Learning Interpretable Collective Variables for Spreading Processes on Networks

TL;DR

This paper introduces a data-driven approach to learn interpretable collective variables for binary spreading processes on various network topologies, revealing low-dimensional structures that enhance understanding of complex network dynamics.

Contribution

The authors develop a novel algorithmic method to identify and interpret collective variables for spreading processes on arbitrary networks, bridging the gap between system dynamics and network measures.

Findings

Existence of low-dimensional CVs in complex networks.

Method successfully applied to diverse network types.

Provides insights into emergent behaviors of spreading processes.

Abstract

Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this work, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barab\'asi model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically.