Uncertainty Quantification in Computational Science

Abstract

In the past three decades, computer simulation tools have achieved widespread use in the design and analysis of engineering devices. This has shortened the overall product design cycle and it has also provided better understanding of the operating behavior of the systems of interest. As a consequence, numerical simulations have lead to a reduction of physical prototyping and to lower costs. In spite of this considerable success, it remains difficult to provide objective confidence levels in quantitative information obtained from numerical predictions. The complexity arises from the amount of uncertainties related to the inputs of any computation attempting to represent a physical system. As a result, especially in the area of reliability and safety, physical testing remains the dominant mechanism of certification of new devices. Rigorous quantification of the errors and uncertainties introduced in numerical simulations is required to establish objectively their predictive capabilities (the difference between errors and uncertainties will be given later). Procedures to establish the quality of numerical simulations have been organized within the framework of Verification and Validation (V&V) activities [1]. Verification is a mathematical process that aims at answering the question: “are we solving the equations correctly?”. The objective is to quantify the errors associated to the algorithms used to obtain the solution of the governing equations. Validation, on the other hand, aims at answering the question “are we solving the correct equations?”. The goal is to identify the appropriateness of the selected mathematical/physical formulation to represent the device to be analyzed. Validation always involves comparisons of the numerical predictions to reality, whereas verification only involves numerical analysis and tests.

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