Imperial College London

Imperial is home to around 23,000 students from more than 145 countries and 8,000 staffs.

Ranked 2nd in the world (QS World University Rankings, 2025), 1st in UK for graduate prospects (The Guardian, 2024) and 1st in UK for research quality, and awarded University of the Year for graduate employment (The Times, 2024).

Imperial focuses on the four main disciplines of science, engineering,medicine and business and is renowned for its application of these skills to industry and enterprise.

Imperial holds a Silver Athena Swan award which recognises advancing women’s careers in science, technology, engineering, maths and medicine in academia.

Distinguished members of the College have included 14 Nobel laureates and three Fields Medallists.

Potential PhD projects

1. Data Assimilation in Misspecified Models with Applications to Geophysical Models
   This project will consider the problem of data assimilation and stochastic filtering when the assumed physical models are imperfect which is the case in the real world. It will explore statistical theory and practical mitigation of model misspecification (or model mismatch). The produced insights and algorithmic innovation will be tested on geophysical models arising in ocean modelling.
2. Statistical characterisation of wave events
   This project will tackle the statistical description of crucial wave-related processes, such as the occurrence of breaking, overtopping and extreme waves. Experimental, computational and theoretical approaches to the project can be developed with a range of marine applications in mind.
3. Turbulence in stratified flows
   This project will tackle the stochastic parameterisation of mixing processes and tracer transport in density-stratified flows. Computational, experimental and theoretical approaches can be developed with applications to ocean dynamics and the built environment.
4. Bayesian causal inference
   Causal inference aims to understand the challenging question of ‘what would happen’ in different scenarios, thus helping decision-makers make reliable choices. Bayesian methods are increasingly used for such tasks, especially for uncertainty quantification. This project will investigate such methods in theory and practice, seeking to improve their reliability and performance.
5. Next generation numerics for ocean modelling
   This project will take the first steps towards a new ocean model based upon innovative numerical methods that allow the use of unstructured meshes that can resolve coastlines, topography and have spatially varying resolution to focus on specific regions of interest (to study e.g. global climate impacts on regional processes). These numerical methods (based on compatible finite element methods) have already been introduced into the next generation Met Office forecasting system (LFRic), and in this project we take on the challenge of designing an efficient, accurate, scalable ocean modelling system using them.
6. Differentiable programming abstractions for coupled climate model components.
   In this project you will develop simulation coupling technology that enables climate scientists to write models of multiple, coupled, components of the Earth system in a high level mathematical language, and have high performance parallel forward and adjoint code be generated and executed automatically.
7. Statistical hydrodynamics and geophysical flows
   The project is related to the longtime behaviour of the two-dimensional Euler equations, with the goal of explaining the formation of large scale structures in the ocean. It is related to fluid mixing, the dynamics of vortex patches, and has links with classical work on point vortices.
8. Reconciling the Eulerian and Lagrangian Models for Turbulent Transport
   The underlying idea is both fundamental and highly practical: to close the profound gap between the existing approaches for characterizing turbulent transport, which is ubiquitous in geophysical fluids and climate-type models. One approach is based on observing turbulence at fixed spatial locations, and the other one follows trajectories of elementary fluid particles. The former approach is more suitable for modelling purposes, whereas the latter approach is more suitable for experimental observations of the turbulence. We don’t fully understand the differences between these approaches, and we don’t yet know how to translate one into the other.
9. Statistical space-time models for our climate
   Data collected from the climate and geological sciences are increasingly huge in their volume, posing both significant statistical and computational challenges in their analysis. This project focuses on spatio-temporal data, by developing novel models and inference procedures to tractably capture the intricate dependency structures in real-world spatio-temporal data from the British Geological Survey.
10. Time varying parameter models: theory and applications
    The project is concerned with the wide area of models for time-varying parameters, that find applications in climate econometrics and environmental risk management:
    i) Robust models and filters for time-varying location parameters
    ii) Score-driven filters, quasi score-driven filters and their properties
    iii) Dynamic models for multiple quantiles.
11. Analysis and simulations of novel carbon capture processes.
    Game-changing technologies are needed to address the climate crisis. This project will model, analyse and optimise patented novel microchannel systems for direct air carbon capture using mathematical models of CO2, laden air flow over liquid sorbent infused structured microchannels. Modelling these complex systems entails description of the transport phenomena in a two-phase, reacting system.