Date of Award
2025
Degree Type
Open Access Dissertation
Degree Name
Mathematics, PhD
Program
Institute of Mathematical Sciences
Advisor/Supervisor/Committee Chair
Allon Percus
Dissertation or Thesis Committee Member
Alfonso Castro
Dissertation or Thesis Committee Member
Marina Chugunova
Dissertation or Thesis Committee Member
Dan O’Malley
Terms of Use & License Information
Rights Information
© 2025 John Kath
Keywords
Geologic networks, Multi-fidelity estimation, Quantum algorithms, Uncertainty quantification
Subject Categories
Mathematics
Abstract
This dissertation addresses the challenge of modeling complex geophysical systems by developing efficient surrogate models and scalable quantum algorithms. Our approaches provide uncertainty quantification, assessing confidence in estimates while accounting for subsurface heterogeneity. These innovations are designed to replace costly solvers with parsimonious emulators. In combination with multi-fidelity and quantum techniques, they make physics-informed modeling computationally feasible. One of our studies involves the use of Gaussian process regression to generate Bayesian predictions for gas transport in 3D discrete fracture networks. This provides accurate estimates while offering substantial savings over computationally intensive high-fidelity simulations. Additionally, we study multi-fidelity modeling through the formulation of linear Gaussian networks that integrate low- and high-fidelity information sources, improving predictive accuracy while further reducing computational cost. Our quantum computing approaches include quantum state preparation and its integration with quantum linear systems algorithms, enabling data-efficient analysis of large-scale hydrogeologic problems with potentially exponential runtime advantages over classical methods. Finally, building on these advances, we address uncertainty quantification through quantum amplitude estimation, exploiting quantum parallelism to attain a quadratic reduction in the number of Monte Carlo simulations needed to reach a specified error tolerance.
ISBN
9798265475640
Recommended Citation
Kath, John. (2025). Classical and Quantum Computational Methods for Predicting Fluid Transport in Fracture Networks. CGU Theses & Dissertations, 1051. https://scholarship.claremont.edu/cgu_etd/1051.
