Ποσοτικοποίηση Αβεβαιότητας μέσω (Αυθαίρετου) Πολυωνυμικού Αναπτύγματος Χάους με χρήση Γραμμικής Παλινδρόμησης και της Συζυγούς Μεθόδου

In modern computational science and engineering, Uncertainty Quantification (UQ) plays a pivotal role in enabling reliable and robust simulations by accounting for variabilities in input parameters.This diploma thesis investigates efficient UQ methodologies, with a particular focus on the implementation and enhancement of regression-based non-intrusive Polynomial Chaos Expansion (PCE), as well as its extension to adjoint-assisted as well as arbitrary PCE (aPCE) frameworks.The aim is to significantly reduce the computational cost of UQ in complex engineering systems, such as those governed by Computational Fluid Dynamics (CFD), without compromising accuracy.