Introduction to Focus Issue: When Machine Learning Meets Complex Systems: Networks, Chaos, and Nonlinear Dynamics

Machine learning (ML), a subset of artificial intelligence, refers to methods that have the ability to “learn” from experience, enabling them to carry out designated tasks. Examples of machine learning tasks are detection, recognition, diagnosis, optimization, and prediction. Machine learning can also often be used in different areas of complex systems research involving identification of the basic system structure (e.g., network nodes and links) and study of the dynamic behavior of nonlinear systems (e.g., determining Lyapunov exponents, prediction of future evolution, and inferring causality of interactions). Conversely, machine learning procedures, such as “reservoir computing” and “long short-term memory”, are often dynamical in nature, and the understanding of when, how, and why they are able to function so well can potentially be addressed using tools from dynamical systems theory. For example, a recent consequence of this has been the realization of new optics-based physical realizations of reservoir computers. In the area of the application of machine learning to complex physical problems, it has been successfully used to construct and recover the complex structures and dynamics of climate networks, genetic regulatory systems, spatiotemporal chaotic systems, and neuronal networks. On the other hand, complex systems occur in a wide variety of practical settings, including engineering, neuroscience, social networks, geoscience, economics, etc. Since complex systems research and machine learning have a close relationship between each other, they provide a common basis for a wide range of cross-disciplinary interactions. Hence, exploring how machine learning works for issues involving complex systems has been a subject of significant research interest. With the advent of machine learning, it has become possible to develop new algorithms and strategies for identification, control, and data analytics of complex systems, thereby promoting the application of machine learning in many fields.

The main focus of this Focus Issue is on the new algorithms, strategies, and techniques with machine learning applied to complex systems and on applying complex system techniques to leverage the performance of machine learning techniques with high-efficiency. This Focus Issue provides a platform to facilitate interdisciplinary research and to share the most recent developments in various related fields. The specific areas represented include reservoir computing, modeling of complex systems, prediction and manipulations of complex systems, data-driven research, control and optimization, and applications.

For the Focus Issue, 58 papers were accepted for publication. In the following, we will divide the editorial into the following five parts, including reservoir computing, model of complex systems, prediction and manipulations of complex systems, data-driven research, control and optimization, and applications.