# Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptography

arXiv: https://arxiv.org/abs/1802.02844 · HTML: https://mlsanity.com/paper/1802.02844/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2018.

## Built on by (most cited first, 16 of 16)

- [Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems](https://mlsanity.com/paper/2207.00521/) (2022)
- [Catch-22s of reservoir computing](https://mlsanity.com/paper/2210.10211/) (2022)
- [Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstruction](https://mlsanity.com/paper/2401.00885/) (2023)
- [Asymptotic Stability in Reservoir Computing](https://mlsanity.com/paper/2206.03854/) (2022)
- [Stochastic Reservoir Computers](https://mlsanity.com/paper/2405.12382/) (2024)
- [Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatio-temporal systems using scalable neural networks](https://mlsanity.com/paper/2111.03706/) (2021)
- [Efficient Optimisation of Physical Reservoir Computers using only a Delayed Input](https://mlsanity.com/paper/2401.14371/) (2024)
- [Improving the Performance of Echo State Networks Through State Feedback](https://mlsanity.com/paper/2312.15141/) (2023)
- [Interpretable Design of Reservoir Computing Networks using Realization Theory](https://mlsanity.com/paper/2112.06891/) (2021)
- [Characterizing Learning in Spiking Neural Networks with Astrocyte-Like Units](https://mlsanity.com/paper/2503.06798/) (2025)
- [Reservoir observer enhanced with residual calibration and attention mechanism](https://mlsanity.com/paper/2604.08592/) (2026)
- [Reservoir Computers Modal Decomposition and Optimization](https://mlsanity.com/paper/2101.07219/) (2021)
- [Universal replication of chaotic characteristics by classical and quantum machine learning](https://mlsanity.com/paper/2405.08484/) (2024)
- [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)
- [Stabilizing autoregressive forecasts in chaotic systems via multi-rate latent recurrence](https://mlsanity.com/paper/2601.14487/) (2026)

## Abstract (arXiv)

Using the machine learning approach known as reservoir computing, it is possible to train one dynamical system to emulate another. We show that such trained reservoir computers reproduce the properties of the attractor of the chaotic system sufficiently well to exhibit chaos synchronisation. That is, the trained reservoir computer, weakly driven by the chaotic system, will synchronise with the chaotic system. Conversely, the chaotic system, weakly driven by a trained reservoir computer, will synchronise with the reservoir computer. We illustrate this behaviour on the Mackey-Glass and Lorenz systems. We then show that trained reservoir computers can be used to crack chaos based cryptography and illustrate this on a chaos cryptosystem based on the Mackey-Glass system. We conclude by discussing why reservoir computers are so good at emulating chaotic systems.