PhD Projects

The following projects are advertised for 2025 entry into the CDT.

Domain-specific Compiler Technology for Finite Element Simulation on Tensor Hardware

Imperial: Mathematics or Computing

Principal advisor: Prof Paul Kelly and Prof David Ham

Accumulation and absorption of active particles at surfaces

Imperial: Mathematics

Principal advisor: Dr Thibault Bertrand and Prof. Paul Bressloff

Stochastic resetting in many-body interacting particle systems

Imperial: Mathematics

Principal advisor: Dr Thibault Bertrand and Prof. Paul Bressloff

Out-of-distribution detection with long-tailed learning and vision-language models

UCL: Statistics

Principal advisor: Prof Jinghao Xue

Computational modelling for educational research

Imperial: Mathematics

Principal advisor: Dr Andreas Joergensen (with Prof Camille Kandiko Howson (CHERS))

Robust Multi-objective and Mutli-fidelity Bayesian Optimisation of Fusion Breeder Blankets

Imperial: Mathematics

Principal advisor: Dr Andrew Duncan (with cosupervision from Dr Lorenzo Zanisi and Dr Helen Brooks at UKAEA)

Particles for Fusion

Imperial: Mathematics

Principal advisor: Prof David Ham (with UKAEA cosupervision)

Numerical methods for Mean Field Games

UCL: Mathematics

Principal advisor: Dr Iain Smears

The propagation of uncertainties across coupled climate models

UCL: Statistics

Principal advisor: Prof Serge Guillas

Single Cell Ageing and mtDNA: learning and simulation

Imperial: Mathematics

Principal advisor: Prof Nick Jones

Constrained Generative Models for Optimisation and Scientific Modelling

Imperial: Mathematics

Principal advisor: Dr Deniz Akyildiz

Mathematical and Computational Modeling of Resilience in Multilayer Networks

Imperial: Computing

Principal advisor: Dr. Giuliano Casale and Prof. Emil Lupu

Taming Time and Dimension: Advanced Scientific Computing for Next-Generation Diffusion Models

Imperial: Mathematics

Principal advisor: Dr Dante Kalise Prof Greg Pavliotis

Smart Image-Based Sensor Optimisation for Fusion Simulation Validation

Imperial: Mathematics

Principal advisor: Dr Andrew Duncan, Dr Dante Kalise and Lloyd Fletcher (UKAEA)

Differentiable probabilistic deep learning with generative denoising diffusion models

UCL: MSSL

Principal advisor: Prof Jason McEwen

Optimal control methods for agent-based models

Imperial: Mathematics

Principal advisor: Prof Greg Pavliotis and Dr Dante Kalise

Deep learning with symmetry

Imperial: Mathematics

Principal advisor: Prof Jeroen Lamb

UCL - Scalable Collider Data Analysis with Optimised Predictions and Machine-Learning Anomaly Detection

: Advanced Research Computing

Principal advisor: Christian Gutschow

Aligned diffusion models for machine learning

Imperial: Mathematics

Principal advisor: Dr Felipe Tobar

Large-scale high-performance solver for therapeutic ultrasound applications

UCL: Division of Surgery and Interventional Science

Principal advisor: Dr Pierre Gélat

Renormalisation Group Perspective on Neural Networks

Imperial: Mathematics

Principal advisor: Dr Thibaut Bertrand and Dr Gunnar Pruessner

Backpropagation through rough differential equations

Imperial: Mathematics & Imperial-X

Principal advisor: Dr Christopher Salvi

High-performance solver for ultrasound propagation in mixed domains with complex fluid and solid materials

UCL: Mechanical Engineering

Principal advisor: Dr Reza Haqshenas

Developing multi-physics, multi-scale wave modelling on graphics cards

Imperial: Mechanical Engineering

Principal advisor: Dr Peter Huthwaite

Next generation implicit numerics for atmosphere models

Imperial: Mathematics

Principal advisor: Prof Colin Cotter

Optimization methods for high-dimensional reinforcement learning

Imperial: Mathematics

Principal advisor: Dr Yufei Zhang

Optimising Experimental Design for Nuclear Materials Research Using Foundation Models

Imperial: Mathematics and Materials

Principal advisor: Dr Sam Cooper and Dr Felipe Tobar

Model correlation and the version control tree

UCL: ARC

Principal advisor: Prof James Hetherington

AI code generation and numerical codes

UCL: ARC

Principal advisor: Prof James Hetherington

Re-griding the TROVE nuclear motion program

UCL: Physics and Astronomy

Principal advisor: Prof Jonathan Tennyson

Transfer Learning for Monte Carlo

UCL: Statistical Science

Principal advisor: Dr.Francois-Xavier Briol

A Unified Form Language for PDEs in non-divergence form

UCL: Mathematics

Principal advisor: Dr Max Jensen

Data-driven multi-scale modelling of bacterial biofilms

UCL: Mathematics

Principal advisor: Dr. Philip Pearce

Simulation-based Inference for Expensive Scientific Simulators

UCL: Statistical Science

Principal advisor: Dr.Francois-Xavier Briol

Automated Bayesian inference in stochastic differential equation models

UCL: Advanced Research Computing Centre

Principal advisor: Dr Matt Graham

Improving impaired hearing through sound reconstruction from neural activity patterns

UCL: Computer Science

Principal advisor: Prof Martin Benning

Koopman operator learning of nonlinear PDEs

Imperial: Mathematics

Principal advisor: Dr.Nicholas Boulle

Reinforcement Learning for Full-Hexahedral Mesh Generation

Imperial: Aeronautics

Principal advisor: Prof Joaquim Peiro and Dr Mashy Green (UCL ARC)

A computational framework for heterogeneous coupling in large scale computations

UCL: Mathematics

Principal advisor: Prof Erik Burman

Optimal transport for probabilistic machine learning

Imperial: Mathematics

Principal advisor: Dr Felipe Tobar

Advanced Computational Methods for Bayesian Calibration of High-Dimensional Dynamical Models

UCL: Statistics

Principal advisor: Prof Alexandros Beskos

Time Reversal Imaging and Learned Physics with Neural ODEs

UCL: Computer Science

Principal advisor: Prof Simon Arridge

Developing Quasi-Geostrophic Coupled Ocean–Atmosphere Model

Imperial: Mathematics

Principal advisor: Prof Pavel Berloff

Transfer Learning and Few-Shot Learning for Science: Learning with Limited Data and Compute

UCL: Computer Science

Principal advisor: Dr Benjamin Guedj

Grid-independent pseudospectral models of broadband acoustic wave propagation (k-Wave 2.0)

UCL: Medical Physics and Biomedical Engineering

Principal advisor: Prof Ben Cox

Inference of gene regulatory networks from single cell data

Imperial: Mathematics

Principal advisor: Prof Vahid Shahrezaei and Dr. Philipp Thomas

Quantifying and eliminating floating point pathologies in the simulation of chaotic dynamical systems

UCL: Chemistry and Advanced Research Computing

Principal advisor: Prof Peter V. Coveney

Fast Multipole Methods on modern architectures

UCL: Maths and Advanced Research Computing Centre

Principal advisor: Prof Timo Betcke

Numerical methods for PDEs in fractal domains

UCL: Mathematics

Principal advisor: Prof David Hewett

A differentiable Gillespie algorithm for exact gradients through discrete stochastic systems

Imperial: Mathematics

Principal advisor: Dr.Cristopher Salvi

All-at-once deep learning methods for nonlinear PDE based inverse problems

UCL: Computer Science

Principal advisor: Prof Marta Betcke

Algorithms and software for differentiable programming at the ML/PDE/DAE interface

Imperial: Computing and Mathematics

Principal advisor: Prof Ruth Misener and Prof David Ham

Drift detection in graph streams and its applications in healthcare

UCL: Computer Science and Advanced Research Computing Centre

Principal advisor: Dr. Yevgeniya Kovalchuk

Agent-based simulation of tissue self-organization

Imperial: Mathematics

Principal advisor: Dr.Omer Karin

Machine Learning for Low-Cost Data Assimilation

UCL: Computer Science

Principal advisor: Prof Marc Deisenroth

PDE-driven Digital Twins

Imperial: Mathematics

Principal advisor: Prof Colin Cotter

HemeLB at the exascale and beyond: Implementing and studying whole human scale cardiovascular hemodynamics on the world’s most powerful supercomputers

UCL: Chemistry and Advanced Research Computing

Principal advisor: Prof Peter V. Coveney

Accelerated multi-level Bayesian calibration of expensive simulations on high performance computing systems

UCL: Advanced Research Computing Centre

Principal advisor: Dr Matt Graham

PARALIFT – A PARAllel framework for LIFTed training of neural networks

UCL: Computer Science

Principal advisor: Prof Martin Benning

Efficient Computation of Transition States in Molecular Dynamics

Imperial: Computing

Principal advisor: Dr. Panos Parpas

A Unified Solver for Optimal Transport, Schroedinger Bridges, and Variational Mean Field Games

Imperial: Mathematics

Principal advisor: Prof Colin Cotter and Dr. Dante Kalise

Robust Bayesian Inference at Scale

UCL: Statistical Science

Principal advisor: Dr.Francois-Xavier Briol

Inference and inverse problems for stochastic interacting particle systems

Imperial: Mathemetics

Principal advisor: Prof Greg A. Pavliotis

Accelerating parabolic Stochastic PDE solver via a weak adversarial network approach

UCL: Mathematics

Principal advisor: Prof Hao Ni

Computational solution of inverse problems using large datasets of low rank

UCL: Mathematics

Principal advisor: Prof Erik Burman

Machine learning-based biophysical models of antibody properties and function

Imperial: Mathematics

Principal advisor: Dr. Barbara Bravi and Prof Mauricio Barahona
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