2016/01/17 by Alexandre Mauroy, Julien M. Hendrickx, Mauroy, A. +1 · 1 citation
Decision Sciences · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design #Systems and Control (eess.SY) #electronic engineering #information engineering #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1601.04364
openalex publication_date 2016/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new method to recover global information about a network of interconnected dynamical systems based on observations made at a small number (possibly one) of its nodes. In contrast to classical identification of full graph topology, we focus on the identification of the spectral graph-theoretic properties of the network, a framework that we call spectral network identification. The main theoretical results connect the spectral properties of the network to the spectral properties of the dynamics, which are well-defined in the context of the so-called Koopman operator and can be extracted from data through the Dynamic Mode Decomposition algorithm. These results are obtained for networks of diffusively-coupled units that admit a stable equilibrium state. For large networks, a statistical approach is considered, which focuses on spectral moments of the network and is well-suited to the case of heterogeneous populations. Our framework provides efficient numerical methods to infer global information on the network from sparse local measurements at a few nodes. Numerical simulations show for instance the possibility of detecting the mean number of connections or the addition of a new vertex using measurements made at one single node, that need not be representative of the other nodes' properties.