Complex Systems, Emergence, and Multiscale Analysis: A Tutorial and Brief Survey

Mankind has long been fascinated by emergence in complex systems. With the rapidly accumulating big data in almost every branch of science, engineering, and society, a golden age for the study of complex systems and emergence has arisen. Among the many values of big data are to detect changes in system dynamics and to help science to extend its reach, and most desirably, to possibly uncover new fundamental laws. Unfortunately, these goals are hard to achieve using black-box machine-learning based approaches for big data analysis. Especially, when systems are not functioning properly, their dynamics must be highly nonlinear, and as long as abnormal behaviors occur rarely, relevant data for abnormal behaviors cannot be expected to be abundant enough to be adequately tackled by machine-learning based approaches. To better cope with these situations, we advocate to synergistically use mainstream machine learning based approaches and multiscale approaches from complexity science. The latter are very useful for finding key parameters characterizing the evolution of a dynamical system, including malfunctioning of the system. One of the many uses of such parameters is to design simpler but more accurate unsupervised machine learning schemes.