Computational uncertainty quantification in a probabilistic setting is a special case of a parametric problem. Parameter dependent state vectors lead via association to a linear operator to analogues of covariance, its spectral decomposition, and the associated Karhunen-Loève expansion. From this one obtains a generalised tensor representation. The parameter in question may be a tuple of number...

Important quantities in aerodynamic flow simulations are the aerodynamic force coefficients including the pressure induced and the viscous stress induced drag, lift and moment coefficients. In addition to the exact approximation of these quantities it is of increasing importance, in particular in the field of uncertainty quantification, to estimate the error in the computed quantities. In recen...

In numerous critical areas from across science and engineering, models and simulations share a common base of mathematical formulations and algorithms that are multi-physics, multi-scale and/or multi-domain in nature. The crucial demand for predictive computational results in these areas motivates the development of uncertainty quantification approaches for coupled models that feature multiple ...

The survival signature has been introduced to simplify quantification of reliability of systems which consist of components of different types, with multiple components of at least one of these types. The survival signature generalizes the system signature, which has attracted much interest in the theoretical reliability literature but has limited practical value as it can only be used for syst...

While there exist a number of mathematical approaches to modeling the spread of disease on a network, analyzing such systems in the presence of uncertainty introduces significant complexity. In scenarios where system parameters must be inferred from limited observations, general approaches to uncertainty quantification can generate approximate distributions of the unknown parameters, but these ...

We study the level-one irreducible highest weight representations of the quantum affine superalgebra Uq[ ̂ sl(N |1)], and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible Uq[ ̂ sl(N |1)]-modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multi-component super t− J model by usi...

Bound-to-Bound Data Collaboration (B2BDC) provides a natural framework for addressing both forward and inverse uncertainty quantification problems. In this approach, QOI (quantity of interest) models are constrained by related experimental observations with interval uncertainty. A collection of such models and observations is termed a dataset and carves out a feasible region in the parameter sp...

The locations of seismic events are used to infer reservoir properties and to guide future production activity, as well as to determine and understand the stress field. Thus, locating seismic events with uncertainty quantification remains an important problem. Using Bayesian analysis, a joint probability density function of all event locations was constructed from prior information about pickin...

This paper presents a comprehensive methodology that combines uncertainty quantification, propagation and robustness-based design optimization using a Bayesian framework. Two types of epistemic uncertainty regarding model inputs/parameters are emphasized: (1) uncertainty modeled as p-box, and (2) uncertainty modeled as interval data. A Bayesian approach is used to calibrate the uncertainty mode...