PhD Studentship: Regularized dynamical parametric approximations for gradient flows
Overview
The School of Mathematics at the University of Birmingham is offering a PhD studentship on regularized dynamical parametric approximations for gradient flows. Parametric integrators approximate solutions of high-dimensional partial differential equations by restricting the numerical approximation to a closed form that depends nonlinearly on a set of parameters. They are popular in quantum dynamics, where many-body wavefunctions are approximated by multiple Gaussians, and the same approach appears in approximations by tensor networks and neural networks. In all these cases the parametrization is typically irregular, so the linear systems that arise are generally ill-conditioned.
The project sits between classical numerical analysis, scientific machine learning and computational chemistry. Using regularization techniques and time-stepping schemes for gradient systems, it aims to contribute to the treatment of high-dimensional optimisation problems such as the electronic structure problem.
Requirements
The university is looking for a highly enthusiastic and motivated student with a strong first class degree in mathematics at MMath, MSci or MSc level or equivalent, a solid background in numerical analysis of differential equations, excellent programming skills and excellent oral and written communication skills.
What you get
Funding may be available through a college or EPSRC scholarship, in competition with all other PhD applications. The scholarship covers tuition fees, training support and a stipend at standard rates for 3.5 years.
Who can apply
Early application is strongly recommended. There is an annual scholarship deadline, typically at the end of January, although later applications may also be considered. Applications from overseas candidates can only be considered until the beginning of September. Strong self-funded applicants from anywhere in the world will also be considered.
Key dates
The closing date is 6 November 2026.