Detecting Hidden Units and Network Size from Perceptible Dynamics

TL;DR

This paper introduces a model-free detection matrix method that accurately estimates the size of a network dynamical system from limited observable data, applicable across various dynamics and topologies.

Contribution

The paper presents a novel detection matrix approach that enables exact network size detection from partial observations, regardless of system type or dynamics.

Findings

Exact size detection feasible even with few observable units.

Method applicable to nonlinear, heterogeneous, and noisy systems.

Demonstrated on biochemical reaction networks.

Abstract

The number of units of a network dynamical system, its size, arguably constitutes its most fundamental property. Many units of a network, however, are typically experimentally inaccessible such that the network size is often unknown. Here we introduce a \emph{detection matrix }that suitably arranges multiple transient time series from the subset of accessible units to detect network size via matching rank constraints. The proposed method is model-free, applicable across system types and interaction topologies and applies to non-stationary dynamics near fixed points, as well as periodic and chaotic collective motion. Even if only a small minority of units is perceptible and for systems simultaneously exhibiting nonlinearities, heterogeneities and noise, \emph{exact} size detection is feasible. We illustrate applicability for a paradigmatic class of biochemical reaction networks.