Data-driven modeling from biased small training data using periodic orbits

Kengo Nakai; Yoshitaka Saiki

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arXiv · 2407.06229

Data-driven modeling from biased small training data using periodic orbits

Kengo Nakai·Yoshitaka Saiki

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Abstract

In this study, we investigate the effect of reservoir computing training data on the reconstruction of chaotic dynamics. Our findings indicate that a training time series comprising a few periodic orbits of low periods can successfully reconstruct the Lorenz attractor. We also demonstrate that biased training data does not negatively impact reconstruction success. Our method's ability to reconstruct a physical measure is much better than the so-called cycle expansion approach, which relies on weighted averaging. Additionally, we demonstrate that fixed point attractors and chaotic transients can be accurately reconstructed by a model trained from a few periodic orbits, even when using different parameters.

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Kengo Nakai, Yoshitaka Saiki. 2024-07-06. Data-driven modeling from biased small training data using periodic orbits. https://arxiv.org/abs/2407.06229

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