# Learning unidirectional coupling using echo-state network

arXiv: https://arxiv.org/abs/2303.13562 · HTML: https://mlsanity.com/paper/2303.13562/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 54 references that are in the map.
- First posted on arXiv 23 Mar 2023.

## Builds on (most cited first, 12 of 12)

- [Physical reservoir computing -- An introductory perspective](https://mlsanity.com/paper/2005.00992/) (2020)
- [Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers](https://mlsanity.com/paper/1910.00659/) (2019)
- [Adaptable Hamiltonian neural networks](https://mlsanity.com/paper/2102.13235/) (2021)
- [Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing](https://mlsanity.com/paper/2108.04074/) (2021)
- [Forecasting Hamiltonian dynamics without canonical coordinates](https://mlsanity.com/paper/2010.15201/) (2020)
- [Bayesian optimization of hyper-parameters in reservoir computing](https://mlsanity.com/paper/1611.05193/) (2016)
- [Separation of Chaotic Signals by Reservoir Computing](https://mlsanity.com/paper/1910.10080/) (2019)
- [Learn to Synchronize, Synchronize to Learn](https://mlsanity.com/paper/2010.02860/) (2020)
- [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)
- [On the low dimensional dynamics of structured random networks](https://mlsanity.com/paper/1509.02546/) (2015)
- [Critical Neuromorphic Computing based on Explosive Synchronization](https://mlsanity.com/paper/1810.10944/) (2018)
- [Role of assortativity in predicting burst synchronization using echo state network](https://mlsanity.com/paper/2110.05139/) (2021)

## Built on by (most cited first, 2 of 2)

- [Enhancing Trust in LLMs: Algorithms for Comparing and Interpreting LLMs](https://mlsanity.com/paper/2406.01943/) (2024)
- [Suppressing unknown disturbances to dynamical systems using machine learning](https://mlsanity.com/paper/2307.03690/) (2023)

## Abstract (arXiv)

Reservoir Computing has found many potential applications in the field of complex dynamics. In this article, we exploit the exceptional capability of the echo-state network (ESN) model to make it learn a unidirectional coupling scheme from only a few time series data of the system. We show that, once trained with a few example dynamics of a drive-response system, the machine is able to predict the response system's dynamics for any driver signal with the same coupling. Only a few time series data of an A-B type drive-response system in training is sufficient for the ESN to learn the coupling scheme. After training even if we replace drive system A with a different system C, the ESN can reproduce the dynamics of response system B using the dynamics of new drive system C only.