Predicting and Controlling Complex Networks

Abstract

The research on the topology and dynamics of complex networks is one of the most focused area in complex system science. The goals are to structure our understanding of the real-world social, economical, technological, and biological systems in the aspect of networks consisting a large number of interacting units and to develop corresponding detection, prediction, and control strategies. In this highly interdisciplinary field, my research mainly concentrates on universal estimation schemes, physical controllability, as well as mechanisms behind extreme events and cascading failure for complex networked systems.Revealing the underlying structure and dynamics of complex networked systems from observed data without of any specific prior information is of fundamental importance to science, engineering, and society. We articulate a Markov network based model, the sparse dynamical Boltzmann machine (SDBM), as a universal network structural estimator and dynamics approximator based on techniques including compressive sensing and K-means algorithm. It recovers the network structure of the original system and predicts its short-term or even long-term dynamical behavior for a large variety of representative dynamical processes on model and real-world complex networks.One of the most challenging problems in complex dynamical systems is to control complex networks. Upon finding that the energy required to approach a target state with reasonable precision is often unbearably large, and the energy of controlling a set of networks with similar structural properties follows a fat-tail distribution, we identify fundamental structural "short boards" that play a dominant role in the enormous energy and offer a theoretical interpretation for the fat-tail distribution and simple strategies to significantly reduce the energy.Extreme events and cascading failure, a type of collective behavior in complex networked systems, often have catastrophic consequences. Utilizing transportation and evolutionary game dyi namics as prototypical settings, we investigate the emergence of extreme events in simplex complex networks, mobile ad-hoc networks and multi-layer interdependent networks. A striking resonancelike phenomenon and the emergence of global-scale cascading breakdown are discovered. We derive analytic theories to understand the mechanism of control at a quantitative level and articulate cost-effective control schemes to significantly suppress extreme events and the cascading process.