Gaussian Process Emulators in coastal wave modelling

A majority of the coastal wave modelling analysis require using historical data from physical observations or from computer simulations. Such simulators are often computationally expensive (takes long for a single evaluation run) and therefore it is normally a bottleneck in the analysis. Meta models are increasingly used as surrogates of the complex simulators to improve the efficiency of the bottleneck step. The performance of the meta model is vital when selecting the model as this would greatly influence the conclusions that are drawn from the analysis.
In this thesis we apply the Gaussian Process Emulator as a meta model of a wave transformation simulator, SWAN. The GPE is advantageous compared to other meta models as the predictions from the GPE are in the form of a distribution (mean and variance) and predicting at an event used to train the GPE returns perfect predictions with no uncertainty. Univariate and multivariate approaches of the GPE are presented and compared in case studies. In addition simple diagnostics to validate the GPE are discussed.
Look–up table (LUT) approach is a commonly used traditional meta model in coastal modelling. This is based on multidimensional linear interpolation of points on a regular grid. A case study shows the performance improvement that can be gained by using GPE over this traditional LUT approach. The GPE needs less than 2% of the simulator runs required for the LUT to obtain a similar accuracy. When introducing the multivariate GPE we identify two types of multiple outputs. We present a principal component GPE (PC-GPE) and a separable GPE for highly correlated and high dimensional output. These methods are compared to fitting multiple univariate GPE’s. In terms of accuracy the multiple univariate GPE outperformed the other methods however the PC-GPE tends to be moreefficient with only a small compromise on accuracy. For low dimensional output that is weekly correlated we present the linear model of coregionalisation (LMC) GPE which is a more flexible technique than the separable GPE. We compared this with the separable GPE and to fitting multiple univariate GPEs. The LMC GPE gave similar results as the multiple univariate GPE, but it is unstable and took a significant amount of time to fit.
Finally, we describe three approaches of selecting a design (simulator runs used to train the GPE). We aim to select a design that will maximise the information we can get from the simulator in order to inform the GPE given the limited simulator runs.
The aim of this thesis is to present the GPE methodology in a concise manner with running examples throughout. The novelty here is to show the application of GPEs to coastal wave modelling in order to help alleviate the computational burden and improve accuracy when using meta-models to avoid the bottleneck in the analysis.