Model-free inference of direct network interactions from nonlinear collective dynamics

TL;DR

This paper introduces a model-free method to infer direct network interactions from nonlinear collective dynamics, applicable across various regimes without prior system modeling, using a dependency matrix and block-orthogonal regression.

Contribution

It presents a novel, model-independent framework for detecting direct interactions in complex nonlinear systems, including hypernetwork interactions, without requiring a priori system models.

Findings

Works reliably across multiple dynamical regimes

Reveals both pairwise and higher-order interactions

Applicable to chaotic, transient, and steady-state dynamics

Abstract

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.