Robust dynamical network reconstruction

Abstract — This paper addresses the problem of robustly reconstructing network structure from input-output data. Pre-vious work identified necessary and sufficient conditions for network reconstruction of LTI systems, assuming perfect mea-surements (no noise) and perfect system identification. This paper assumes that the previously identified necessary and sufficient conditions for network reconstruction are satisfied but here we additionally take into account noise and unmodelled dynamics (including nonlinearities). In order to identify the network structure that generated the data, we compute the smallest distances between the measured data and the data that would have been generated by particular Boolean networks. By striking a compromise between such distance and network complexity, we provide methods for revealing the correct network structure from data despite the presence of noise and nonlinearities. I