Iterative Methods for Scalable Uncertainty Quantification in Complex Networks

TL;DR

This paper introduces scalable iterative methods combining graph theory and waveform relaxation with polynomial chaos and collocation techniques to efficiently manage uncertainty in large, complex networks with many uncertain parameters.

Contribution

It presents novel intrusive and non-intrusive iterative schemes that exploit weak network interconnections to overcome the curse of dimensionality in uncertainty quantification.

Findings

Methods are scalable for large networks.

Convergence properties are analyzed.

Illustrated on several complex network examples.

Abstract

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 non-intrusive iterative schemes that exploit such weak interconnections to overcome dimensionality curse associated with traditional uncertainty quantification methods (e.g. generalized Polynomial Chaos, 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 generalized Polynomial Chaos, and Probabilistic Collocation, rendering these techniques scalable. We analyze convergence properties of this scheme and illustrate it on several examples.