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We use recent advances in the machine learning area known as 'reservoir computing' to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process.
E. N. Lorenz, Journal of the Atmospheric Sciences 20
1963
Earlier work this paper cites.
B. I. Cohen, J. Krommes, W. Tang, and M. Rosenbluth, Nuclear Fusion 16
1976
Earlier work this paper cites.
Y. Kuramoto and T. Tsuzuki, Progress of Theoretical Physics 55
1976
Earlier work this paper cites.
N. Tikhonov, Andreĭ, V. I. Arsenin, and F. John, Solutions of ill-posed problems , Vol. 14 (Winston Washington, DC, 1977)
1977
Earlier work this paper cites.
J. L. Kaplan and J. A. Yorke, in Functional Differential Equations and Approximation of Fixed Points (Springer, 1979) pp. 204–227
1979
Earlier work this paper cites.
F. Takens, by DA Rand and L.-S. Young Springer, Berlin 898
1981
Earlier work this paper cites.
G. Sivashinsky, Physica D: Nonlinear Phenomena 4
1982
Earlier work this paper cites.
D. S. Broomhead and G. P. King, Physica D: Nonlinear Phenomena 20
1986
Earlier work this paper cites.
J.-P. Eckmann, S. O. Kamphorst, D. Ruelle, and S. Ciliberto, Physical Review A 34
1986
Earlier work this paper cites.
R. Livi, A. Politi, and S. Ruffo, Journal of Physics A: Mathematical and General 19
1986
Earlier work this paper cites.
A. Brandstater and H. L. Swinney, Physical Review A 35
1987
Cited alongside, same era.
T. Sauer, J. A. Yorke, and M. Casdagli, Journal of Statistical Physics 65
1991
Cited alongside, same era.
V. Petrov, V. Gaspar, J. Masere, and K. Showalter, Nature 361
1993
Cited alongside, same era.
M. C. Cross and P. C. Hohenberg, Reviews of Modern Physics 65
1993
Cited alongside, same era.
E. Ott, T. Sauer, and J. A. Yorke, Wiley Series in Nonlinear Science, New York: John Wiley (1994)
1994
Cited alongside, same era.
D. A. Egolf and H. S. Greenside, Nature 369
1994
Cited alongside, same era.
H. Kantz and T. Schreiber, Nonlinear time series analysis , Vol. 7 (Cambridge University Press, 2004)
2004
Later among the works it cites.
H. Jaeger and H. Haas, Science 304
2004
Later among the works it cites.
M. Lukosevivcius and H. Jaeger, Computer Science Review 3
2009
Later among the works it cites.
X. Yan and X. Su, Linear regression analysis: theory and computing (World Scientific, 2009)
2009
Later among the works it cites.
G. Hinton, L. Deng, D. Yu, G. E. Dahl, A.-R. Mohamed, N. Jaitly, A. Senior, V. Vanhoucke, P. Nguyen, T. N. Sainath, et al. , IEEE Signal Processing Magazine 29
2012
Later among the works it cites.
H. Abarbanel, Analysis of observed chaotic data (Springer Science & Business Media, 2012)
2012
alphaXiv searches the wider corpus for related work and actual follow-ups.
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1998
Cited alongside, same era.
T. D. Sauer, J. A. Tempkin, and J. A. Yorke, Physical Review Letters 81
1998
Cited alongside, same era.
H. Jaeger, Bonn, Germany: German National Research Center for Information Technology GMD Technical Report 148
2001
Cited alongside, same era.
W. Maass, T. Natschlager, and H. Markram, Neural Computation 14
2002
Cited alongside, same era.
Later among the works it cites.
H. Kantz, G. Radons, and H. Yang, Journal of Physics A: Mathematical and Theoretical 46
2013
Later among the works it cites.
I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT Press, 2016)
2016
Later among the works it cites.
D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, et al. , Nature 529
2016
Later among the works it cites.
Z. Lu, J. Pathak, B. Hunt, M. Girvan, R. Brockett, and E. Ott, Chaos: An Interdisciplinary Journal of Nonlinear Science 27
2017
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