### 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.

langue | Anglais |
---|---|

Pages | 479-513 |

Nombre de pages | 35 |

journal | SIAM Journal on Applied Dynamical Systems |

Volume | 16 |

Numéro | 1 |

Les DOIs | |

état | Publié - 2017 |

### Empreinte digitale

### mots-clés

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*SIAM Journal on Applied Dynamical Systems*,

*16*(1), 479-513. https://doi.org/10.1137/16M105722X

}

*SIAM Journal on Applied Dynamical Systems*, VOL. 16, Numéro 1, p. 479-513. https://doi.org/10.1137/16M105722X

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

Résultats de recherche: Contribution à un journal/une revue › Article

TY - JOUR

T1 - Spectral identification of networks using sparse measurements

AU - Mauroy, Alexandre

AU - HENDRICKX, Jan

PY - 2017

Y1 - 2017

N2 - 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.

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

KW - Network identification

KW - Spectral graph theory

UR - http://www.scopus.com/inward/record.url?scp=85018721925&partnerID=8YFLogxK

U2 - 10.1137/16M105722X

DO - 10.1137/16M105722X

M3 - Article

VL - 16

SP - 479

EP - 513

JO - SIAM Journal on Applied Dynamical Systems

T2 - SIAM Journal on Applied Dynamical Systems

JF - SIAM Journal on Applied Dynamical Systems

SN - 1536-0040

IS - 1

ER -