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

 Mathematics Department Potential Projects

1. Random graphs for climate science
   This project focus on random graphs (also know as random networks) for climate modelling. It has been recently shown that the network approach substantially improves the prediction of high-impact climate phenomena in comparison with classical numerical modelling. In this project we will initially focus on correlation networks applied to extreme rainfall in the UK.
2. Examining Variants of Hasselmann’s Paradigm in Simplified Models of Climate Dynamics 
   Hasselmann’s approach to climate modelling divides the fast-slow weather-climate system into, respectively, stochastic and deterministic components. The simplified weather-climate systems to be investigated in this project will close the Hasselmann approach by regarding the slow part of the system as the expectation of the stochastic fast part. 
3. Robust Dynamic Models
   The project is concerned with the broad area of robust dynamic models for signal extraction, variance estimation, density forecasts, with a focus on theory and methods, and potential applications involving climate risk, energy, wind speed, environmental statistics. In this setting, a mini-project may focus on one of the following topics: robust dynamic models in high dimensions, score-driven filters, quasi score-driven filters and their optimality properties & dynamic models for multiple quantiles. 
4. Large Scale Data Assimilation using Emulation and Learning
   This project will investigate learning faster model emulators for ocean dynamics for the purpose of data assimilation and prediction.  
5. Weather prediction via parallelisable high-order spectral methods on spherical caps and triangular meshes
   Spherical harmonics are currently used by the European Centre for Mid-range Weather Forecasting (ECMWF), however, they require simulating the whole globe. This project will investigate the practical implementation of recently developed sparse spectral methods on spherical caps for localised simulation of weather forecasting models, with an emphasis on exploiting parallelisationation.
6. Statistical modelling of infectious diseases and environmental data
   Statistical modelling plays a crucial role in understanding and forecasting how infectious diseases emerge and spread in a changing environment. This project will develop methodology for modelling field data that is irregular, partially missing, spanning multiple temporal and spatial scales, and is subject to unforeseen changes. 
   Partner: Natural History Museum(NHM)
7. Koopmanism and critical transitions in geophysical and ecological systems
   The goal of the proposed project is the development of mathematical and statistical tools for identifying the regions in parameter space of geophysical and ecological systems that are close to potentially disruptive critical transitions, and the construction of accurate early warning indicators.This will be done via a systematic use of tools from the theory of dynamical systems and stochastic process, such as Koopmanism and linear response theory. 
   
8. Probabilistic AI for weather extremes
   This project will focus on expanding statistical tools to improve the use of pre-trained foundational weather prediction (FWP) models for accurate probabilistic forecasting of extreme weather events, especially draught,  flooding, and heat wave anomalies. Key topics for this PhD project could center on the following topics, fine-tuning of FWP models with proper scoring rules and calibration aware objectives, accurate uncertainty quantification in downscaling tasks, and enveloping FWP models into direct acyclic graph structures to gain causal insights.  
9. Developing Quasi-Geostrophic coupled ocean-atmosphere model
   This Project would be ideal for a student who seeks to develop skills in software engineering for computational modelling, scientific computing, data science, geophysical fluid dynamics, and climate science research. It aims for a major overhaul and upgrade of the existing QuasiGeostrophic Coupled Model (Q-GCM) of the ocean-atmosphere system to convert this model into a versatile modular community code for extremely fast high-resolution climate modelling in arbitrary geometrical setups. The model’s ability to quickly produce global-scope multi-century climate simulations faithfully representing mesoscale ocean–atmosphere interactions would allow it to set the milestones for future research of fundamental climate processes that are currently out of reach for state-of-the-art coupled General Circulation Models (GCMs) due to prohibitive computational expenses of such simulations.
   Partner: National Oceanography Centre (NOC)
10. Generalized Bayesian inference with applications to weather and climate prediction
    Generalized Bayesian methods, where one replaces the likelihood with a general loss function, are increasingly used in climate modelling (e.g. spatial models, inverse problems, stochastic differential equations), especially for uncertainty quantification. This project will investigate such methods in theory and practice, seeking to improve their reliability and performance.
    

Civil and Environmental Engineering Potential Projects

1.  Turbulent mixing in density-stratified environments – a probabilistic description
   This project represents a collaborative initiative combining probabilistic methods, fluid dynamics and flow data to better model stratified turbulence and mixing processes in density-stratified environments. Probabilistic descriptions offer a simplified and potentially efficient means of representing tracer field complexity and ensemble flow behaviour; the project will investigate the links with the governing dynamics, buoyancy forcing, mixing and energetics of the flows. Depending on personal interests, a candidate undertaking the project will have the option to collect or use data from a variety of sources, including computational simulations, laboratory experiments and field measurements from a building and/or the oceans.
2. Optimising large-scale flood defence management in response to evolving climate scenarios
   The project will focus on the application of Probabilistic Graphical Models (PGMs) for data assimilation, health monitoring, prediction, planning, and optimization. PGMs will be trained to predict key climate-related variables, such as rainfall and evapotranspiration, over the next 100 years. These models will incorporate both real-world spatial-temporal data and synthetic data generated by Finite Element models.
   The resulting framework will facilitate the analysis of life-extension measures for flood defence assets, allowing for the development of optimal maintenance strategies in the face of uncertain climate scenarios, including rare and extreme events (black swan events). This project provides a unique opportunity to contribute to both the mathematical and environmental sciences by addressing critical challenges in climate resilience and infrastructure management.
   Partner: Environment Agency
3. Compound flood modelling for climate extremes
   The project will employ numerical (regional and local) modelling of both waves and on-land flow to determine the likelihood and impact of such compound events in a changing climate. The probability of these extreme scenarios will be stochastically modelled using large scale climate simulations.
   Partner: Environment Agency
   
4. Data-assimilation for Lagrangian atmospheric dispersion models
   The idea behind this project is to incorporate data-assimilation methods to the Met Office atmospheric dispersion model NAME, which is – among other applications – used for operational ash predictions above the Atlantic and Western Europe. NAME is a Lagrangian dispersion model, implying that standard data assimilation techniques are not appropriate.
5. Understanding the socioeconomic implications of resource emergencies and associated mitigation policies using Bayesian material flow analysis
   This PhD project will focus on improving the capability of Bayesian material flow analysis methodology to include multi-regional systems and energy stocks and flows (by incorporating energy balances). This will include application of statistics and scientific programming in our existing Python code. The improved methodology and code will be applied to analyse the supply/demand balance of energy materials in UK and its major trading partners.
6. The fate of Lagrangian particles in the coastal zone
   This project will combine experiments with statistical modelling to provide insights into the trajectories of particles in the coastal zone. We are interested in two types of particles: (a) buoyant particles that float close to the free surface, such as microplastics, and (b) heavy particles that move close to the seabed, such as sand and nuclear particles.