Author ORCID Identifier
https://orcid.org/0009-0003-2868-4977
Defense Date
2026
Document Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Systems Modeling and Analysis
First Advisor
Dr. J. Paul Brooks
Second Advisor
Dr. Craig E. Larson
Abstract
Scientific discovery increasingly relies on identifying interpretable mathematical relation- ships within high-dimensional, noisy datasets. Within computational scientific discovery, Graffiti-like automated mathematical conjecturing systems generate symbolic candidate expressions that capture empirical relationships, but often produce an unmanageable number of candidates, shifting the computational bottleneck from generation to selection. This dissertation presents a dual approach to principled expression selection. First, we introduce the Structural Average Model (SAM), an optimization-based framework that identifies a “best” set of symbolic expressions by balancing robustness, fidelity, and parsi- mony. Second, we formulate the selection process as a Markov Decision Process (MDP) and employ reinforcement learning to optimize set-level interpretability, moving beyond simple additive objectives. We provide theoretical guarantees for the well-posedness and convergence of these methods. Additionally, we demonstrate the utility of these frameworks in forensic microbiome analysis, where the discovery of interpretable symbolic bounds for body fluid and mixture identification is the key to establishing courtroom admissibility and expert testimony. Finally, we demonstrate its application to graph theory, pushing the boundaries of current knowledge regarding the NP-hard independence number problem. This work advances computational scientific discovery by providing principled optimization and learning methodologies for selecting interpretable symbolic conjectures while preserving the central role of human investigation.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
8-5-2026
Included in
Applied Mathematics Commons, Computer Sciences Commons, Forensic Science and Technology Commons, Mathematics Commons, Statistics and Probability Commons