Author ORCID Identifier

https://orcid.org/0009-0008-1599-8850

Semester

Summer

Date of Graduation

2026

Document Type

Dissertation (Campus Access)

Degree Type

PhD

College

Statler College of Engineering and Mineral Resources

Department

Chemical and Biomedical Engineering

Committee Chair

David Mebane

Committee Co-Chair

Fernando Lima

Committee Member

Yuhe Tian

Committee Member

Mario Perhinschi

Committee Member

Katelyn Griffith

Abstract

Machine learning models have revolutionized chemical engineering by providing powerful data-driven alternatives to traditional first-principles modeling. While Artificial Neural Networks (ANNs) have driven much of this progress, there are other machine learning models, which can offer advantages when compared to ANNs for the typical problems found in chemical engineering. Gaussian Processes (GPs) are one such model, providing probabilistic predictions that perform well with small, non-linear datasets. However, standard GPs face limitations in scalability and adaptability, particularly for real-time control applications and complex physics-informed modeling tasks. This dissertation addresses these gaps by advancing frameworks using decomposed GPs and developing novel formulations and frameworks that enhance both computational efficiency and physical interpretation of GP approximations. The research identifies two primary deficiencies in current literature: the underutilization of prior informed Bayesian methods in online control contexts and the lack of GP integration within Physics-Informed Machine Learning (PIML) loss functions. To bridge these gaps, this work proposes a suite of algorithms that leverage the BSS-ANOVA basis set within the Forward-variable Karhunen Loeve (FoKL) framework to tackle both of these issues by systematically integrating prior information and enabling non-linear multi-GP assessment. The work is structured around four specific aims, alternating between mathematical derivation and practical validation on real-world systems. The first aim is the mathematical derivation and implementation of Strong Priors within the FoKL framework. Traditional approaches often rely on weak or non-informative priors, failing to fully utilize historical data. This research formulates a robust Bayesian approach that encodes prior knowledge as probability distributions for model coefficients, guiding term selection and training. To validate the efficacy of the Strong Prior formulation, the second aim applies this technique to an online Model Predictive Control (MPC) system for a cascading tanks experiment. In this dynamic environment, the control algorithm must be updated incrementally to learn system dynamics in real-time. The third aim introduces a novel Embedded Gaussian Processes formulation methodology designed for non-linear, physics-informed models. This methodology uses PIML principles to simultaneously assess multiple GP estimations, offering a streamlined alternative to architectures like Physics-Informed Neural Networks (PINNs). Finally, the fourth aim serves as a validation of the Embedded GP formulation methodology through its application to electrochemical CO2 electrolysis. This research develops a scientific model of the electrolysis process and uses an Embedded GP formulation for selected, physically meaningful parameters to improve the predictive accuracy of the model.

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