Bayesian Inductive Learner for Graph Resiliency under uncertainty

In the quest to improve efficiency, interdependence and complexity are becoming defining characteristics of modern engineered systems. With increasing vulnerability to cascading failures, it is imperative to understand and manage the risk and uncertainty associated with such engineered systems. Graph theory is a widely used framework for modeling interdependent systems and to evaluate their resilience to disruptions. Most existing methods in resilience analysis are based on an iterative approach that explores each node/link of a graph. These methods suffer from high computational complexity and the resulting analysis is network specific. Additionally, uncertainty associated with the underlying graphical model further limits the potential value of these traditional approaches. To overcome these challenges, we propose a Bayesian graph neural network-based framework for quickly identifying critical nodes in a large graph. while systematically incorporating uncertainties. Instead of utilizing the observed graph for training the model, a MAP estimate of the graph is computed based on the observed topology, and node target labels. Further, a Monte-Carlo (MC) dropout algorithm is incorporated to account for the epistemic uncertainty. The fidelity and the gain in computational complexity offered by the Bayesian framework are illustrated using simulation results.