PhD Projects

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

Stochastic resetting in many-body interacting particle systems

Imperial: Mathematics

Principal advisor: Dr Thibault Bertrand and Prof. Paul Bressloff

Accumulation and absorption of active particles at surfaces

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

Smart Image-Based Sensor Optimisation for Fusion Simulation Validation

Imperial: Mathematics

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

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

Imperial: Mathematics

Principal advisor: Dr Dante Kalise Prof Greg Pavliotis

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

Single Cell Ageing and mtDNA: learning and simulation

Imperial: Mathematics

Principal advisor: Prof Nick Jones

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

Optimal control methods for agent-based models

Imperial: Mathematics

Principal advisor: Prof Greg Pavliotis and Dr Dante Kalise

Aligned diffusion models for machine learning

Imperial: Mathematics

Principal advisor: Dr Felipe Tobar

Differentiable probabilistic deep learning with generative denoising diffusion models

UCL: MSSL

Principal advisor: Prof Jason McEwen

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

Large-scale high-performance solver for therapeutic ultrasound applications

UCL: Division of Surgery and Interventional Science

Principal advisor: Dr Pierre Gélat

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

UCL: Mechanical Engineering

Principal advisor: Dr Reza Haqshenas

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

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

Imperial: Mechanical Engineering

Principal advisor: Dr Peter Huthwaite

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

A differentiable Gillespie algorithm for exact gradients through discrete stochastic systems

Imperial: Mathematics

Principal advisor: Dr.Cristopher Salvi

PDE-driven/data-driven hybrid modelling for data assimilation

Imperial: Mathematics

Principal advisor: Prof Colin Cotter

Machine Learning for Low-Cost Data Assimilation

UCL: Computer Science

Principal advisor: Prof Marc Deisenroth

Automated Bayesian inference in stochastic differential equation models

UCL: Advanced Research Computing Centre

Principal advisor: Dr Matt Graham

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

Koopman operator learning of nonlinear PDEs

Imperial: Mathematics

Principal advisor: Dr.Nicholas Boulle

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

Optimal transport for probabilistic machine learning

Imperial: Mathematics

Principal advisor: Dr Felipe Tobar

Robust Bayesian Inference at Scale

UCL: Statistical Science

Principal advisor: Dr.Francois-Xavier Briol

Fast Multipole Methods on modern architectures

UCL: Maths and Advanced Research Computing Centre

Principal advisor: Prof Timo Betcke

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

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

UCL: Computer Science

Principal advisor: Prof Marta Betcke

Re-griding the TROVE nuclear motion program

UCL: Physics and Astronomy

Principal advisor: Prof Jonathan Tennyson

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

UCL: Medical Physics and Biomedical Engineering

Principal advisor: Prof Ben Cox

Time Reversal Imaging and Learned Physics with Neural ODEs

UCL: Medical Physics and Biomedical Engineering

Principal advisor: Prof Ben Cox

Agent-based simulation of tissue self-organization

Imperial: Mathematics

Principal advisor: Dr.Omer Karin

PARALIFT – A PARAllel framework for LIFTed training of neural networks

UCL: Computer Science

Principal advisor: Prof Martin Benning

A Unified Form Language for PDEs in non-divergence form

UCL: Mathematics

Principal advisor: Dr Max Jensen

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

UCL: Advanced Research Computing Centre

Principal advisor: Dr Matt Graham

Accelerating parabolic Stochastic PDE solver via a weak adversarial network approach

UCL: Mathematics

Principal advisor: Prof Hao Ni

Inference of gene regulatory networks from single cell data

Imperial: Mathematics

Principal advisor: Prof Vahid Shahrezaei and Dr. Philipp Thomas

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

UCL: Statistics

Principal advisor: Prof Alexandros Beskos

Drift detection in graph streams and its applications in healthcare

UCL: Computer Science and Advanced Research Computing Centre

Principal advisor: Dr. Yevgeniya Kovalchuk

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

Imperial: Mathematics

Principal advisor: Prof Colin Cotter and Dr. Dante Kalise

Inference and inverse problems for stochastic interacting particle systems

Imperial: Mathemetics

Principal advisor: Prof Greg A. Pavliotis

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

A computational framework for heterogeneous coupling in large scale computations

UCL: Mathematics

Principal advisor: Prof Erik Burman

Improving impaired hearing through sound reconstruction from neural activity patterns

UCL: Computer Science

Principal advisor: Prof Martin Benning

Simulation-based Inference for Expensive Scientific Simulators

UCL: Statistical Science

Principal advisor: Dr.Francois-Xavier Briol

Efficient Computation of Transition States in Molecular Dynamics

Imperial: Computing

Principal advisor: Dr. Panos Parpas

Numerical methods for PDEs in fractal domains

UCL: Mathematics

Principal advisor: Prof David Hewett

Data-driven multi-scale modelling of bacterial biofilms

UCL: Mathematics

Principal advisor: Dr. Philip Pearce

Transfer Learning for Monte Carlo

UCL: Statistical Science

Principal advisor: Dr.Francois-Xavier Briol

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

Stochastic resetting in many-body interacting particle systems

Accumulation and absorption of active particles at surfaces

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

Computational modelling for educational research

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

Particles for Fusion

Numerical methods for Mean Field Games

The propagation of uncertainties across coupled climate models

Smart Image-Based Sensor Optimisation for Fusion Simulation Validation

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

Constrained Generative Models for Optimisation and Scientific Modelling

Mathematical and Computational Modeling of Resilience in Multilayer Networks

Single Cell Ageing and mtDNA: learning and simulation

Deep learning with symmetry

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

Optimal control methods for agent-based models

Aligned diffusion models for machine learning

Differentiable probabilistic deep learning with generative denoising diffusion models

Next generation implicit numerics for atmosphere models

Optimization methods for high-dimensional reinforcement learning

Large-scale high-performance solver for therapeutic ultrasound applications

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

Renormalisation Group Perspective on Neural Networks

Backpropagation through rough differential equations

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

Optimising Experimental Design for Nuclear Materials Research Using Foundation Models

Model correlation and the version control tree

AI code generation and numerical codes

A differentiable Gillespie algorithm for exact gradients through discrete stochastic systems

PDE-driven/data-driven hybrid modelling for data assimilation

Machine Learning for Low-Cost Data Assimilation

Automated Bayesian inference in stochastic differential equation models

Developing Quasi-Geostrophic Coupled Ocean–Atmosphere Model

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

Koopman operator learning of nonlinear PDEs

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

Optimal transport for probabilistic machine learning

Robust Bayesian Inference at Scale

Fast Multipole Methods on modern architectures

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

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

Re-griding the TROVE nuclear motion program

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

Time Reversal Imaging and Learned Physics with Neural ODEs

Agent-based simulation of tissue self-organization

PARALIFT – A PARAllel framework for LIFTed training of neural networks

A Unified Form Language for PDEs in non-divergence form

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

Accelerating parabolic Stochastic PDE solver via a weak adversarial network approach

Inference of gene regulatory networks from single cell data

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

Drift detection in graph streams and its applications in healthcare

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

Inference and inverse problems for stochastic interacting particle systems

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

A computational framework for heterogeneous coupling in large scale computations

Improving impaired hearing through sound reconstruction from neural activity patterns

Simulation-based Inference for Expensive Scientific Simulators

Efficient Computation of Transition States in Molecular Dynamics

Numerical methods for PDEs in fractal domains

Data-driven multi-scale modelling of bacterial biofilms

Transfer Learning for Monte Carlo

Computational solution of inverse problems using large datasets of low rank

Machine learning-based biophysical models of antibody properties and function

Feel free to drop us a line with questions or feedback!

CCMI is a collaboration between UCL and Imperial College, funded by EPSRC.