# Separation of Chaotic Signals by Reservoir Computing

arXiv: https://arxiv.org/abs/1910.10080 · HTML: https://mlsanity.com/paper/1910.10080/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2019.

## Built on by (most cited first, 12 of 12)

- [Model-free prediction of emergence of extreme events in a parametrically driven nonlinear dynamical system by Deep Learning](https://mlsanity.com/paper/2107.08819/) (2021)
- [Signal-noise separation using unsupervised reservoir computing](https://mlsanity.com/paper/2404.04870/) (2024)
- [Learning unidirectional coupling using echo-state network](https://mlsanity.com/paper/2303.13562/) (2023)
- [Tailored Forecasting from Short Time Series via Meta-learning](https://mlsanity.com/paper/2501.16325/) (2025)
- [Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computing](https://mlsanity.com/paper/2506.05292/) (2025)
- [Prediction of Occurrence of Extreme Events using Machine Learning](https://mlsanity.com/paper/2110.09304/) (2021)
- [Denoising and Reconstruction of Nonlinear Dynamics using Truncated Reservoir Computing](https://mlsanity.com/paper/2504.13355/) (2025)
- [Evolutionary Optimization Reveals Structural Constraints on Reservoir Architecture for Spatiotemporal Chaos](https://mlsanity.com/paper/2606.22765/) (2026)
- [Using Echo-State Networks to Reproduce Rare Events in Chaotic Systems](https://mlsanity.com/paper/2505.16208/) (2025)
- [Attractor learning for spatiotemporally chaotic dynamical systems using echo state networks with transfer learning](https://mlsanity.com/paper/2505.24099/) (2025)
- [Reservoir Computing as a Language Model](https://mlsanity.com/paper/2507.15779/) (2025)
- [Feasibility and Memory Mechanisms of Chern-Simons Context Reservoir Computation](https://mlsanity.com/paper/2609.13315/) (2026)

## Abstract (arXiv)

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.