Spectral identification of networks : using cross-validation to improve the Dynamic Mode Decomposition algorithm

Details

Supervisors

Hendrickx, Julien ; Mauroy, Alexandre

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées

Abstract

Spectral network identification allows to infer global topological properties of a network system from measurements of its dynamics at a few nodes. The Dynamic Mode Decomposition algorithm is used in this framework to estimate the dynamics spectrum, or Koopman eigenvalues, from which those topological properties can be deduced. However, it is not always effective and accurate and, most importantly, not optimized to capture the Koopman eigenvalues. We propose a method that aims at enhancing the Dynamic Mode Decomposition algorithm performance with respect to the estimation of the dynamics spectrum, based on the cross-validation technique. We show that our method does not enable any improvement in case of linear local dynamics but allows a slight enhancement in case of nonlinear local dynamics. We finally expose a modified version of our method which leads to significantly better results but only for small networks.