TY - JOUR

T1 - Time-series-based prediction of complex oscillator networks via compressive sensing

AU - Wang, Wen Xu

AU - Yang, Rui

AU - Lai, Ying-Cheng

AU - Kovanis, Vassilios

AU - Harrison, Mary Ann F

PY - 2011/5

Y1 - 2011/5

N2 - 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=Ga, 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 L1-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.

AB - 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=Ga, 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 L1-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.

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U2 - 10.1209/0295-5075/94/48006

DO - 10.1209/0295-5075/94/48006

M3 - Article

AN - SCOPUS:79957517337

SN - 0295-5075

VL - 94

JO - EPL

JF - EPL

IS - 4

M1 - 48006

ER -