{"id":{"repo_id":"tdl","oai_identifier":"oai:tdl-ir.tdl.org:10735.1/10168"},"canonical_url":"https://search.dev.ndltd.org/etd/tdl/oai:tdl-ir.tdl.org:10735.1/10168","repository":{"repo_id":"tdl","name":"Texas Digital Library","base_url":"https://tdl-ir.tdl.org/server/oai/request"},"display":{"title":"Gaussian Process Emulation: Theory and Application to Coupled Physics","abstract":"This dissertation focuses on uncertainty quantification (UQ) for complex multiphysics mod- els. One of the defining features of these multiphysics models is large output dimensions because the quantities of interest typically depend on both space and time. We develop Gaussian process (GP) emulators as fast surrogates of computationally expensive coupled computer models for uncertainty estimation. A GP can be thought of as an interpolator for a limited number of computer runs of a physics simulator. The predictive mean of the GP is conditioned to agree with the output of the multiphysics model. A GP is computation- ally inexpensive, enabling numerous rapid evaluations of the emulator across various input parameter regimes. Furthermore, Gaussian process emulators offer a mechanism to quantify uncertainty at untested inputs (where the computer model is not evaluated) because GP’s provide credible intervals estimates. However, standard GPs are not designed to handle coupling or high-dimensional outputs. We develop a Gaussian process methodology suitable for coupled, vector-valued systems. The approach combines a vector-valued emulator (parallel partial emulator) with an emulator for coupled multiphysics functions (a linked emulator). The main assumption of the parallel partial emulator is that the predictive mean and variance of each component of the vector- valued function are independent, while the correlation parameters are shared. Meanwhile, the linked emulator mimics the coupling structure of the emulated function. We test this new method on a simple composition of trigonometric functions as well as on the Terzaghi consolidation problem. The classical Terzaghi problem models fluid flow and compaction of a one-dimensional column of mud when a large load is dropped on the top. We choose the following metrics to measure emulation performance: training and prediction time, root mean squared error and the average length of the credible intervals. For both test problems our parallel partial linked emulator outperforms both traditional composite emulation techniques and techniques that involve a separate emulator at each value of the independent variable (here depth). Simulation studies of hydraulic fracturing can identify and isolate parameter regimes that create the most volume in the fracture, allowing oil and gas to flow more freely to the wells. In the field, volume creation can be estimated by monitoring microseismic activity (namely locations and magnitudes of these events). We use a hydraulic fracturing simulator, the Complex ReseArch Fracture Code (CFRAC) for numerically realistic experiments. However, the CFRAC simulator is computationally prohibitive for a large range of input parameter values. To avoid running the physics-based computer model for all of these input values, we employ a GP in place of CFRAC to search the input space for combinations of parameters that lead to simultaneous changes in void aperture and sliding displacement which indicate successful volume creation. Through emulator evaluations, we show that seismic data is not always reliable for selecting parameter regimes that ensure volume creation. In some cases, input parameter values identified by observing larger magnitudes of cumulative moment do not lead to the opening of the fracture, and thus do not result in volume creation.","abstract_html":"This dissertation focuses on uncertainty quantification (UQ) for complex multiphysics mod- els. One of the defining features of these multiphysics models is large output dimensions because the quantities of interest typically depend on both space and time. We develop Gaussian process (GP) emulators as fast surrogates of computationally expensive coupled computer models for uncertainty estimation. A GP can be thought of as an interpolator for a limited number of computer runs of a physics simulator. The predictive mean of the GP is conditioned to agree with the output of the multiphysics model. A GP is computation- ally inexpensive, enabling numerous rapid evaluations of the emulator across various input parameter regimes. Furthermore, Gaussian process emulators offer a mechanism to quantify uncertainty at untested inputs (where the computer model is not evaluated) because GP’s provide credible intervals estimates. However, standard GPs are not designed to handle coupling or high-dimensional outputs. We develop a Gaussian process methodology suitable for coupled, vector-valued systems. The approach combines a vector-valued emulator (parallel partial emulator) with an emulator for coupled multiphysics functions (a linked emulator). The main assumption of the parallel partial emulator is that the predictive mean and variance of each component of the vector- valued function are independent, while the correlation parameters are shared. Meanwhile, the linked emulator mimics the coupling structure of the emulated function. We test this new method on a simple composition of trigonometric functions as well as on the Terzaghi consolidation problem. The classical Terzaghi problem models fluid flow and compaction of a one-dimensional column of mud when a large load is dropped on the top. We choose the following metrics to measure emulation performance: training and prediction time, root mean squared error and the average length of the credible intervals. For both test problems our parallel partial linked emulator outperforms both traditional composite emulation techniques and techniques that involve a separate emulator at each value of the independent variable (here depth). Simulation studies of hydraulic fracturing can identify and isolate parameter regimes that create the most volume in the fracture, allowing oil and gas to flow more freely to the wells. In the field, volume creation can be estimated by monitoring microseismic activity (namely locations and magnitudes of these events). We use a hydraulic fracturing simulator, the Complex ReseArch Fracture Code (CFRAC) for numerically realistic experiments. However, the CFRAC simulator is computationally prohibitive for a large range of input parameter values. To avoid running the physics-based computer model for all of these input values, we employ a GP in place of CFRAC to search the input space for combinations of parameters that lead to simultaneous changes in void aperture and sliding displacement which indicate successful volume creation. Through emulator evaluations, we show that seismic data is not always reliable for selecting parameter regimes that ensure volume creation. In some cases, input parameter values identified by observing larger magnitudes of cumulative moment do not lead to the opening of the fracture, and thus do not result in volume creation.","abstract_has_math":false,"creators":["Dolski, Tamara"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Minkoff, Susan E.","Spiller, Elaine T.","Winkler, Duane D.","Zweck, John","Lou, Yifei","Pereira, L. Felipe"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-05","date_published":"2024-05","updated_at":"2026-07-27T21:19:37Z","subjects":["Gaussian process","Mathematics","Hydraulic fracturing","Uncertainty quantification"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10735.1/10168","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Minkoff, Susan E.","Spiller, Elaine T.","Winkler, Duane D.","Zweck, John","Lou, Yifei","Pereira, L. 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One of the defining features of these multiphysics models is large output dimensions because the quantities of interest typically depend on both space and time. We develop Gaussian process (GP) emulators as fast surrogates of computationally expensive coupled computer models for uncertainty estimation. A GP can be thought of as an interpolator for a limited number of computer runs of a physics simulator. The predictive mean of the GP is conditioned to agree with the output of the multiphysics model. A GP is computation- ally inexpensive, enabling numerous rapid evaluations of the emulator across various input parameter regimes. Furthermore, Gaussian process emulators offer a mechanism to quantify uncertainty at untested inputs (where the computer model is not evaluated) because GP’s provide credible intervals estimates. However, standard GPs are not designed to handle coupling or high-dimensional outputs. We develop a Gaussian process methodology suitable for coupled, vector-valued systems. The approach combines a vector-valued emulator (parallel partial emulator) with an emulator for coupled multiphysics functions (a linked emulator). The main assumption of the parallel partial emulator is that the predictive mean and variance of each component of the vector- valued function are independent, while the correlation parameters are shared. Meanwhile, the linked emulator mimics the coupling structure of the emulated function. We test this new method on a simple composition of trigonometric functions as well as on the Terzaghi consolidation problem. The classical Terzaghi problem models fluid flow and compaction of a one-dimensional column of mud when a large load is dropped on the top. We choose the following metrics to measure emulation performance: training and prediction time, root mean squared error and the average length of the credible intervals. For both test problems our parallel partial linked emulator outperforms both traditional composite emulation techniques and techniques that involve a separate emulator at each value of the independent variable (here depth). Simulation studies of hydraulic fracturing can identify and isolate parameter regimes that create the most volume in the fracture, allowing oil and gas to flow more freely to the wells. In the field, volume creation can be estimated by monitoring microseismic activity (namely locations and magnitudes of these events). We use a hydraulic fracturing simulator, the Complex ReseArch Fracture Code (CFRAC) for numerically realistic experiments. However, the CFRAC simulator is computationally prohibitive for a large range of input parameter values. To avoid running the physics-based computer model for all of these input values, we employ a GP in place of CFRAC to search the input space for combinations of parameters that lead to simultaneous changes in void aperture and sliding displacement which indicate successful volume creation. Through emulator evaluations, we show that seismic data is not always reliable for selecting parameter regimes that ensure volume creation. In some cases, input parameter values identified by observing larger magnitudes of cumulative moment do not lead to the opening of the fracture, and thus do not result in volume creation."]},{"key":"dc:title","label":"Title","values":["Gaussian Process Emulation: Theory and Application to Coupled Physics"]}]}],"canonical_facts":{"dc:contributor":["Minkoff, Susan E.","Spiller, Elaine T.","Winkler, Duane D.","Zweck, John","Lou, Yifei","Pereira, L. Felipe"],"dc:creator":["Dolski, Tamara"],"dc:date.accessioned":["2024-11-22T20:15:55Z","2026-06-05T22:45:04Z"],"dc:date.available":["2024-11-22T20:15:55Z"],"dc:date.issued":["2024-05"],"dc:description.abstract":["This dissertation focuses on uncertainty quantification (UQ) for complex multiphysics mod- els. One of the defining features of these multiphysics models is large output dimensions because the quantities of interest typically depend on both space and time. We develop Gaussian process (GP) emulators as fast surrogates of computationally expensive coupled computer models for uncertainty estimation. A GP can be thought of as an interpolator for a limited number of computer runs of a physics simulator. The predictive mean of the GP is conditioned to agree with the output of the multiphysics model. A GP is computation- ally inexpensive, enabling numerous rapid evaluations of the emulator across various input parameter regimes. Furthermore, Gaussian process emulators offer a mechanism to quantify uncertainty at untested inputs (where the computer model is not evaluated) because GP’s provide credible intervals estimates. However, standard GPs are not designed to handle coupling or high-dimensional outputs. We develop a Gaussian process methodology suitable for coupled, vector-valued systems. The approach combines a vector-valued emulator (parallel partial emulator) with an emulator for coupled multiphysics functions (a linked emulator). The main assumption of the parallel partial emulator is that the predictive mean and variance of each component of the vector- valued function are independent, while the correlation parameters are shared. Meanwhile, the linked emulator mimics the coupling structure of the emulated function. We test this new method on a simple composition of trigonometric functions as well as on the Terzaghi consolidation problem. The classical Terzaghi problem models fluid flow and compaction of a one-dimensional column of mud when a large load is dropped on the top. We choose the following metrics to measure emulation performance: training and prediction time, root mean squared error and the average length of the credible intervals. For both test problems our parallel partial linked emulator outperforms both traditional composite emulation techniques and techniques that involve a separate emulator at each value of the independent variable (here depth). Simulation studies of hydraulic fracturing can identify and isolate parameter regimes that create the most volume in the fracture, allowing oil and gas to flow more freely to the wells. In the field, volume creation can be estimated by monitoring microseismic activity (namely locations and magnitudes of these events). We use a hydraulic fracturing simulator, the Complex ReseArch Fracture Code (CFRAC) for numerically realistic experiments. However, the CFRAC simulator is computationally prohibitive for a large range of input parameter values. To avoid running the physics-based computer model for all of these input values, we employ a GP in place of CFRAC to search the input space for combinations of parameters that lead to simultaneous changes in void aperture and sliding displacement which indicate successful volume creation. Through emulator evaluations, we show that seismic data is not always reliable for selecting parameter regimes that ensure volume creation. In some cases, input parameter values identified by observing larger magnitudes of cumulative moment do not lead to the opening of the fracture, and thus do not result in volume creation."],"dc:identifier":["https://hdl.handle.net/10735.1/10168"],"dc:identifier.uri":["https://hdl.handle.net/10735.1/10168"],"dc:language":["English"],"dc:subject":["Gaussian process","Mathematics","Hydraulic fracturing","Uncertainty quantification"],"dc:title":["Gaussian Process Emulation: Theory and Application to Coupled Physics"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T21:19:37Z"}