Emulation of Stochastic Computer Models with an Application to Building Design

Abstract

Computer models are becoming increasingly common in many areas of science and engineering; aiding in the understanding of scientific processes and providing critical information for important decisions. These models often rely on complex mathematics, and they can use a large amount of computing power to perform a single simulation. This greatly limits the usefulness of these models, because many simulations are needed for most real world problems. A common solution to this is to train a second, statistical, model using a small set of initial simulations. This statistical model is simpler and quicker to run (and is often known as an emulator, with the computer model known as a simulator). This may initially seem like a convoluted approach, but it has shown great promise and continues to gain use in practice. Properly designing emulators often depends on properties of the simulator in question, and so tailoring emulators to the specific problem at hand is essential. Stochastic simulators are one type of computer model which give randomly different outputs each time they are run, even if they are run for the exact same scenario (i.e. the exact same inputs). This thesis deals primarily with stochastic simulators, and how to build and use emulators for these. These simulators can be very difficult to build emulators for, as the emulator will need to learn both the underlying trends and the structure of the randomness. This thesis also uses the engineering design of buildings to exemplify some of the issues and the developed techniques. Before a building is made, engineers can simulate different properties of the building (such as its internal temperature), and use that to make modifications to the design. We argue in this thesis that this process should be done stochastically, modifying the simulators to produce random outputs as a result of the random nature of weather (which affects the internal properties of any building). This then provides motivation for the stochastic emulation techniques and also acts as an interesting case-study. Outside of these two guiding objectives, the first three chapters in this thesis (after the introduction) can generally be read independently: we develop techniques for checking the quality of a stochastic emulator; we develop a methodology for improved stochastic emulation by using deterministic (non-stochastic) simulations; and we propose a framework for deciding on an acceptable building design. The remaining chapters then discuss some attributes of specific emulation techniques, and provide concluding remarks.