Spectral identification of networks using sparse measurements

Alexandre Mauroy, Jan HENDRICKX

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

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 graphtheoretic 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 wellsuited 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.

langueAnglais
Pages479-513
Nombre de pages35
journalSIAM Journal on Applied Dynamical Systems
Volume16
Numéro1
Les DOIs
étatPublié - 2017

Empreinte digitale

Numerical methods
Dynamical systems
Spectral Properties
Topology
Decomposition
Vertex of a graph
Computer simulation
Decomposition Algorithm
Equilibrium State
Well-defined
Dynamical system
Numerical Methods
Moment
Numerical Simulation
Unit
Graph in graph theory
Operator
Framework

mots-clés

    Citer ceci

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    Spectral identification of networks using sparse measurements. / Mauroy, Alexandre; HENDRICKX, Jan.

    Dans: SIAM Journal on Applied Dynamical Systems, Vol 16, Numéro 1, 2017, p. 479-513.

    Résultats de recherche: Contribution à un journal/une revueArticle

    TY - JOUR

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    AU - HENDRICKX, Jan

    PY - 2017

    Y1 - 2017

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    AB - 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 graphtheoretic 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 wellsuited 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.

    KW - Koopman operator

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