Uncertainty Quantification in Machine Learning Models Via Gaussian Process Regression: A Comparative Study

As the use of Machine learning models in science and engineering continues to increase, there is an increasing need for quantifying the uncertainties inherent in the predictions of these models. The more complex a model is, the more the uncertainties in its predictions increase. Amongst the plethora of methodologies used in quantifying uncertainties lies Gaussian Process Regression (GPR). GPR surmounts some of the popular shortfalls of other state-of-the-art methodologies. Although GPR has some quick wins in its application for uncertainty quantification, it is plagued with some shortfalls, such as scalability issues when the feature space increases as well as an increase in computational time. Our current study compares the computational time besides quantifying the uncertainties in the predictions from the machine learning models across different covariance structures. Specifically, we used 2D diffraction patterns recorded on a 2D area detector using high-energy X-ray diffraction (HEXRD) to predict the volume fraction of the β-phase of Ti-6Al-4v (Ti64). To achieve this, we reduced the features through Principal Component Analysis and used components that account for 95%, 99% and 99.5% variation in the 2D diffraction images for each of the four datasets used respectively. With the current methodology, we have scaled the application of GPR to high-dimensional cases while we are exploring other methodologies that will reduce the computational time when the sample size becomes large. The goal of the project is to integrate these methodologies to achieve scalability with shorter computational time