UCLA

Computer experiments are increasingly being used to build high-quality surrogate models for complex emulation systems. Space-filling designs, frequently employed for planning computer experiments, help explore the design space uniformly and thus effectively. Among those, maximin distance designs are heavily investigated for its intuitive meaning and asymptotic D-optimality for the Gaussian process modeling when observations are nearly independent. In this thesis, we propose two deterministic approaches to constructing maximin distance designs with flexible sizes and extra favorable structures efficiently, including one-dimensional projection uniformity and mirror-symmetry among design rows. Besides, both classes of designs are nearly column-orthogonal, which guarantees low correlation between factors and improves the identification of linear trend of factorial effects. Meanwhile, we propose a new Bayesian-inspired space-filling criterion for the Gaussian Process modeling by meticulously planning the prior imposed on the correlation parameters, which ensures a better quantification of the significance of different design factors. A systematic procedure is introduced to rigorously select the hyperparameter within and two metaheuristic algorithms together with our novel implementations are presented to search for the corresponding optimal design in a timely fashion. Furthermore, we illustrate the merits of this newly-introduced criterion in terms of its space-filling properties against other existing measures and Gaussian Process model-fitting performances against extensive simulation functions potentially with many inert factors.