Time-series–based prediction of complex oscillator networks via compressive sensing
Wen-Xu Wang, Rui Yang, Ying-Cheng Lai, Vassilios I. Kovanis, Mary Ann F. Harrison · Europhysics Letters (EPL) · 2011
Complex dynamical networks consisting of a large number of interacting units are ubiquitous in nature and society. There are situations where the interactions in a network of interest are unknown and one wishes to reconstruct the full topology of the network through measured time series. We present a general method based on compressive sensing. In particular, by using power series expansions to arbitrary order, we demonstrate that the network-reconstruction problem can be casted into the form X = G · a , where the vector X and matrix G are determined by the time series and a is a sparse vector to be estimated that contains all nonzero power series coefficients in the mathematical functions of all existing couplings among the nodes. Since a is sparse, it can be solved by the standard L 1 -norm technique in compressive sensing. The main advantages of our approach include sparse data requirement and broad applicability to a variety of complex networked dynamical systems, and these are illustrated by concrete examples of model and real-world complex networks.