Inference, Causality and Control in Networks of Dynamical Systems: Data Science and Modeling Perspectives to Network Physiology with Implications for Artificial Intelligence

From genomic, proteomic and metabolic networks to microbial communities, neural systems and human network physiology of organ systems interactions, complex interdependent systems with distinct dynamics and intrinsic mechanisms of control display complex multi-scale spatio-temporal patterns that are frequently classified as non-linear, non-Gaussian, scale invariant and multi-fractal. While there is a wealth of theoretical research devoted to characterize first-, second-, and third-order statistics of networks (e.g., degree distributions, assortativity, clustering and squared clustering coefficients), only recently higher order statistics and geometric characterizations of complex networks has become a focus of investigation. Along these lines, mining the structure and dynamics of complex networks has opened new frontiers in research to establish connections between network topology and network function, infer their degree of emergence, self-organization, robustness, criticality, intelligence and complexity from temporal patterns in dynamic networks, and uncover universal conservation laws.

Despite recent progress in the theory of dynamic networks, there are fundamental methodological and conceptual challenges in understanding how global states and functions emerge in networks of diverse dynamical systems with time varying interactions and the basic principles of their hierarchical integration. Currently, we still do not have reliable estimation algorithms and a theoretical framework to assess and quantify the topology and global behavior of time-varying complex (weighted) networks as a function of interaction intensity, the embedding of metric spaces and the dynamics of individual nodes, and the diversity of coupling functional forms among network nodes. Moreover, in many practical situations related to investigations of biological and physiological systems from the sub-cellular to the organism levels, we can only partially observe the dynamics of complex networks, and we lack methodological approaches to investigate how global behaviors emerge in networks of diverse dynamical systems operating over a broad range of time scales. When mining the time-varying complex networks structure and dynamics, one has to also overcome various internal or external perturbations that can transiently or permanently mask the activity of certain nodes and their causal interactions. Understanding the multiscale dynamics of time-varying networks, detecting signs of instability hidden in noisy data, predicting rare extreme events and critical transitions in dynamical systems with time-varying interactions calls for radical mathematical and algorithmic tools to infer and quantify the dynamics of individual systems and their coupling. Novel AI and machine learning algorithms and architectures are needed to classify and predict the emergent behavior in dynamical networks based simultaneously on network topology and temporal patterns in network dynamics. In addition, new data science and artificial intelligence (AI) techniques are required to identify the unknown stimuli and unobserved variables in order to reconstruct the time-varying networks of dynamical systems from various heterogeneous nonstationary output data, model their fractal spatio-temporal dynamics and show how concepts from multifractal and differential geometry can help analyze and quantify their complexity. Lastly, we require mathematical foundations and algorithmic tools to establish connections between network dynamics and physiological states in health and disease, determine the most efficient network architecture to generate a given function, quantify key universalities, and identify new theoretical directions for artificial intelligence and machine learning based on biological and physiological principles.

The aim of this Research Topic is to coordinate interdisciplinary efforts and unify different visions, approaches and methodologies around the field of networks of dynamical systems. We welcome multidisciplinary contributions that review the current state of the art in different subfields of network science and their applications, opinion and review papers pointing towards urging open challenges, and original research articles. We aim for this Research Topic to provide a forward and visionary perspective on the emerging field of networks of dynamical systems, new insights into the mechanisms of communication and control in such networks, and a comprehensive understanding of the principles of integration across levels in biological and physiological systems.