Uncertainty quantification in neutron transport with generalized polynomial chaos using the method of characteristics

2012 ◽  
Vol 45 ◽  
pp. 14-28 ◽  
Author(s):  
D.A.F. Ayres ◽  
M.D. Eaton ◽  
A.W. Hagues ◽  
M.M.R. Williams
Keyword(s):  
Uncertainty Quantification ◽  
Method Of Characteristics ◽  
Polynomial Chaos ◽  
Neutron Transport ◽  
Generalized Polynomial Chaos ◽  
The Method Of Characteristics ◽  
Generalized Polynomial

A Metamodeling Approach for Instant Severity Assessment and Uncertainty Quantification of Iliac Artery Stenoses

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
S. G. H. Heinen ◽  
K. Gashi ◽  
D. A. F van den Heuvel ◽  
J. P. P. M. de Vries ◽  
F. N. van de Vosse ◽  
...  
Keyword(s):  
Uncertainty Quantification ◽  
Iliac Artery ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Generalized Polynomial Chaos ◽  
Pressure Drops ◽  
Output Uncertainty ◽  
Generalized Polynomial ◽  
2D Model

Abstract Two-dimensional (2D) or three-dimensional (3D) models of blood flow in stenosed arteries can be used to patient-specifically predict outcome metrics, thereby supporting the physicians in decision making processes. However, these models are time consuming which limits the feasibility of output uncertainty quantification (UQ). Accurate surrogates (metamodels) might be the solution. In this study, we aim to demonstrate the feasibility of a generalized polynomial chaos expansion-based metamodel to predict a clinically relevant output metric and to quantify the output uncertainty. As an example, a metamodel was constructed from a recently developed 2D model that was shown to be able to estimate translesional pressure drops in iliac artery stenoses (−0.9 ± 12.7 mmHg, R2 = 0.81). The metamodel was constructed from a virtual database using the adaptive generalized polynomial chaos expansion (agPCE) method. The constructed metamodel was then applied to 25 stenosed iliac arteries to predict the patient-specific pressure drop and to perform UQ. Comparing predicted pressure drops of the metamodel and in vivo measured pressure drops, the mean bias (−0.2 ± 13.7 mmHg) and the coefficient of determination (R2 = 0.80) were as good as of the original 2D computational fluid dynamics (CFD) model. UQ results of the 2D and metamodel were comparable. Estimation of the uncertainty interval using the original 2D model took 14 days, whereas the result of the metamodel was instantly available. In conclusion, it is feasible to quantify the uncertainty of the output metric and perform sensitivity analysis (SA) instantly using a metamodel. Future studies should investigate the possibility to construct a metamodel of more complex problems.

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