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

2025-05-22

AI Summary

This work addresses the challenge of modeling time-series dynamics and extreme events in chaotic competitive Lotka–Volterra systems. Methodologically, it introduces a data-driven forecasting framework based on echo state networks (ESNs), marking the first application of ESNs to fully learn the nonlinear dynamics of this chaotic ecological model; it further integrates the generalized extreme value (GEV) distribution to statistically characterize rare events. The approach not only accurately reconstructs the geometric structure of the chaotic attractor and long-term dynamical behavior but also faithfully reproduces state-variable histograms—including their heavy-tailed features. Experimental results demonstrate that the ESN reliably captures intrinsic nonlinearities and the probabilistic structure of extremes; GEV fitting confirms significantly lower errors in reproducing both the frequency and magnitude of rare events compared to conventional methods. This study extends the applicability of reservoir computing to chaotic ecological modeling and extreme-risk prediction.

Technology Category

Machine Learning: Multi-class/Multi-label Learning & Extreme ClassificationIntelligent Robots: State EstimationCognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

Web Mining and Content Analysis: Models for Web evolutionGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsEconomics, Online Markets and Human Computation: Social networks and social learning

Abstract

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.

Problem

• Predict chaotic time series using Echo-State Networks
• Reproduce rare events in competitive Lotka-Volterra model
• Quantify tail behavior with Generalized Extreme Value distribution

Innovation

• Echo-State Networks predict chaotic time series
• Reproduce rare events using statistical properties
• Generalized Extreme Value quantifies tail behavior