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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Kath, John"],"institution":null,"degree_name":"Mathematics, PhD","degree_level":"Open Access Dissertation","degree_discipline":"Institute of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Alfonso Castro","Marina Chugunova","Dan O’Malley"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-01-01T08:00:00Z","date_published":"2025-01-01T08:00:00Z","updated_at":"2026-07-24T01:41:17Z","subjects":["Geologic networks","Multi-fidelity estimation","Quantum algorithms","Uncertainty quantification","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarship.claremont.edu/cgu_etd/1051","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Alfonso Castro","Marina Chugunova","Dan O’Malley"]},{"key":"dc:creator","label":"Author","values":["Kath, John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2026-05-12T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Institute of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Mathematics, PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Geologic networks","Multi-fidelity estimation","Quantum algorithms","Uncertainty quantification","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarship.claremont.edu/cgu_etd/1051"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Classical and Quantum Computational Methods for Predicting Fluid Transport in Fracture Networks"]}]}],"canonical_facts":{"dc:contributor":["Alfonso Castro","Marina Chugunova","Dan O’Malley"],"dc:creator":["Kath, John"],"dc:date.available":["2026-05-12T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://scholarship.claremont.edu/cgu_etd/1051"],"dc:subject":["Geologic networks","Multi-fidelity estimation","Quantum algorithms","Uncertainty quantification","Mathematics"],"dc:title":["Classical and Quantum Computational Methods for Predicting Fluid Transport in Fracture Networks"],"thesis:degree_discipline":["Institute of Mathematical Sciences"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Mathematics, PhD"]},"updated_at":"2026-07-24T01:41:17Z"}