André Röhm,1 Kohei Tsuchiyama,1 Takatomo Mihana,1 Ryoichi Horisakihttps://orcid.org/0000-0002-2280-5921,1 Daniel J. Gauthier,2 Ingo Fischer,3 Makoto Naruse1
1The Univ. of Tokyo (Japan) 2The Ohio State Univ. (United States) 3Instituto de Física Interdisciplinar y Sistemas Complejos (Spain)
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Reservoir computing is a powerful tool for creating digital twins of a target systems. They can both predict future values of a chaotic timeseries to a high accuracy and also reconstruct the general properties of a chaotic attractor. In this. We show that their ability to learn the dynamics of a complex system can be extended to systems with multiple co-existing attractors, here a four-dimensional extension of the well-known Lorenz chaotic system.
Even parts of the phase space that were not in the training set can be explored with the help of a properly-trained reservoir computer. This includes entirely separate attractors, which we call "unseen". Training on a single noisy trajectory is sufficient. Because Reservoir Computers are substrate-agnostic, this allows the creation of conjugate autonomous reservoir computers for any target dynamical systems.
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André Röhm, Kohei Tsuchiyama, Takatomo Mihana, Ryoichi Horisaki, Daniel J. Gauthier, Ingo Fischer, Makoto Naruse, "Reconstructing seen and unseen attractors from data via autonomous-mode reservoir computing," Proc. SPIE PC12438, AI and Optical Data Sciences IV, PC124380E (17 March 2023); https://doi.org/10.1117/12.2648645