rick Chartrand · 2011
Earlier work this paper cites.
Detecting causality in complex ecosystems
George Sugihara, Robert May, Hao Ye, Chih-hao Hsieh, Ethan Deyle, Michael Fogarty, and Stephan Munch · 2012
Earlier work this paper cites.
Symbolic regression of multiple-time-scale dynamical systems
Theodore Cornforth and Hod Lipson · 2012
Earlier work this paper cites.
Turbulence, coherent structures, dynamical systems and symmetry
P. J. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley · 2012
Earlier work this paper cites.
Applied Koopmanism
Marko Budisic, Ryan Mohr, and Igor Mezic · 2012
Earlier work this paper cites.
Imagenet classification with deep convolutional neural networks
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton · 2012
Earlier work this paper cites.
Deep neural networks for acoustic modeling in speech recognition
Geoffrey Hinton, Li Deng, Dong Yu, George Dahl, Abdel-rahman Mohamed, Navdeep Jaitly, Andrew Senior, Vincent Vanhoucke, Patrick Nguyen, Brian Kingsbury, et al · 2012
Earlier work this paper cites.
Analysis of fluid flows via spectral properties of the Koopman operator
Igor Mezic · 2013
Earlier work this paper cites.
Model emergent dynamics in complex systems
Anthony John Roberts · 2014
Cited alongside, same era.
Adam: A method for stochastic optimization
Diederik P. Kingma and Jimmy Ba · 2014
Cited alongside, same era.
A survey of projection-based model reduction methods for parametric dynamical systems
Peter Benner, Serkan Gugercin, and Karen Willcox · 2015
Cited alongside, same era.
Automated adaptive inference of phenomenological dynamical models
Bryan C Daniels and Ilya Nemenman · 2015
Cited alongside, same era.
Efficient inference of parsimonious phenomenological models of cellular dynamics using s-systems and alternating regression
Bryan C Daniels and Ilya Nemenman · 2015
Cited alongside, same era.
Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling
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
Later among the works it cites.
Chaos as an intermittently forced linear system
Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, Eurika Kaiser, and J. Nathan Kutz · 2017
Later among the works it cites.
Ergodic theory, dynamic mode decomposition and computation of spectral properties of the Koopman operator
Hassan Arbabi and Igor Mezić · 2017
Later among the works it cites.
Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator
Qianxiao Li, Felix Dietrich, Erik M. Bollt, and Ioannis G. Kevrekidis · 2017
Later among the works it cites.
Turbulence modeling in the age of data
Karthik Duraisamy, Gianluca Iaccarino, and Heng Xiao · 2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Hao Ye, Richard J Beamish, Sarah M Glaser, Sue CH Grant, Chih-hao Hsieh, Laura J Richards, Jon T Schnute, and George Sugihara · 2015
Cited alongside, same era.
A critical review of recurrent neural networks for sequence learning
Zachary C Lipton, John Berkowitz, and Charles Elkan · 2015
Cited alongside, same era.
A data–driven approximation of the Koopman operator: Extending dynamic mode decomposition
Matthew O. Williams, Ioannis G. Kevrekidis, and Clarence W. Rowley · 2015
Cited alongside, same era.
A kernel-based method for data-driven Koopman spectral analysis
Matthew O Williams, Clarence W Rowley, and Ioannis G Kevrekidis · 2015
Cited alongside, same era.
Statistical learning with sparsity: the lasso and generalizations
Robert Tibshirani, Martin Wainwright, and Trevor Hastie · 2015
Cited alongside, same era.
Data-driven operator inference for nonintrusive projection-based model reduction
Benjamin Peherstorfer and Karen Willcox · 2016
Cited alongside, same era.
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz · 2016
Cited alongside, same era.
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
Later among the works it cites.
Relational inductive biases, deep learning, and graph networks
Peter W Battaglia, Jessica B Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, Vinicius Zambaldi, Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner, et al · 2018
Later among the works it cites.
Deep learning for universal linear embeddings of nonlinear dynamics
Bethany Lusch, J Nathan Kutz, and Steven L Brunton · 2018
Later among the works it cites.
VAMPnets: Deep learning of molecular kinetics
Andreas Mardt, Luca Pasquali, Hao Wu, and Frank Noé · 2018
Later among the works it cites.
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
Later among the works it cites.
Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
Christoph Wehmeyer and Frank Noé · 2018
Later among the works it cites.
Multistep neural networks for data-driven discovery of nonlinear dynamical systems
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2018
Later among the works it cites.
Yohai Bar-Sinai, Stephan Hoyer, Jason Hickey, and Michael P Brenner · 2018
Later among the works it cites.
Constrained sparse Galerkin regression
J.-C. Loiseau and S. L. Brunton · 2018
Later among the works it cites.
On the convergence of the SINDy algorithm
Linan Zhang and Hayden Schaeffer · 2018
Later among the works it cites.
Sparse reduced-order modeling: sensor-based dynamics to full-state estimation
J.-C. Loiseau, B. R. Noack, and S. L. Brunton · 2018
Later among the works it cites.
Sparse identification of nonlinear dynamics for model predictive control in the low-data limit
Eurika Kaiser, J Nathan Kutz, and Steven L Brunton · 2018
Later among the works it cites.
Data-driven identification of parametric partial differential equations
Samuel Rudy, Alessandro Alla, Steven L Brunton, and J Nathan Kutz · 2018
Later among the works it cites.
Extracting sparse high-dimensional dynamics from limited data
Hayden Schaeffer, Giang Tran, and Rachel Ward · 2018
Later among the works it cites.
Kevin T Carlberg, Antony Jameson, Mykel J Kochenderfer, Jeremy Morton, Liqian Peng, and Freddie D Witherden · 2018
Later among the works it cites.
Learning low-dimensional feature dynamics using deep convolutional recurrent autoencoders
Francisco J Gonzalez and Maciej Balajewicz · 2018
Later among the works it cites.
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
Kookjin Lee and Kevin Carlberg · 2018
Later among the works it cites.
Deep learning of dynamics and signal-noise decomposition with time-stepping constraints
Samuel H Rudy, J Nathan Kutz, and Steven L Brunton · 2018
Later among the works it cites.
A unified framework for sparse relaxed regularized regression: Sr3
Peng Zheng, Travis Askham, Steven L Brunton, J Nathan Kutz, and Aleksandr Y Aravkin · 2019
Closest in time.
Reactive SINDy: Discovering governing reactions from concentration data
Moritz Hoffmann, Christoph Fröhner, and Frank Noé · 2019
Closest in time.
Sparse structural system identification method for nonlinear dynamic systems with hysteresis/inelastic behavior
Zhilu Lai and Satish Nagarajaiah · 2019
Closest in time.
Discovery of nonlinear multiscale systems: Sampling strategies and embeddings
Kathleen P Champion, Steven L Brunton, and J Nathan Kutz · 2019
Closest in time.
Model selection for hybrid dynamical systems via sparse regression
Niall M Mangan, Travis Askham, Steven L Brunton, J Nathan Kutz, and Joshua L Proctor · 2019
Closest in time.