%0 Journal Article %A Surana, Amit %A Sahai, Tuhin %A Banaszuk, Andrzej %D 2012 %I Begell House %K collocation, polynomial chaos, graph decomposition, waveform relaxation %N 4 %P 413-439 %R 10.1615/Int.J.UncertaintyQuantification.2012004138 %T ITERATIVE METHODS FOR SCALABLE UNCERTAINTY QUANTIFICATION IN COMPLEX NETWORKS %U https://www.dl.begellhouse.com/journals/52034eb04b657aea,43e225911b944538,1ab26df934531fb2.html %V 2 %X 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 intrusive and nonintrusive iterative schemes that exploit such weak interconnections to overcome the dimensionality curse associated with traditional uncertainty quantification methods (e.g., generalized polynomial chaos, probabilistic collocation) and accelerate uncertainty propagation in systems with a large number of uncertain parameters. This approach relies on integrating graph theoretic methods and waveform relaxation with generalized polynomial chaos, and probabilistic collocation, rendering these techniques scalable. We introduce an approximate Galerkin projection that based on the results of graph decomposition computes "strong" and "weak" influence of parameters on states. An appropriate order of expansion, in terms of the parameters, is then selected for the various states. We analyze convergence properties of this scheme and illustrate it in several examples. %8 2012-06-05