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 -