Uncertainty Quantification for Numerical Solutions of the Nonlinear Partial Differential Equations by Using the Multi-Fidelity Monte Carlo Method

Du, Wenting; Jin, S.

doi:10.3390/app12147045

Cited by 1 publication

(1 citation statement)

References 36 publications

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“…Qian et al 38 proposed a multifidelity estimator for the main and total Sobol' indices, demonstrating its advantages on the Ishigami function and a 2D hydrogen combustion model. This method has also been applied to nonlinear Schroedinger and Bøøurgers equations, 39 to determine particle distributions in turbulent pipe flow, 40 and to analyze thermal distortions in the James Webb Space Telescope. 41 In the medical field, multifidelity SA has been used in cardiac electrophysiology, 42,43 but not for the analysis of vascular flow with fluid-structure interaction (FSI).…”

Section: Introductionmentioning

confidence: 99%

Global sensitivity analysis with multifidelity Monte Carlo and polynomial chaos expansion for vascular haemodynamics

Schäfer,

Schiavazzi,

Hellevik

et al. 2024

Numer Methods Biomed Eng

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Computational models of the cardiovascular system are increasingly used for the diagnosis, treatment, and prevention of cardiovascular disease. Before being used for translational applications, the predictive abilities of these models need to be thoroughly demonstrated through verification, validation, and uncertainty quantification. When results depend on multiple uncertain inputs, sensitivity analysis is typically the first step required to separate relevant from unimportant inputs, and is key to determine an initial reduction on the problem dimensionality that will significantly affect the cost of all downstream analysis tasks. For computationally expensive models with numerous uncertain inputs, sample‐based sensitivity analysis may become impractical due to the substantial number of model evaluations it typically necessitates. To overcome this limitation, we consider recently proposed Multifidelity Monte Carlo estimators for Sobol’ sensitivity indices, and demonstrate their applicability to an idealized model of the common carotid artery. Variance reduction is achieved combining a small number of three‐dimensional fluid–structure interaction simulations with affordable one‐ and zero‐dimensional reduced‐order models. These multifidelity Monte Carlo estimators are compared with traditional Monte Carlo and polynomial chaos expansion estimates. Specifically, we show consistent sensitivity ranks for both bi‐ (1D/0D) and tri‐fidelity (3D/1D/0D) estimators, and superior variance reduction compared to traditional single‐fidelity Monte Carlo estimators for the same computational budget. As the computational burden of Monte Carlo estimators for Sobol’ indices is significantly affected by the problem dimensionality, polynomial chaos expansion is found to have lower computational cost for idealized models with smooth stochastic response.

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