Predicting collective states of a star network using reservoir computing.

Area of Science:

• Complex Systems
• Network Science
• Machine Learning

Background:

• Inferring dynamics of oscillator networks is challenging without explicit equations.
• Data-driven approaches are needed for complex system analysis.

Purpose of the Study:

• To develop a machine learning technique for predicting dynamical states in star-structured oscillator networks.
• To utilize a parameter-aware reservoir computing scheme for efficient learning.

Main Methods:

• Employed echo-state network (ESN) framework, a type of reservoir computing.
• Utilized topological symmetry of the star network to minimize training cost.
• Used a minimal setup with only two ESN units to learn parameter-dependent dynamics.

Main Results:

• Successfully predicted multi-stable dynamics across varied coupling strengths.
• Demonstrated efficient prediction of unseen attractors like chimera, coherent, incoherent, and cluster synchronization.
• Validated performance for both identical and non-identical central and peripheral oscillators.

Conclusions:

• The proposed reservoir computing framework efficiently learns dynamics of large-scale oscillator networks.
• The method is effective even with limited training data.
• This data-driven approach offers a powerful tool for analyzing complex network behaviors.