providing estimations of uncertainty. By leveraging a defined prior, GPR facilitates the derivation of a prior distribution from labeled data through Bayesian inference, embodying a principled approach to UQ. A critical component of GPR is the kernel function, also known as the covariance function, such as the Radial Basis Function (RBF) or exponential kernel. This function underpins the correlation structure across the variable space, enabling nuanced modeling of data relationships. Additionally, GPR permits the incorporation of noise into the data or kernel function, a mechanism that serves to refine the precision of uncertainty estimates. Aleatoric uncertainty is explicitly captured through a noise term in the Gaussian likelihood, while epistemic uncertainty is represented by the predictive variance derived from the kernel function. This dual capability allows GPR to simultaneously model variability inherent in the data and gaps in the model's knowledge.