scholarly journals Efficient sampling for polynomial chaos‐based uncertainty quantification and sensitivity analysis using weighted approximate Fekete points

2020 ◽  
Vol 36 (11) ◽  
Author(s):  
Kyle M. Burk ◽  
Akil Narayan ◽  
Joseph A. Orr
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Polynomial Chaos ◽  
Fekete Points ◽  
Efficient Sampling

Uncertainty quantification and sensitivity analysis of thermoacoustic stability with non-intrusive polynomial chaos expansion

2018 ◽  
Vol 189 ◽  
pp. 300-310 ◽  
Author(s):  
Alexander Avdonin ◽  
Stefan Jaensch ◽  
Camilo F. Silva ◽  
Matic Češnovar ◽  
Wolfgang Polifke
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion

Application of an Adaptive Polynomial Chaos Expansion on Computationally Expensive Three-Dimensional Cardiovascular Models for Uncertainty Quantification and Sensitivity Analysis

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Sjeng Quicken ◽  
Wouter P. Donders ◽  
Emiel M. J. van Disseldorp ◽  
Kujtim Gashi ◽  
Barend M. E. Mees ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Polynomial Chaos ◽  
Computational Cost ◽  
Three Dimensional ◽  
Polynomial Chaos Expansion ◽  
Patient Specific ◽  
Chaos Expansion ◽  
Model Input ◽  
Cardiovascular Models

When applying models to patient-specific situations, the impact of model input uncertainty on the model output uncertainty has to be assessed. Proper uncertainty quantification (UQ) and sensitivity analysis (SA) techniques are indispensable for this purpose. An efficient approach for UQ and SA is the generalized polynomial chaos expansion (gPCE) method, where model response is expanded into a finite series of polynomials that depend on the model input (i.e., a meta-model). However, because of the intrinsic high computational cost of three-dimensional (3D) cardiovascular models, performing the number of model evaluations required for the gPCE is often computationally prohibitively expensive. Recently, Blatman and Sudret (2010, “An Adaptive Algorithm to Build Up Sparse Polynomial Chaos Expansions for Stochastic Finite Element Analysis,” Probab. Eng. Mech., 25(2), pp. 183–197) introduced the adaptive sparse gPCE (agPCE) in the field of structural engineering. This approach reduces the computational cost with respect to the gPCE, by only including polynomials that significantly increase the meta-model’s quality. In this study, we demonstrate the agPCE by applying it to a 3D abdominal aortic aneurysm (AAA) wall mechanics model and a 3D model of flow through an arteriovenous fistula (AVF). The agPCE method was indeed able to perform UQ and SA at a significantly lower computational cost than the gPCE, while still retaining accurate results. Cost reductions ranged between 70–80% and 50–90% for the AAA and AVF model, respectively.

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