An operator-theoretic approach to network identification
The so-called Koopman operator is a powerful tool to study and identify nonlinear systems.
Through this framework, nonlinear systems are turned into linear (but infinite-dimensional) systems that are amenable to spectral analysis.
Focusing on network identification, we will show that the Koopman operator framework can be used to infer spectral properties of networks from partial measurements of the dynamics of a few units. This approach allows to uncover global topological properties using only local information. The case of large networks and heterogeneous populations will be considered. Finally, we will briefly exploit the Koopman operator framework to develop a "lifting" method for nonlinear system identification and network inference.