  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.
