# Mr Nathan Owen

## Postgraduate

Telephone: **01392 726403**

Extension: **(Streatham) 6403**

After graduating from the University of Exeter in 2013 with first class honours degree in MSci Mathematics (Climate Science), I have continued my studies at the University by beginning a PhD in Mathematics.

My PhD project is entitled, 'A comparison of polynomial chaos and Gaussian process emulation for uncertainty quantification in computer experiments', and I am working under the supervision of Professor Peter Challenor and Dr Prathyush Menon.

My research interests are in uncertainty quantification and surrogate modelling. Computer models are now used in many areas of science to describe and analyse the real world, because physical experimentation is too time consuming, expensive or even dangerous. Such models generally comprise of a system of equations in terms of a high number of inputs and outputs, and due to their complexity can take a long time (minutes, hours, days) to complete just a single run. Designing and executing a suite of model runs - in what is known as a computer experiment - comes at a considerable cost.

In uncertainty quantification for computer models, we aim to address questions such as: how does uncertainty on the inputs propagate to the outputs? Can we calibrate our model to best match the real world? What are the most influential inputs in the process? Answering these questions typically requires a large number of model runs, which is simply not feasible if the model is compuationally expensive. A more sophiscated solution is to use a small number of model runs to build what is known as a surrogate - an approximation to the computer model which runs at a fraction of the cost. Polynomial chaos (PC) and Gaussian process (GP) emulation are two contrasting approaches for building a surrogate, developed independently over the last 25 years. Despite tackling similar problems in the field, there has been a lack of studies in the literature comparing the two methods. During my PhD I will comparing PC and GP surrogate methodologies for a range of modelling scenarios and computer models, in an effort to identify areas where either method might be preferable. I will also be investigating whether it is possible to combine PC and GP approaches to form a hybrid model.

Publications:

Owen, N. E., P. Challenor, P. P. Menon and S. Bennani, Comparison of surrogate-based uncertainty quantification methods for computationally expensive simulators, preprint arXiv.org/abs/1511.00926