On the approximations of the Koopman operator and applications to spectral identification of networks

This research project focuses on the study of networks considered as complex dynamic systems, meaning they evolve over time, are high-dimensional, and exhibit nonlinear behavior. Such networks consist of agents interacting with each other and can model, for example, neural connections in the brain or the evolution of opinions in a social network. While a classical approach involves predicting the collective behavior emerging from a network based on its structure, many data analysis problems are motivated by the inverse objective: reconstructing an unknown network from measurements of its dynamics. This problem is encountered notably in neuroscience (reconstructing a brain network from medical imaging data) and in genetics (reconstructing a network of genetic interactions from gene expression data). The proposed research will thus aim to develop, both theoretically and numerically, original methods within the framework of this network identification problem.