Complex networks are pervasive in critical infrastructures such as energy, transportation, and cyber systems. In order to operate successfully in uncertain and adversarial environments, complex networks must mitigate natural and malicious disruptions. The goal of network resilience is to develop mitigation strategies that ensure performance, connectivity, and functionality during and after a disturbance. Such mitigation strategies will need to incorporate both discrete (locations of nodes/edges) and continuous (control inputs) decision variables that affect network dynamics at multiple time-scales, creating a hybrid system. We propose to investigate and develop a dynamic hybrid submodular framework for network resilience across multiple time-scales. We will identify fundamental properties (e.g., safety, stability, connectivity) that need to be maintained under topology changes, failures, and attacks, which we term resilient network invariants. To ensure computational tractability, we will explore hybrid submodular structures of the invariants, which generalize submodular optimization techniques from discrete functions to functions with both discrete and continuous variables. We will develop submodular techniques to model and mitigate large statistical models such as Deep Neural Networks that are used for perception and decision-making by complex networks.

Sponsor: Air Force Office of Scientific Research  (AFOSR)