Uncertainty quantification for linear hyperbolic equations with stochastic process or random field coefficients

Abstract

In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein-Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings.

Parameter Identification in Population Balance Models Using Uncertainty and Sensitivity Analysis

“…Thus, it becomes inevitable for a modeler to identify and quantify various sources of uncertainty in order to obtain actual model estimates. 1,2 Uncertainty quantification (UQ) is, thus, essential to report the uncertainties riddled in model predictions to maintain the credibility of the mathematical formulation of a model. 3,4 Parametric uncertainty deals with estimating values for several unknown parameters that could be estimated using experimental observations of the physical process.…”

“…This variability of a model prediction should be as minimum as possible to be confident about the results produced by the model. Thus, it becomes inevitable for a modeler to identify and quantify various sources of uncertainty in order to obtain actual model estimates. , …”