Using Echo-State Networks to Reproduce Rare Events in Chaotic Systems
Chaotic Dynamics
2026-05-06 v2 Artificial Intelligence
Machine Learning
Dynamical Systems
Abstract
We apply Echo-State Networks to predict 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 also demonstrate that the Echo-State Networks reproduce rare events in the non-equilibrium simulations of the Lotka-Volterra system. We use the Generalized Extreme Value distribution to quantify the tail behavior.
Keywords
Cite
@article{arxiv.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 = {2026}
}