A Complete Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing

This paper gives a broad overview of a complete framework for assessing the predictive uncertainty of scientific computing applications. The framework is complete in the sense that it treats both types of uncertainty (aleatory and epistemic) and incorporates uncertainty due to the form of the model and any numerical approximations used. Aleatory (or random) uncertainties in model inputs are treated using cumulative distribution functions, while epistemic (lack of knowledge) uncertainties are treated as intervals. Approaches for propagating both types of uncertainties through the model to the system response quantities of interest are discussed. Numerical approximation errors (due to discretization, iteration, and round off) are estimated using verification techniques, and the conversion of these errors into epistemic uncertainties is discussed. Model form uncertainties are quantified using model validation procedures, which include a comparison of model predictions to experimental data and then extrapolation of this uncertainty structure to points in the application domain where experimental data do not exist. Finally, methods for conveying the total predictive uncertainty to decision makers are presented.