Scalable Uncertainty Quantification in Complex Dynamic Networks

In this paper we address the problem of uncertainty management for robust design, and verification of large dynamic networks whose performance is affected by an equally large number of uncertain parameters. Many such networks (e.g. power, thermal and communication networks) are often composed of weakly interacting subnetworks. We propose an iterative scheme that exploits such weak interconnections to overcome dimensionality curse associated with traditional uncertainty quantification methods (e.g. Quasi Monte Carlo, Probabilistic Collocation) and accelerate uncertainty propagation in systems with large number of uncertain parameters. This approach relies on integrating graph theoretic methods and waveform relaxation with traditional uncertainty quantification techniques like probabilistic collocation and polynomial chaos. We analyze convergence properties of this scheme and illustrate it on two examples.