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This work introduces the network uncertainty quantification (NetUQ) methodfor performing uncertainty propagation in systems composed of interconnectedcomponents. The method assumes the existence of a collection of components,each of which is characterized by exogenous-input random variables,endogenous-input random variables, output random variables, and a localuncertainty-propagation operator that computes output random variables frominput random variables. The method assembles the full-system network byconnecting components, which is achieved simply by associating endogenous-inputrandom variables for each component with output random variables from othercomponents; no other inter-component compatibility conditions are required. Thenetwork uncertainty-propagation problem is: Compute output random variables forall components given all exogenous-input random variables. To solve thisproblem, the method applies classical relaxation methods (i.e., Jacobi andGauss--Seidel iteration with Anderson acceleration), which require onlyblack-box evaluations of component uncertainty-propagation operators. Comparedwith other available methods, this approach is applicable to any networktopology, promotes component independence by enabling components to employtailored uncertainty-propagation operators, supports general functionalrepresentations of random variables, and requires no offline preprocessingstage. Also, because the method propagates functional representations of randomvariables throughout the network (and not, e.g., probability densityfunctions), the joint distribution of any set of random variables throughoutthe network can be estimated a posteriori in a straightforward manner. Weperform supporting convergence and error analysis and execute numericalexperiments that demonstrate the weak- and strong-scaling performance of themethod.

The network uncertainty quantification method for propagating uncertainties in component-based systems