Fetching the paper…
Reading the bibliography…
We propose spectral methods for long-term forecasting of temporal signals stemming from linear and nonlinear quasi-periodic dynamical systems.
On the structure of time-delay embedding in linear models of non-linear dynamical systems
S. Pan and K. Duraisamy · 1902
Earlier work this paper cites.
Physics-informed autoencoders for Lyapunov-stable fluid flow prediction
N. B. Erichson, M. Muehlebach, and M. W. Mahoney · 1905
Earlier work this paper cites.
S. Pan and K. Duraisamy · 1906
Earlier work this paper cites.
Proof of the ergodic theorem
G. D. Birkhoff · 1931
Earlier work this paper cites.
Hamiltonian systems and transformation in Hilbert space
B. O. Koopman · 1931
Earlier work this paper cites.
Recent contributions to the ergodic theory
G. D. Birkhoff and B. Koopman · 1932
Earlier work this paper cites.
Dynamical systems of continuous spectra
B. O. Koopman and J. v. Neumann · 1932
Earlier work this paper cites.
An algorithm for the machine calculation of complex Fourier series
J. W. Cooley and J. W. Tukey · 1965
Earlier work this paper cites.
Long-range forecasting
J. S. Armstrong · 1985
Earlier work this paper cites.
Akaike information criterion statistics
Y. Sakamoto, M. Ishiguro, and G. Kitagawa · 1986
Earlier work this paper cites.
Bayesian spectrum and chirp analysis
E. Jaynes · 1987
Earlier work this paper cites.
Time series analysis , volume 2
J. D. Hamilton · 1994
Earlier work this paper cites.
Long short-term memory
S. Hochreiter and J. Schmidhuber · 1997
Earlier work this paper cites.
Fourier neural networks
A. Silvescu · 1999
Earlier work this paper cites.
Learning with kernels: support vector machines, regularization, optimization, and beyond
B. Scholkopf and A. J. Smola · 2001
Earlier work this paper cites.
Convergence of a block coordinate descent method for nondifferentiable minimization
P. Tseng · 2001
Earlier work this paper cites.
Coupled oscillators utilised as gait rhythm generators of a two-legged walking machine
T. Zielińska · 2004
Earlier work this paper cites.
Dynamic wavelet neural network model for traffic flow forecasting
X. Jiang and H. Adeli · 2005
Earlier work this paper cites.
Spectral properties of dynamical systems, model reduction and decompositions
I. Mezić · 2005
Earlier work this paper cites.
Automatic time series for forecasting: the forecast package for R
R. J. Hyndman, Y. Khandakar, et al · 2007
Earlier work this paper cites.
Echo state network
H. Jaeger · 2007
Cited alongside, same era.
The discrete Fourier transform, part 4: spectral leakage
D. A. Lyon · 2009
Cited alongside, same era.
Forecasting with univariate Box-Jenkins models: Concepts and cases , volume 224
A. Pankratz · 2009
Cited alongside, same era.
Spectral analysis of nonlinear flows
C. W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D. S. Henningson · 2009
Cited alongside, same era.
Dynamic mode decomposition of numerical and experimental data
P. J. Schmid · 2010
Cited alongside, same era.
Applied Koopmanism
M. Budišić, R. Mohr, and I. Mezić · 2012
Cited alongside, same era.
Load/price forecasting and managing demand response for smart grids: Methodologies and challenges
Ergodic theorem, ergodic theory, and statistical mechanics
C. C. Moore · 2015
Later among the works it cites.
Discovering dynamic patterns from infectious disease data using dynamic mode decomposition
J. L. Proctor and P. A. Eckhoff · 2015
Later among the works it cites.
Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
S. T. Dawson, M. S. Hemati, M. O. Williams, and C. W. Rowley · 2016
Later among the works it cites.
Modeling time series data with deep Fourier neural networks
M. S. Gashler and S. C. Ashmore · 2016
Later among the works it cites.
Dynamic mode decomposition: data-driven modeling of complex systems
J. N. Kutz, S. L. Brunton, B. W. Brunton, and J. L. Proctor · 2016
Later among the works it cites.
Dynamic mode decomposition with control
J. L. Proctor, S. L. Brunton, and J. N. Kutz · 2016
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
S.-C. Chan, K. M. Tsui, H. Wu, Y. Hou, Y.-C. Wu, and F. F. Wu · 2012
Cited alongside, same era.
Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses
K. K. Chen, J. H. Tu, and C. W. Rowley · 2012
Cited alongside, same era.
Optoelectronic reservoir computing
Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar · 2012
Cited alongside, same era.
Bayesian spectrum analysis and parameter estimation , volume 48
G. L. Bretthorst · 2013
Cited alongside, same era.
Linearization in the large of nonlinear systems and Koopman operator spectrum
Y. Lan and I. Mezić · 2013
Cited alongside, same era.
Analysis of fluid flows via spectral properties of the Koopman operator
I. Mezic · 2013
Cited alongside, same era.
Later among the works it cites.
Chaos as an intermittently forced linear system
S. L. Brunton, B. W. Brunton, J. L. Proctor, E. Kaiser, and J. N. Kutz · 2017
Later among the works it cites.
De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets
M. S. Hemati, C. W. Rowley, E. A. Deem, and L. N. Cattafesta · 2017
Later among the works it cites.
Re-europe, a large-scale dataset for modeling a highly renewable european electricity system
T. V. Jensen and P. Pinson · 2017
Later among the works it cites.
Learning Koopman invariant subspaces for dynamic mode decomposition
N. Takeishi, Y. Kawahara, and T. Yairi · 2017
Later among the works it cites.
Bifurcations in a quasi-two-dimensional kolmogorov-like flow
J. Tithof, B. Suri, R. K. Pallantla, R. O. Grigoriev, and M. F. Schatz · 2017
Later among the works it cites.
Variable projection methods for an optimized dynamic mode decomposition
T. Askham and J. N. Kutz · 2018
Later among the works it cites.
Time-delay observables for Koopman: Theory and applications
M. Kamb, E. Kaiser, S. L. Brunton, and J. N. Kutz · 2018
Later among the works it cites.
Deep learning for universal linear embeddings of nonlinear dynamics
B. Lusch, J. N. Kutz, and S. L. Brunton · 2018
Later among the works it cites.
Generalizing Koopman theory to allow for inputs and control
J. L. Proctor, S. L. Brunton, and J. N. Kutz · 2018
Later among the works it cites.
Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
C. Wehmeyer and F. Noé · 2018
Later among the works it cites.
Data-driven discovery of coordinates and governing equations
K. Champion, B. Lusch, J. N. Kutz, and S. L. Brunton · 2019
Later among the works it cites.
Linearly recurrent autoencoder networks for learning dynamics
S. E. Otto and C. W. Rowley · 2019
Later among the works it cites.
Human gait database for normal walk collected by smart phone accelerometer
A. Vajdi, M. R. Zaghian, S. Farahmand, E. Rastegar, K. Maroofi, S. Jia, M. Pomplun, N. Haspel, and A. Bayat · 2019
Later among the works it cites.
Learning deep neural network representations for Koopman operators of nonlinear dynamical systems
E. Yeung, S. Kundu, and N. Hodas · 2019
Later among the works it cites.