A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing

An overview of a comprehensive framework is given for estimating the predictive uncertainty of scientific computing applications. The framework is comprehensive in the sense that it treats both types of uncertainty (aleatory and epistemic), incorporates uncertainty due to the mathematical form of th...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 200; no. 25; pp. 2131 - 2144
Main Authors: Roy, Christopher J., Oberkampf, William L.
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 15.06.2011
Elsevier
Subjects:
Applied sciences
Compressible flows; shock and detonation phenomena
Computation
Computational methods in fluid dynamics
Computational simulation
Computer science; control theory; systems
Computer simulation
Discretization
Errors
Estimating
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Mathematical models
Modeling
Physics
Propagation
Simulation
Software
Supersonic and hypersonic flows
Uncertainty
Uncertainty quantification
Validation
Verification
Validation
Uncertainty quantification
Verification
Modeling
Computational simulation
Uncertainty
Error estimation
Quantization
Probability distribution
Numerical approximation
Interval analysis
Uncertain system
Model matching
Discretization
Incomplete information
Random variable
Experimental data
Probabilistic approach
Computational fluid dynamics
Decision making
Wind tunnel test
Conversion
Extrapolation
Scientific computation
Statistical model
Approximation error
Artificial intelligence
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary:An overview of a comprehensive framework is given for estimating the predictive uncertainty of scientific computing applications. The framework is comprehensive in the sense that it treats both types of uncertainty (aleatory and epistemic), incorporates uncertainty due to the mathematical form of the model, and it provides a procedure for including estimates of numerical error in the predictive uncertainty. Aleatory (random) uncertainties in model inputs are treated as random variables, while epistemic (lack of knowledge) uncertainties are treated as intervals with no assumed probability distributions. Approaches for propagating both types of uncertainties through the model to the system response quantities of interest are briefly discussed. Numerical approximation errors (due to discretization, iteration, and computer round off) are estimated using verification techniques, and the conversion of these errors into epistemic uncertainties is discussed. Model form uncertainty is quantified using (a) model validation procedures, i.e., statistical comparisons of model predictions to available experimental data, and (b) 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. The different steps in the predictive uncertainty framework are illustrated using a simple example in computational fluid dynamics applied to a hypersonic wind tunnel.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2011.03.016