Revealing physical interaction networks from statistics of collective dynamics

TL;DR

This paper introduces a method using changes in invariant measures and compressed sensing to reconstruct physical interaction networks from collective dynamics, even with limited, disordered, or sparse data.

Contribution

It presents a novel approach that infers physical connectivity in complex systems from minimal and imperfect observational data without requiring detailed models.

Findings

High accuracy in reconstructing existence of interactions.

Effective in identifying types of interactions.

Works with disordered and sparse data.

Abstract

Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of detail often not available. We exploit changes in invariant measures, in particular distributions of sampled states of the system in response to driving signals, and use compressed sensing to reveal physical interaction networks. Dynamical observations following driving suffice to infer physical connectivity even if they are temporally disordered, are acquired at large sampling intervals, and stem from different experiments. Testing various nonlinear dynamic processes emerging on artificial and real network topologies indicates high reconstruction quality for existence as well as type of interactions. These results advance our ability to reveal physical interaction networks in complex synthetic and natural systems.