Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems

摘要

The problem of reconstructing nonlinear and complex dynamical systems frommeasured data or time series is central to many scientific disciplinesincluding physical, biological, computer, and social sciences, as well asengineering and economics. In this paper, we review the recent advances in thisforefront and rapidly evolving field, aiming to cover topics such ascompressive sensing (a novel optimization paradigm for sparse-signalreconstruction), noised-induced dynamical mapping, perturbations, reverseengineering, synchronization, inner composition alignment, global silencing,Granger Causality and alternative optimization algorithms. Often, these rely onvarious concepts from statistical and nonlinear physics such as phasetransitions, bifurcation, stabilities, and robustness. The methodologies havethe potential to significantly improve our ability to understand a variety ofcomplex dynamical systems ranging from gene regulatory systems to socialnetworks towards the ultimate goal of controlling such systems. Despite recentprogress, many challenges remain. A purpose of this Review is then to point outthe specific difficulties as they arise from different contexts, so as tostimulate further efforts in this interdisciplinary field.