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

TL;DR

This paper demonstrates that Echo-State Networks can effectively learn and reproduce the chaotic attractor and rare events of the Lotka-Volterra model, including tail behaviors, in chaotic regimes.

Contribution

It shows for the first time that Echo-State Networks can accurately reproduce rare events and statistical properties of chaotic systems like the Lotka-Volterra model.

Findings

Echo-State Networks successfully learn the chaotic attractor.

They reproduce histograms including tails and rare events.

They quantify tail behavior using the Generalized Extreme Value distribution.

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.