Detecting Hidden Units and Network Size from Perceptible Dynamics

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.

Supplement available via the DOI below. https://doi.org/10.1103/PhysRevLett.122.158301

References in corpus (16)

• Spontaneous synchrony in power-grid networks
• Analysis of a power grid using the Kuramoto-like model
• Revealing Network Connectivity From Dynamics
• Reconstructing propagation networks with natural diversity and identifying hidden sources
• Inferring Network Topology from Complex Dynamics
• Revealing networks from dynamics: an introduction
• Robust Reconstruction of Complex Networks from Sparse Data
• Model-free inference of direct network interactions from nonlinear collective dynamics
• Observability and Controllability of Nonlinear Networks: The Role of Symmetry
• A Unified Approach to Attractor Reconstruction
• Critical links and nonlocal rerouting in complex supply networks
• Revealing physical interaction networks from statistics of collective dynamics
• Epidemic Spreading on Weighted Complex Networks
• Spreading dynamics on networks: the role of burstiness, topology and non-stationarity
• Antagonistic Phenomena in Network Dynamics
• Transition to Reconstructibility in Weakly Coupled Networks

Cited by in corpus (5)

• Tomography of time-dependent quantum spin networks with machine learning
• System Size Identification from Sinusoidal Probing in Diffusive Complex Networks
• The detection matrix as a model-agnostic tool to estimate the number of degrees of freedom in mechanical systems and engineering structures
• Network Inference using Sinusoidal Probing
• Network Reconstruction Problem for an Epidemic Reaction-Diffusion