A unified and automated approach to attractor reconstruction

TL;DR

This paper introduces an automated, unified method for optimal state space reconstruction from time series data, capable of handling noise, multiple time scales, and determining embedding parameters without thresholds.

Contribution

It generalizes time delay embedding by combining non-uniform delays and cost function minimization, enabling robust reconstruction without manual parameter tuning.

Findings

Successfully reconstructs systems with different time scales.

Handles noise and stochastic data effectively.

Outperforms established methods on models and experimental data.

Abstract

We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data from chaotic chemical oscillators.