Abstract

Mathematical modeling is an integral part of science, including atomistic-scale simulations in materials science for investigating material properties. These simulations depend on interatomic potentials (IPs), which define the potential energy surface governing atomic motion. A central challenge is developing IPs that accurately capture the relevant features of this surface to enable accurate predictions of material properties. Equally important is assessing the reliability and precision of these predictions through uncertainty quantification (UQ), especially for large-scale simulations where ground-truth data are scarce and uncertainties often serve as proxies for predictive confidence. However, many complex models exhibit sloppiness, characterized by numerous poorly constrained parameters that may contribute to large uncertainties and unreliable predictions. This dissertation investigates the challenges posed by model sloppiness in UQ through the lens of information geometry, a mathematical framework that treats statistical models as geometric objects to analyze their sensitivity to parameter perturbations. Building on this perspective, I identify key UQ challenges for interatomic potentials arising from parameter insensitivity and information mismatch. I introduce a novel information-matching method to mitigate these issues through data selection that adequately constrain relevant parameters, and demonstrate it on representative materials-science problems to show how information-geometric insights enable more robust modeling. In a complementary study, I examine the behavior of uncertainty estimates for modern machine learning interatomic potentials (MLIPs), especially in out-of-distribution regimes. While this analysis does not directly apply the proposed method, it highlights parallel challenges and suggests potential directions for extending the information-matching approach to ML-based frameworks. In addition to these methodological contributions, this work highlights my involvement in the Open Knowledgebase of Interatomic Models (OpenKIM) project, which seeks to democratize and standardize aspects of atomistic simulations. Finally, to underscore the broader relevance of this analysis, this dissertation also examines UQ challenges in geophysical modeling, illustrating both the shared issues of poorly constrained models and the unique domain-specific considerations that arise in that context. Together, these contributions represent an initial step toward improving the reliability and trustworthiness of computational modeling through robust uncertainty quantification, while outlining directions for future research in this area.

Degree

PhD

College and Department

Computational, Mathematical, and Physical Sciences; Physics and Astronomy

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2025-08-13

Document Type

Dissertation

Keywords

uncertainty quantification, sloppy model, experimental design, interatomic potential, machine learning

Language

english

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