PhD in Relevant Science

This 3.5 year PhD project is fully funded and home students, and EU students with settled status, are eligible to apply. The successful candidate will receive an annual tax-free stipend set at the UKRI rate (£20,780 for 2025/26) and tuition fees will be paid. We expect the stipend to increase each year. High-dimensional computations are ubiquitous in science and engineering, often arising from models with numerous parameters. For instance, uncertainty quantification (UQ) in fields such as climate modelling, nuclear reactor design, and finance often involves models with thousands of variables, posing significant mathematical challenges. Our aim is to develop and analyse implementable, fully discrete methods for function approximation, density estimation, and/or time-dependent PDEs or SDEs in high dimensions, with links to UQ and theoretical aspects of machine learning. Applications include improving the efficiency of data assimilation methods and understanding why and how deep learning works.