Separation of Chaotic Signals by Reservoir Computing

TL;DR

This paper presents a reservoir computing approach for separating superimposed chaotic signals without prior knowledge of their underlying equations, outperforming traditional linear methods especially when signals have similar spectra.

Contribution

The study introduces a novel reservoir computing technique for chaotic signal separation that surpasses Wiener filtering, particularly in challenging spectral similarity cases.

Findings

Reservoir computing significantly outperforms Wiener filter in separating chaotic signals.

The method is effective even when component signals have indistinguishable frequency spectra.

The approach requires only finite training data and no knowledge of the underlying dynamical equations.

Abstract

We demonstrate the utility of machine learning in the separation of superimposed chaotic signals using a technique called Reservoir Computing. We assume no knowledge of the dynamical equations that produce the signals, and require only training data consisting of finite time samples of the component signals. We test our method on signals that are formed as linear combinations of signals from two Lorenz systems with different parameters. Comparing our nonlinear method with the optimal linear solution to the separation problem, the Wiener filter, we find that our method significantly outperforms the Wiener filter in all the scenarios we study. Furthermore, this difference is particularly striking when the component signals have similar frequency spectra. Indeed, our method works well when the component frequency spectra are indistinguishable - a case where a Wiener filter performs essentially no separation.