PhD in Mathematics

This PhD forms part of an ongoing collaboration between IBM and the Department of Engineering at the University of Cambridge, centred on the mathematical and computational modelling of Earth and planetary systems./nThe project will investigate Probabilistic Numerical Computation for large scale Inverse Problems, with a particular focus on cases governed by Partial Differential Equations (PDEs)./nRecent developments in probabilistic numerics- where uncertainty in numerical computation is explicitly represented and quantified-offer a promising new perspective for addressing inverse problems in complex geophysical and planetary models./nIBM faces several such challenges in practice, many of which are currently approached using Foundation-Model (FM) surrogates. However, certain inverse problems arise in data scarce settings where FM training is not feasible, prompting the exploration of synthetic data generation via direct PDE solvers./nThis PhD will examine how probabilistic numerical methods can enhance, supplement, or replace existing approaches, enabling more principled uncertainty quantification and improved performance in large scale inverse modelling tasks relevant to Earth and planetary systems.