Parametric integrators approximate solutions of (high-dimensional) partial differential equations by restricting the numerical approximation to a closed form that nonlinearly depends on, and is identified by, a set of parameters. Such methods are a popular choice in quantum dynamics, where the wavefunctions of many-body systems are approximated by multiple Gaussians. The methodology of interest further appears in the approximation of various dynamical problems by tensor networks and neural networks. In all these cases, the parametrization is typically irregular, meaning that the occurring linear systems are generally ill-conditioned. The project sits at the intersection of classical numerical analysis, scientific machine learning and computational chemistry. Based on regularization techniques and time-stepping schemes applied to gradient systems, the project aims to contribute towards the treatment of high-dimensional optimisation problems, such as the electronic structure problem. We are looking for a highly enthusiastic and motivated student with - a strong 1st class degree in Mathematics at the MMath/MSci/MSc level, or equivalent; - a solid background in numerical analysis of differential equations; - excellent programming skills; - excellent communication skills (oral and written). Informal inquiries should be directed to Dr Jörg Nick, e-mail: j.a.nick@bham.ac.uk
Funding notes:
Funding may be available through a college or EPSRC scholarship in competition with all other PhD applications.
The scholarship will cover tuition fees, training support, and a stipend at standard rates for 3.5 years. Early application is strongly recommended; there is an annual deadline (typically at the end of January) for scholarship applications; however, later applications may also be considered. Applications of overseas candidates can only be considered until the beginning of September. Strong self-funded applicants worldwide will also be considered.
Strong candidates are encouraged to make an informal inquiry at j.a.nick@bham.ac.uk.
References: https://link.springer.com/article/10.1007/s00211-026-01551-5
