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A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited.
A new approach to linear filtering and prediction problems
Rudolph Emil Kalman · 1960
Earlier work this paper cites.
Effective construction of linear state-variable models from input/output data
B. L. Ho and R. E. Kalman · 1965
Earlier work this paper cites.
An eigensystem realization algorithm for modal parameter identification and model reduction
J. N. Juang and R. S. Pappa · 1985
Earlier work this paper cites.
Representations of non-linear systems: the narmax model
Sheng Chen and Steve A Billings · 1989
Earlier work this paper cites.
Recursive form of the eigensystem realization algorithm for system identification
Richard W Longman and Jer-Nan Juang · 1989
Earlier work this paper cites.
Non-linear system identification using neural networks
Sheng Chen, SA Billings, and PM Grant · 1990
Earlier work this paper cites.
Construction of higher order symplectic integrators
Haruo Yoshida · 1990
Earlier work this paper cites.
Approximation capabilities of multilayer feedforward networks
Kurt Hornik · 1991
Earlier work this paper cites.
Identification of observer/Kalman filter Markov parameters: Theory and experiments
J. N. Juang, M. Phan, L. G. Horta, and R. W. Longman · 1991
Earlier work this paper cites.
Identification of linear-multivariable systems by identification of observers with assigned real eigenvalues
M. Phan, J. N. Juang, and R. W. Longman · 1992
Earlier work this paper cites.
Linear system identification via an asymptotically stable observer
M. Phan, L. G. Horta, J. N. Juang, and R. W. Longman · 1993
Earlier work this paper cites.
Applied System Identification
J. N. Juang · 1994
Earlier work this paper cites.
Algorithm 778: L-bfgs-b: Fortran subroutines for large-scale bound-constrained optimization
Ciyou Zhu, Richard H Byrd, Peihuang Lu, and Jorge Nocedal · 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.
System Identification: Theory for the User
L. Ljung · 1999
Earlier work this paper cites.
Overfitting in neural nets: Backpropagation, conjugate gradient, and early stopping
Rich Caruana, Steve Lawrence, and C Lee Giles · 2001
Earlier work this paper cites.
Discrete mechanics and variational integrators
Jerrold E Marsden and Matthew West · 2001
Earlier work this paper cites.
Neural network modeling for near wall turbulent flow
Michele Milano and Petros Koumoutsakos · 2002
Earlier work this paper cites.
A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
B. R. Noack, K. Afanasiev, M. Morzynski, G. Tadmor, and F. Thiele · 2003
Earlier work this paper cites.
Automated reverse engineering of nonlinear dynamical systems
Josh Bongard and Hod Lipson · 2007
Earlier work this paper cites.
Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems
Randall J LeVeque · 2007
Earlier work this paper cites.
The immersed boundary method: a projection approach
K. Taira and T. Colonius · 2007
Earlier work this paper cites.
A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions
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Michael Schmidt, Ravishankar Vallabhajosyula, J. Jenkins, Jonathan Hood, Abhishek Soni, John Wikswo, and Hod Lipson · 2011
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Predicting catastrophes in nonlinear dynamical systems by compressive sensing
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
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Learning partial differential equations via data discovery and sparse optimization
Hayden Schaeffer · 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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W. X. Wang, R. Yang, Y. C. Lai, V. Kovanis, and C. Grebogi · 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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On dynamic mode decomposition: theory and applications
J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz · 2014
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Closed-loop turbulence control: Progress and challenges
S. L. Brunton and B. R. Noack · 2015
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Automated adaptive inference of phenomenological dynamical models
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Learning koopman invariant subspaces for dynamic mode decomposition
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Giang Tran and Rachel Ward · 2017
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Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
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Learning deep neural network representations for koopman operators of nonlinear dynamical systems
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Constrained sparse Galerkin regression
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