Learning interpretable collective variables for spreading processes on networks

Area of Science:

• Complex Systems
• Network Science
• Data Science

Background:

• Collective variables (CVs) simplify high-dimensional system states for analyzing emergent dynamics on networks.
• Understanding the link between CVs and network measures is challenging, often requiring deep knowledge of system dynamics and network topology.

Purpose of the Study:

• To develop a data-driven method for algorithmically learning and understanding CVs in binary-state spreading processes on networks.
• To explore the relationship between CVs and network properties across diverse network structures.

Main Methods:

• A novel data-driven methodology was employed to identify and analyze CVs.
• The method was applied to binary-state spreading processes on various network topologies, including stochastic block models, ring graphs, random regular graphs, and scale-free networks (Albert-Barabási model).

Main Results:

• The study successfully demonstrated the algorithmic learning of CVs for spreading processes on networks of arbitrary topology.
• Evidence for the existence of low-dimensional CVs was found, even in network configurations lacking prior theoretical understanding.

Conclusions:

• The developed data-driven method effectively identifies collective variables in complex network dynamics.
• This approach advances the understanding of emergent behaviors in networked systems and highlights the prevalence of low-dimensional collective variables.