Volume 94, Number 4, May 2011
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||16 May 2011|
Time-series–based prediction of complex oscillator networks via compressive sensing
School of Electrical, Computer and Energy Engineering, Arizona State University - Tempe, AZ 85287, USA
2 Department of Physics, Arizona State University - Tempe, AZ 85287, USA
3 Sensors Directorate - 2241 Avionics Circle,Wright Patterson AFB, OH 45433, USA
4 Physical Sciences and Technology, Scientific Research Group, WVHTC Foundation - Fairmont, WV 26554, USA
Accepted: 13 April 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 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.
PACS: 89.75.Hc – Networks and genealogical trees / 89.20.Hh – World Wide Web, Internet / 05.10.-a – Computational methods in statistical physics and nonlinear dynamics
© EPLA, 2011
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