PhD Studentship - Fully Discrete Computational Methods in High Dimensions

Application deadline: All year round
Research theme: Numerical Analysis

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.

We recommend that you apply early as the advert may be removed before the deadline.

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.

Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline. Applicants should be familiar with at least one, and preferably two, of:

(a) numerical analysis and real or elementary functional analysis;
(b) probability theory;
(c) implementation of computational methods using, for example, Julia or Python.

To apply, please contact the main supervisor, Dr Yoshihito Kazashi - y.kazashi@manchester.ac.uk. Please include details of your current level of study, academic background and any relevant experience and include a paragraph about your motivation to study this PhD project.

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