Machine learning, alignment of covariant Lyapunov vectors, and predictability in Rikitake's geomagnetic dynamo model.

Area of Science:

• Geophysics
• Dynamo Theory
• Machine Learning

Background:

• Chaotic time series analysis is crucial for understanding complex systems.
• Rikitake's geomagnetic dynamo model exhibits chaotic behavior.
• Predicting the duration of regimes in chaotic systems remains a challenge.

Purpose of the Study:

• To develop a machine learning approach for predicting regime durations in chaotic time series.
• To investigate the role of covariant Lyapunov vectors in regime duration prediction.
• To apply these methods to Rikitake's geomagnetic dynamo model.

Main Methods:

• Training multi-layer perceptron ensembles using aligned covariant Lyapunov vectors.
• Employing a classification procedure linking regime features to duration.
• Analyzing chaotic time series data from Rikitake's dynamo model.

Main Results:

• Accurate predictions of regime durations, including long regimes (approx. 17.5 Lyapunov times).
• Identification of the alignment of covariant Lyapunov vectors as key predictors.
• Discovery of unusual statistical behavior in long-duration regimes, with longer regimes being more probable.

Conclusions:

• Machine learning, particularly using covariant Lyapunov vectors, offers a powerful tool for predicting chaotic system dynamics.
• The findings advance our understanding of Rikitake's dynamo model and chaotic time series analysis.
• The observed statistical anomalies in regime durations warrant further investigation.