How to Improve Prediction Accuracy in the Analysis of Computer Experiments, Exploitation of Low-Order Effects and Dimensional Analysis

Computer codes simulate natural phenomena and engineering processes where physical experimentation is too costly or infeasible. Hence a computer experiment obtains data by running such a code. Nonetheless, the code can be too resource-consuming to run numerous times. Thus we replace a code with a Gaussian Stochastic Process (GaSP) statistical model, as a computationally faster surrogate.

The dissertation outlines two strategies to improve prediction accuracy of these surrogates: novel correlation structures for GaSPs based on principles for physical factorial designs, and Dimensional Analysis. It then focuses on Dimensional Analysis, which pays attention to fundamental physical dimensions when modelling scientific and engineering systems. Dimensional Analysis goes back at least a century but has recently caught statisticians' attention, in the design of physical and computer experiments. The core idea is to analyze dimensionless quantities derived from the original variables and possibly design for them.

Dimensional Analysis has significant challenges in variable selection, which the dissertation addresses with Functional Analysis of Variance. It applies this strategy in various case studies to improve prediction accuracy. Thus, this work proposes new modelling frameworks in computer experiments to accomplish more accurate surrogate models.