American Institute of Aeronautics and Astronautics 092407 1 A Complete Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing (Invited) Christopher J. Roy 1 Virginia Polytechnic Institute and State University, Blacksburg, Virginia William L. Oberkampf 2 Consultant, Austin, Texas 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. I. Introduction cientific computing plays an ever-growing role in predicting the behavior of natural and engineered systems. In many cases, scientific computing is based on mathematical models that take the form of highly-coupled systems of nonlinear partial differential equations. The application of a model to produce a result, often including associated numerical approximation errors, is called a simulation. While scientific computing has undergone extraordinary increases in sophistication over the years, a fundamental disconnect often exists between simulations and practical applications. Whereas the simulations are generally deterministic in nature, applications are steeped in uncertainty arising from a number of sources such as those due to manufacturing processes, natural material variability, initial conditions, condition of the system, and the system surroundings. Furthermore, the modeling and simulation process itself introduces uncertainty related to the form of the model as well as the numerical approximations employed in the simulations. The former is commonly addressed through model validation, while the latter is addressed by code and solution verification. Each of these different sources of uncertainty must be estimated and included in order to estimate the total uncertainty in a simulation prediction. In addition, an understanding of the sources of the uncertainty can provide guidance on how to reduce uncertainty in the prediction in the most efficient and cost- effective manner. Information on the magnitude, composition, and sources of uncertainty in simulation predictions is critical in the decision-making process for natural and engineered systems. Without forthrightly estimating and clearly presenting the total uncertainty in a prediction, decision makers are ill advised, possibly resulting in inadequate safety, reliability, and performance of the system. This paper presents a high level overview of our comprehensive framework for verification, validation, and uncertainty quantification (VV&UQ) in scientific computing. This framework has much in common with previous work in VV&UQ, but it also includes new concepts for estimating and combining various uncertainties. For more details on the approach, see Ref. [1]. The organization of this paper is as follows. First, the two different types of 1 Associate Professor, cjroy@vt.edu, Associate Fellow AIAA. 2 Consultant, wloconsulting@gmail.com, AIAA Fellow. S 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition 4 - 7 January 2010, Orlando, Florida AIAA 2010-124 Copyright © 2010 by Christopher J. Roy and William L. Oberkampf. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.