Doctoral Dissertations

Date of Award

8-2025

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Ioannis Sgouralis

Committee Members

Manolis Doxastakis, Olivia Feldman, Xinyue Zhao

Abstract

This dissertation explores the application of statistical learning frameworks to various challenges in the polymer chemistry and microbiology modeling domains. The underlying techniques of these frameworks are Bayesian methods, rigorous mathematical techniques, advanced Markov Chain Monte Carlo (MCMC) practices, and continuous integration of domain knowledge to achieve results. Specifically, we develop a Gillespie algorithm-based statistical learning polymerization tracking scheme to produce processable polyester networks. To aid understanding of the individual monomer contributions of acid and alcohol monomers in the formation of complex polyester structure-property relations, we implement a Bayesian learning framework. We then extend this framework by leveraging matrix operation simplifications to bring our modeling schemes up to speed with the modern cheminformatics computational requirements. For each of these applications in polymer modeling, we demonstrate the ability of our methods to make accurate predictions pertinent to real experimental data, while offering insights that extend beyond traditional learning methods. We implement statistical learning innovations for microbiology modeling tailored to address the challenges of initial value problem (IVP) parameter estimation, which are exacerbated by data aggregation conditions. Here, the sampling process of the statistical learning framework is heavily modified to address complex constraints and data structures that regular MCMC methods encounter. This method is demonstrated on real experimental batch-culture data and provides valuable information on the IVP parameter posterior distributions.

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