Using Echo-State Networks to Reproduce Rare Events in Chaotic Systems

We apply the Echo-State Networks to predict the time series and statistical properties of the competitive Lotka-Volterra model in the chaotic regime. In particular, we demonstrate that Echo-State Networks successfully learn the chaotic attractor of the competitive Lotka-Volterra model and reproduce histograms of dependent variables, including tails and rare events. We use the Generalized Extreme Value distribution to quantify the tail behavior.

@article{erofeev2025_2505.16208,
  title={ Using Echo-State Networks to Reproduce Rare Events in Chaotic Systems },
  author={ Anton Erofeev and Balasubramanya T. Nadiga and Ilya Timofeyev },
  journal={arXiv preprint arXiv:2505.16208},
  year={ 2025 }
}