Abstract

This PhD thesis focuses on the non-intrusive and semi-intrusive uncertainty quantification (UQ) analysis of the in-stent restenosis (ISR) multiscale model. We study the uncertainty forward propagation problems and apply various surrogate modelling techniques, such as reduced-order modelling and Gaussian process to reduce the expensive computational cost of the multiscale model in the UQ. In Chapter 2, a comparison of non-intrusive and semi-intrusive UQ methods based on the ISR2D model is presented and discussed. The results on uncertainty propagation allow us to draw conclusions on the advantages and limitations of these methods. A UQ of ISR3D with four biological uncertain parameters is studied in Chapter 3. A surrogate model, based on Gaussian process regression with proper orthogonal decomposition, was developed and subsequently used for model response evaluation in the UQ. A detailed analysis of the uncertainty propagation and sensitivity analysis is presented. Chapter 4 presents a data-driven surrogate model for blood flow simulations in unparameterised vessels. The surrogate model is based on non-intrusive reduced-order modelling and surface registration. Two examples of blood flow through a stenosis and a bifurcation are analysed. Chapter 5 introduces a series of UQ patterns for efficient UQ of multiscale models, and categorises them by the level of intrusiveness and optimization method. We demonstrate how these patterns can be implemented in multiscale models, using the formalism of the multiscale modelling and simulation framework.