Data-Driven Learning and Geometric Embedding for Reduction and Control of Complex Heterogeneous Networks

Washington University, Saint Louis MO

Investigators

Abstract

Complex systems in which multiple agents (components) affect each other dynamically are prevalent in nature and human society in different scales, such as neurons in the brain, bees in a hive, and human beings in a social network. Undesirable behavior of such systems, in the form of disease, economic collapse, rumor spreading, and social unrest, has generated considerable interest in understanding the dynamic structures of such complex networks and devising ways to control them. Despite the abundance of data, ease of access, and advances in data science, obtaining reliable models of such networks remains a very challenging problem. The scale of these emerging complex systems also poses a great difficulty. These obstacles also form a bottleneck for analyzing and engineering the dynamic structures (e.g., synchrony and clustering) and for controlling the collective behavior in such complex networks. This project will develop a unified data-driven framework to investigate fundamental questions regarding how to extract dynamics of a large-scale complex system or network from its simulation or measurement data, and how to control this system if the dynamics reconstruction is successful and reliable. The project will also support new initiatives to promote interdisciplinary education for students from traditionally underserved populations in local high schools in the city of St. Louis, MO, through the creation of summer research opportunities. By bridging systems and control theory with concepts and methods from algebraic geometry, time-series analysis, and machine learning, a unified data-driven framework will be established. Specifically, a novel approach based on spectral decomposition will be developed to extract the dynamics of a complex system and decode the topology of a complex network using its time-series data. The properties of the reconstructed network, e.g., connectivity and the coupling strength of nodes, will then be utilized to synthesize a dynamically-proximate reduced network that is tractable for control-theoretic analysis and design. Furthermore, novel topological and geometrical approaches will be derived to construct local and global embedding of high-dimensional data to low-dimensional manifolds, which will reveal hidden topological structures in large data sets and characterize transitions of flow of the underlying dynamical system. In collaboration with researchers in biology and chemistry, the network inference, dimensionality reduction, and control techniques will be applied to a diverse set of complex systems from cells to societies, for example, for decoding functional connectivity in cellular networks and analyzing social synchronization in groups of animals. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.