Mark Girolami

The University of Cambridge, in collaboration with IBM and the Department of Engineering, is offering a PhD studentship under the EPSRC Industrial Doctoral Landscape Award (IDLA) focused on Probabilistic Numerics and Inverse Problems. This research opportunity is at the intersection of mathematical and computational modelling, targeting large-scale inverse problems governed by Partial Differential Equations (PDEs) in Earth and planetary systems. The project aims to advance the field of probabilistic numerics, where uncertainty in numerical computation is explicitly represented and quantified, providing new approaches to complex geophysical and planetary models. IBM's practical challenges in modelling Earth and planetary systems often involve data-scarce environments where traditional Foundation-Model (FM) surrogates are not feasible. This studentship will explore synthetic data generation using direct PDE solvers and investigate how probabilistic numerical methods can enhance, supplement, or replace existing approaches. The goal is to enable more principled uncertainty quantification and improved performance in large-scale inverse modelling tasks relevant to both academic and industrial contexts. Applicants should hold or expect to obtain a good UK Master's degree (or overseas equivalent) in a relevant science subject such as Engineering, Physics, Computer Science, or Mathematics. The ideal candidate will be self-motivated, capable of independent research, and able to communicate their findings effectively. Application materials must include a short research statement (maximum 1 page), curriculum vitae, publication list, and contact details for two referees who can provide recommendation letters. There is a £20 application fee, and early applications are encouraged as the position may be filled before the advertised deadline. EPSRC IDLA studentships are available for eligible home students and a limited number of international students. The University of Cambridge actively supports equality, diversity, and inclusion, welcoming applications from all backgrounds. For queries, applicants may contact Professor Mark Girolami at [email protected], with a copy to [email protected]. To apply, visit the University of Cambridge Application Portal and follow the instructions to submit your documents. This is an excellent opportunity to contribute to cutting-edge research in probabilistic numerics, inverse problems, and computational modelling, with direct relevance to both academic and industrial applications.

This PhD studentship at the University of Cambridge is part of the EPSRC Industrial Doctoral Landscape Award (IDLA) and is offered in collaboration with IBM and the Department of Engineering. The research focuses on Probabilistic Numerics and Inverse Problems, particularly those governed by Partial Differential Equations (PDEs) in Earth and planetary systems. The project aims to advance mathematical and computational modelling by explicitly representing and quantifying uncertainty in numerical computation, a cutting-edge approach in probabilistic numerics. IBM faces practical challenges in large scale inverse problems, often using Foundation-Model (FM) surrogates. However, in data-scarce settings where FM training is not feasible, synthetic data generation via direct PDE solvers is explored. This PhD will investigate how probabilistic numerical methods can enhance, supplement, or replace existing approaches, enabling more principled uncertainty quantification and improved performance in complex geophysical and planetary models. Applicants should hold or expect to obtain a good UK Master's degree (or overseas equivalent) in a relevant science subject such as Engineering, Physics, Computer Science, or Mathematics. Candidates must be self-motivated, able to take ownership of their research, and effectively communicate their findings. Required application documents include a short research statement (maximum 1 page), a CV, a publication list, and contact details for two referees. There is a £20 application fee. EPSRC IDLA studentships are available for eligible home students and a limited number of international students. The University of Cambridge actively supports equality, diversity, and inclusion, encouraging applications from all sections of society. Early applications are recommended as the position may be filled before the advertised deadline. For queries, contact Professor Mark Girolami at [email protected] with a copy to [email protected]. Applications should be submitted via the University Application Portal. The deadline for applications is 14 May 2026.