Transition to Reconstructibility in Weakly Coupled Networks

TL;DR

This paper investigates the challenge of accurately reconstructing physical interaction networks from correlation data, demonstrating that weak coupling conditions enable universal reconstructibility regardless of network structure.

Contribution

It provides a theoretical proof that weakly coupled stationary systems become universally reconstructible, overcoming structural hindrances present at higher coupling strengths.

Findings

Reconstructibility is hindered by local and non-local network structures.

Weak coupling leads to universal reconstructibility across all network topologies.

The study offers a theoretical foundation for network inference in weakly interacting systems.

Abstract

Across scientific disciplines, thresholded pairwise measures of statistical dependence between time series are taken as proxies for the interactions between the dynamical units of a network. Yet such correlation measures often fail to reflect the underlying physical interactions accurately. Here we systematically study the problem of reconstructing direct physical interaction networks from thresholding correlations. We explicate how local common cause and relay structures, heterogeneous in-degrees and non-local structural properties of the network generally hinder reconstructibility. However, in the limit of weak coupling strengths we prove that stationary systems with dynamics close to a given operating point transition to universal reconstructiblity across all network topologies.