Learning transitions to extreme events using reservoir computing.

Area of Science:

• Nonlinear dynamics
• Machine learning
• Complex systems

Background:

• Extreme events in dynamical systems are difficult to predict due to irregular timing and large amplitudes.
• Accurate forecasting of both amplitude and timing remains a significant challenge.

Purpose of the Study:

• To apply reservoir computing machine learning for predicting extreme events in paradigmatic dynamical systems.
• To evaluate the efficacy of machine learning in forecasting event transitions, amplitudes, and statistical properties.
• To determine optimal input parameters for prediction using metrics like prediction horizon and mean square error.

Main Methods:

• Reservoir computing machine learning was employed using partial or complete system variable information.
• The approach was tested on the forced Liénard system, coupled FitzHugh-Nagumo model, and a hidden attractor model.
• Numerical data and real-time experimental data from a forced Liénard circuit were used for training and validation.

Main Results:

• The machine learning model successfully predicted transition points to extreme events via Pomeau-Manneville and crisis-induced intermittency.
• Attractors and statistical properties (event distributions, inter-event intervals) of extreme events were accurately reproduced.
• Time evolution prediction was limited to a few Lyapunov times, but extreme event amplitudes were preserved or accurately predicted.

Conclusions:

• Reservoir computing offers a promising approach for predicting extreme events in complex dynamical systems.
• The method effectively captures the dynamics and statistical characteristics of extreme events, particularly intermittency.
• While short-term time evolution prediction is limited, amplitude forecasting and transition point prediction show high accuracy.