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

TL;DR

This paper shows that reservoir computing can effectively reconstruct chaotic dynamics like the Lorenz attractor using limited, biased training data consisting of a few periodic orbits, outperforming traditional methods.

Contribution

It introduces a data-driven approach that reconstructs chaotic attractors from biased small datasets of periodic orbits, surpassing cycle expansion techniques.

Findings

Successful reconstruction of Lorenz attractor from few periodic orbits

Biased training data does not impair reconstruction quality

Fixed points and chaotic transients are accurately modeled

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.