User:Sez Atamturktur

Model Validation and Uncertainty Quantification

In many branches of science and engineering computer simulations have become integral to the design and analysis of complex systems. This is made feasible by the increasing computing power of advanced computer technologies and by the development of numerical methods and algorithms necessary for efficient computation. These simulation models however, can only provide an approximation of reality, and thus the validity of the model predictions, particularly those that support high-consequence decision making, must be evaluated. The accuracy and precision of model predictions are hindered by three fundamental factors: (i) the inexactness or incompleteness of the model, (ii) uncertainty in model parameters, and (iii) uncertainty in numerical calculations. The first factor is concerned with the inexactness or incompleteness of the physics of the model which arises from our lack of knowledge about a complex phenomenon or simplifying assumptions made to describe such phenomena. For example, assuming the material behavior to be linear in the numerical model when in fact it is nonlinear would result in inexact solutions. Uncertain model parameters, the second factor, are the variables known to the analyst, while neither their exact values nor distributions are known. The third factor, numerical uncertainties, includes the uncertainties in the numerical calculations such as round-off, truncation or discretization errors. The first two forms of uncertainties can be addressed through various model validation procedures that aim to answer the following question: Are we solving the right equations? Validation procedures address the inherent disagreement between model prediction and reality and involve sensitivity analysis, model calibration and uncertainty quantification. The third form of uncertainty can be addressed through rigorous verification procedures that aim to answer the following question: Are we solving the equations right? Verification procedures address the mathematical inaccuracies in both the numerical code and the mathematical solution of equations. Simulation models, to be used in a predictive manner, must first undergo a rigorous verification, experiment-based validation and uncertainty quantification (V&V). The ultimate objective of V&V is to reduce the uncertainties and biases caused by these three factors, thus improving the predictive capability of the simulation model.