Learning strange attractors with reservoir systems
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Published:2023-07-27
Issue:9
Volume:36
Page:4674-4708
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ISSN:0951-7715
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Container-title:Nonlinearity
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language:
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Short-container-title:Nonlinearity
Author:
Grigoryeva Lyudmila,Hart Allen,Ortega Juan-Pablo
Abstract
Abstract
This paper shows that the celebrated embedding theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible dynamical system carry in their wake an embedding of the phase space dynamics into the chosen Euclidean state space. This embedding coincides with a natural generalized synchronization that arises in this setup and that yields a topological conjugacy between the state-space dynamics driven by the generic observations of the dynamical system and the dynamical system itself. This result provides additional tools for the representation, learning, and analysis of chaotic attractors and sheds additional light on the reservoir computing phenomenon that appears in the context of recurrent neural networks.
Funder
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Engineering and Physical Sciences Research Council
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
3 articles.
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