Forecasting macroscopic dynamics in adaptive Kuramoto network using reservoir computing.

Area of Science:

• Complex Systems Theory
• Machine Learning
• Nonlinear Dynamics

Background:

• Forecasting complex system behavior is crucial.
• Machine learning, including reservoir computers, can predict time-series data.
• Real-world systems, like brain networks (EEG), present forecasting challenges due to limited information.

Purpose of the Study:

• To train a reservoir computer (RC) for predicting the behavior of a network of phase oscillators.
• To investigate methods for improving RC forecasting of chaotic signals.
• To explore the relationship between feature space dimensionality and prediction accuracy.

Main Methods:

• Utilized a reservoir computer for time-series prediction.
• Performed Lyapunov analysis to identify signal chaos.
• Applied Takkens' theorem to augment the feature space.
• Employed the nearest false neighbors method to estimate embedding dimension.

Main Results:

• The reservoir computer initially failed to forecast the chaotic signal.
• Augmenting the feature space with Takkens' theorem enhanced prediction quality.
• Optimal prediction was achieved when the number of signals matched the estimated embedding dimension.
• Short-time predictions benefited from more features, while long-time predictions required fewer.

Conclusions:

• Reservoir computer performance in forecasting chaotic systems can be significantly improved.
• Feature space augmentation and appropriate embedding dimension selection are critical for accurate predictions.
• The findings highlight the bias-variance trade-off in machine learning for complex systems.