Prevalence and scalable control of localized networks

TL;DR

This paper introduces a concept of network locality that enables scalable control of large nonlinear networks by focusing on localized regions, significantly reducing computational and communication costs.

Contribution

It develops a new locality-based framework for controlling large networks, including algorithms for controllability, driver node placement, and local feedback design, validated on real and model networks.

Findings

Network locality is nearly universal across various networks.

Localized control actions are concentrated in small neighborhoods.

Algorithms achieve near-optimal control with much lower computational costs.

Abstract

The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast with network size. Here, we introduce a notion of network locality that can be exploited to make the control of networks scalable even when the dynamics are nonlinear. We show that network locality is captured by an information metric and is almost universally observed across real and model networks. In localized networks, the optimal control actions and system responses are both shown to be necessarily concentrated in small neighborhoods induced by the information metric. This allows us to develop localized algorithms for determining network controllability and optimizing the placement of driver nodes. This also allows us to develop a localized algorithm for designing local feedback controllers that approach the performance of the corresponding best global controllers while incurring a computational cost orders-of-magnitude lower. We validate the locality, performance, and efficiency of the algorithms in Kuramoto oscillator networks as well as three large empirical networks: synchronization dynamics in the Eastern U.S. power grid, epidemic spreading mediated by the global air transportation network, and Alzheimer's disease dynamics in a human brain network. Taken together, our results establish that large networks can be controlled with computation and communication costs comparable to those for small networks.