Learning strange attractors with reservoir systems
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 spa...
| Main Authors: | , , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Online Access: | https://hdl.handle.net/10356/170965 |
| _version_ | 1811678503782842368 |
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| author | Grigoryeva, Lyudmila Hart, Allen Ortega, Juan-Pablo |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Grigoryeva, Lyudmila Hart, Allen Ortega, Juan-Pablo |
| author_sort | Grigoryeva, Lyudmila |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T02:54:18Z |
| format | Journal Article |
| id | ntu-10356/170965 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:54:18Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1709652023-10-09T15:34:42Z Learning strange attractors with reservoir systems Grigoryeva, Lyudmila Hart, Allen Ortega, Juan-Pablo School of Physical and Mathematical Sciences Science::Mathematics Dynamical Systems Reservoir Computing 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. Submitted/Accepted version 2023-10-09T07:55:07Z 2023-10-09T07:55:07Z 2023 Journal Article Grigoryeva, L., Hart, A. & Ortega, J. (2023). Learning strange attractors with reservoir systems. Nonlinearity, 36(9), 4674-4708. https://dx.doi.org/10.1088/1361-6544/ace492 0951-7715 https://hdl.handle.net/10356/170965 10.1088/1361-6544/ace492 2-s2.0-85167508431 9 36 4674 4708 en Nonlinearity © 2023 IOP Publishing Ltd & London Mathematical Society. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1088/1361-6544/ace492. application/pdf |
| spellingShingle | Science::Mathematics Dynamical Systems Reservoir Computing Grigoryeva, Lyudmila Hart, Allen Ortega, Juan-Pablo Learning strange attractors with reservoir systems |
| title | Learning strange attractors with reservoir systems |
| title_full | Learning strange attractors with reservoir systems |
| title_fullStr | Learning strange attractors with reservoir systems |
| title_full_unstemmed | Learning strange attractors with reservoir systems |
| title_short | Learning strange attractors with reservoir systems |
| title_sort | learning strange attractors with reservoir systems |
| topic | Science::Mathematics Dynamical Systems Reservoir Computing |
| url | https://hdl.handle.net/10356/170965 |
| work_keys_str_mv | AT grigoryevalyudmila learningstrangeattractorswithreservoirsystems AT hartallen learningstrangeattractorswithreservoirsystems AT ortegajuanpablo learningstrangeattractorswithreservoirsystems |