Robust learning of chaotic attractors

Rembrandt Bakker; Jaap C. Sochouten; Marc Olivier Coppens; Floris Takens; C. Lee Giles; Cor M. Van Den Bleek

Robust learning of chaotic attractors

Rembrandt Bakker, Jaap C. Sochouten, Marc Olivier Coppens, Floris Takens, C. Lee Giles, Cor M. Van Den Bleek

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

A fundamental problem with the modeling of chaotic time series data is that minimizing short-term prediction errors does not guarantee a match between the reconstructed attractors of model and experiments. We introduce a modeling paradigm that simultaneously learns to short-term predict and to locate the outlines of the attractor by a new way of nonlinear principal component analysis. Closed-loop predictions are constrained to stay within these outlines, to prevent divergence from the attractor. Learning is exceptionally fast: parameter estimation for the 1000 sample laser data from the 1991 Santa Fe time series competition took less than a minute on a 166 MHz Pentium PC.

Original language	English (US)
Title of host publication	Advances in Neural Information Processing Systems 12 - Proceedings of the 1999 Conference, NIPS 1999
Publisher	Neural information processing systems foundation
Pages	879-885
Number of pages	7
ISBN (Print)	0262194503, 9780262194501
State	Published - 2000
Event	13th Annual Neural Information Processing Systems Conference, NIPS 1999 - Denver, CO, United States Duration: Nov 29 1999 → Dec 4 1999

Publication series

Name	Advances in Neural Information Processing Systems
ISSN (Print)	1049-5258

Other

Other	13th Annual Neural Information Processing Systems Conference, NIPS 1999
Country/Territory	United States
City	Denver, CO
Period	11/29/99 → 12/4/99

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Information Systems
Signal Processing

Cite this

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title = "Robust learning of chaotic attractors",

abstract = "A fundamental problem with the modeling of chaotic time series data is that minimizing short-term prediction errors does not guarantee a match between the reconstructed attractors of model and experiments. We introduce a modeling paradigm that simultaneously learns to short-term predict and to locate the outlines of the attractor by a new way of nonlinear principal component analysis. Closed-loop predictions are constrained to stay within these outlines, to prevent divergence from the attractor. Learning is exceptionally fast: parameter estimation for the 1000 sample laser data from the 1991 Santa Fe time series competition took less than a minute on a 166 MHz Pentium PC.",

author = "Rembrandt Bakker and Sochouten, {Jaap C.} and Coppens, {Marc Olivier} and Floris Takens and Giles, {C. Lee} and {Van Den Bleek}, {Cor M.}",

year = "2000",

language = "English (US)",

isbn = "0262194503",

series = "Advances in Neural Information Processing Systems",

publisher = "Neural information processing systems foundation",

pages = "879--885",

booktitle = "Advances in Neural Information Processing Systems 12 - Proceedings of the 1999 Conference, NIPS 1999",

note = "13th Annual Neural Information Processing Systems Conference, NIPS 1999 ; Conference date: 29-11-1999 Through 04-12-1999",

}

Bakker, R, Sochouten, JC, Coppens, MO, Takens, F, Giles, CL & Van Den Bleek, CM 2000, Robust learning of chaotic attractors. in Advances in Neural Information Processing Systems 12 - Proceedings of the 1999 Conference, NIPS 1999. Advances in Neural Information Processing Systems, Neural information processing systems foundation, pp. 879-885, 13th Annual Neural Information Processing Systems Conference, NIPS 1999, Denver, CO, United States, 11/29/99.

Robust learning of chaotic attractors. / Bakker, Rembrandt; Sochouten, Jaap C.; Coppens, Marc Olivier et al.
Advances in Neural Information Processing Systems 12 - Proceedings of the 1999 Conference, NIPS 1999. Neural information processing systems foundation, 2000. p. 879-885 (Advances in Neural Information Processing Systems).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Robust learning of chaotic attractors

AU - Bakker, Rembrandt

AU - Sochouten, Jaap C.

AU - Coppens, Marc Olivier

AU - Takens, Floris

AU - Giles, C. Lee

AU - Van Den Bleek, Cor M.

PY - 2000

Y1 - 2000

N2 - A fundamental problem with the modeling of chaotic time series data is that minimizing short-term prediction errors does not guarantee a match between the reconstructed attractors of model and experiments. We introduce a modeling paradigm that simultaneously learns to short-term predict and to locate the outlines of the attractor by a new way of nonlinear principal component analysis. Closed-loop predictions are constrained to stay within these outlines, to prevent divergence from the attractor. Learning is exceptionally fast: parameter estimation for the 1000 sample laser data from the 1991 Santa Fe time series competition took less than a minute on a 166 MHz Pentium PC.

AB - A fundamental problem with the modeling of chaotic time series data is that minimizing short-term prediction errors does not guarantee a match between the reconstructed attractors of model and experiments. We introduce a modeling paradigm that simultaneously learns to short-term predict and to locate the outlines of the attractor by a new way of nonlinear principal component analysis. Closed-loop predictions are constrained to stay within these outlines, to prevent divergence from the attractor. Learning is exceptionally fast: parameter estimation for the 1000 sample laser data from the 1991 Santa Fe time series competition took less than a minute on a 166 MHz Pentium PC.

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M3 - Conference contribution

AN - SCOPUS:84899004937

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SN - 9780262194501

T3 - Advances in Neural Information Processing Systems

SP - 879

EP - 885

BT - Advances in Neural Information Processing Systems 12 - Proceedings of the 1999 Conference, NIPS 1999

PB - Neural information processing systems foundation

T2 - 13th Annual Neural Information Processing Systems Conference, NIPS 1999

Y2 - 29 November 1999 through 4 December 1999

ER -

Robust learning of chaotic attractors

Abstract

Publication series

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All Science Journal Classification (ASJC) codes

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