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

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.