Uncertainty Quantification for Computer Experiments

Abstract

A computer experiment studies a physical system using a computer model (simulator) of that system. Simulators of practical interest are often resource intensive, limiting the number of times the simulator can be run, meaning there is uncertainty in the simulator response at untried input combinations. A statistical emulator is one approach for incorporating this uncertainty into analyses involving the simulator. This thesis identifies a property of simulators, called grounding, and develops novel methodology to emulate simulators with this property. We identify conditions under which our novel emulator can outperform conventional methodology.

In Chapter 3 we introduce grounding, propose a novel emulator which is tailored to grounding simulators, and compare our emulator to existing methodology using synthetic simulators. Our emulator combines a classifier, which estimates the region where the simulator grounds, with a Gaussian process emulator fit using the non-grounded runs. Our results show that our emulator often outperforms the conventional emulator when the simulator grounds with a discontinuity in its first derivative and the grounded region is moderately sized. Our results include a novel derivation of the CRPS score specific to our emulator.

In Chapter 4 we apply the novel emulator to a real-world simulator which models the early stage corrosion of uranium in water vapour. This is the first application of emulation methodology to this simulator and highlights that our emulator provides comparable results in a real-world setting.

In Chapter 5 we introduce a novel sequential design scheme tailored to our emulator, resulting in higher quality emulation compared to when our emulator is trained using conventional static designs. We systematically investigate the role of the classifier and demonstrate that our emulator provides excellent out-of-the-box performance.

We conclude the thesis by discussing directions for further work.

Date of Award	4 Feb 2025
Original language	English
Awarding Institution	University of Bristol
Supervisor	Oliver T Johnson (Supervisor) & Jonty C Rougier (Supervisor)