Fast deep gaussian process modeling and design for large complex computer experiments

Computer models, or simulators, are widely used as a way to explore complex physical systems, but can be computationally expensive to evaluate or are not readily available to the broad scientific community. In either case, an emulator is used as a surrogate. Stationary Gaussian process emulators are often used to stand in for the computer models. In many cases, the computer model response surface does not resemble a realization of a stationary Gaussian process. Deep Gaussian processes have been shown to be capable of capturing non-stationary behaviors and abrupt regime changes in the response surface. In this thesis, we explore some of the properties of two common deep Gaussian process models for computer model emulation. We propose new methodology for one of the models so that it can serve as a computer model emulator. We introduce a new parameter that controls the amount of smoothness in the deep Gaussian process layers. We also adapt a stochastic variational approach to our deep Gaussian process model which allows for prior specification and posterior exploration of the smoothness of the response surface, thereby giving good predictive performance. Our approach can be applied to a large class of complex computer models, and scales to arbitrarily large simulation designs. The proposed methodology was motivated by the need to emulate an astrophysical model of the formation of binary black holes. Lastly, we propose a sequential design approach by combining the non-stationary deep Gaussian process model with an expected improvement based criterion. An adaptation in the deep Gaussian process prediction method facilitates the proposed sequential design approach. Our methods are illustrated in a series of synthetic examples and the real-world application.