# Machine Learning Link Inference of Noisy Delay-coupled Networks with Opto-Electronic Experimental Tests

arXiv: https://arxiv.org/abs/2010.15289 · HTML: https://mlsanity.com/paper/2010.15289/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2020.

## Built on by (most cited first, 7 of 7)

- [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)
- [Learning to learn ecosystems from limited data -- a meta-learning approach](https://mlsanity.com/paper/2410.07368/) (2024)
- [Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computing](https://mlsanity.com/paper/2506.05292/) (2025)
- [Incorporating Coupling Knowledge into Echo State Networks for Learning Spatiotemporally Chaotic Dynamics](https://mlsanity.com/paper/2504.01532/) (2025)
- [Backpropagation on Dynamical Networks](https://mlsanity.com/paper/2207.03093/) (2022)
- [Machine learning of network inference enhancement from noisy measurements](https://mlsanity.com/paper/2309.02050/) (2023)

## Abstract (arXiv)

We devise a machine learning technique to solve the general problem of inferring network links that have time-delays. The goal is to do this purely from time-series data of the network nodal states. This task has applications in fields ranging from applied physics and engineering to neuroscience and biology. To achieve this, we first train a type of machine learning system known as reservoir computing to mimic the dynamics of the unknown network. We formulate and test a technique that uses the trained parameters of the reservoir system output layer to deduce an estimate of the unknown network structure. Our technique, by its nature, is non-invasive, but is motivated by the widely-used invasive network inference method whereby the responses to active perturbations applied to the network are observed and employed to infer network links (e.g., knocking down genes to infer gene regulatory networks). We test this technique on experimental and simulated data from delay-coupled opto-electronic oscillator networks. We show that the technique often yields very good results particularly if the system does not exhibit synchrony. We also find that the presence of dynamical noise can strikingly enhance the accuracy and ability of our technique, especially in networks that exhibit synchrony.