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...