PhD Projects

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

Computational solution of inverse problems using large datasets of low rank

UCL Mathematics

Principal advisor: Prof Erik Burman

Backpropagation through rough differential equations

Imperial Mathematics & Imperial-X

Principal advisor: Dr Christopher Salvi

Large-scale high-performance solver for therapeutic ultrasound applications

UCL 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

Optimization methods for high-dimensional reinforcement learning

Imperial Mathematics

Principal advisor: Dr Yufei Zhang

Data-driven preconditioning for parallel-in-time PDE solvers

Imperial Mathematics

Principal advisor: Prof Colin Cotter

AI code generation and numerical codes

UCL ARC

Principal advisor: Prof James Hetherington

Model correlation and the version control tree

UCL ARC

Principal advisor: Prof James Hetherington

Accelerating parabolic Stochastic PDE solver via a weak adversarial network approach

UCL Mathematics

Principal advisor: Prof Hao Ni

Improving impaired hearing through sound reconstruction from neural activity patterns

UCL Computer Science

Principal advisor: Prof Martin Benning

A machine learning-informed computational model of cancer-immune interactions

Imperial Mathematics

Principal advisor: Dr. Barbara Bravi

Developing Quasi-Geostrophic Coupled Ocean–Atmosphere Model

Imperial Mathematics

Principal advisor: Prof Pavel Berloff

A Unified Form Language for PDEs in non-divergence form

UCL Mathematics

Principal advisor: Dr Max Jensen

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

Agent-based simulations of tissue dynamics

Imperial Mathematics

Principal advisor: Dr.Omer Karin

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

Imperial Mathematics

Principal advisor: Prof Colin Cotter and Dr. Dante Kalise

Automated Bayesian inference in stochastic differential equation models

UCL Advanced Research Computing Centre

Principal advisor: Dr Matt Graham

Numerical methods for PDEs in fractal domains

UCL Mathematics

Principal advisor: Prof David Hewett

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

UCL Medical Physics and Biomedical Engineering

Principal advisor: Prof Ben Cox

Efficient Computation of Transition States in Molecular Dynamics

Imperial Computing

Principal advisor: Dr. Panos Parpas

Fast Multipole Methods on modern architectures

UCL Maths and Advanced Research Computing Centre

Principal advisor: Prof Timo Betcke

Inference and inverse problems for stochastic interacting particle systems

Imperial Mathemetics

Principal advisor: Prof Greg A. Pavliotis

Robust Bayesian Inference at Scale

UCL Statistical Science

Principal advisor: Dr.Francois-Xavier Briol

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

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

Transfer Learning for Monte Carlo

UCL Statistical Science

Principal advisor: Dr.Francois-Xavier Briol

A computational framework for heterogeneous coupling in large scale computations

UCL Mathematics

Principal advisor: Prof Erik Burman

Simulation-based Inference for Expensive Scientific Simulators

UCL Statistical Science

Principal advisor: Dr.Francois-Xavier Briol

Koopman operator learning of nonlinear PDEs

Imperial Mathematics

Principal advisor: Dr.Nicholas Boulle

Machine Learning for Low-Cost Data Assimilation

UCL Computer Science

Principal advisor: Prof Marc Deisenroth

PARALIFT – A PARAllel framework for LIFTed training of neural networks

UCL Computer Science

Principal advisor: Prof Martin Benning

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

Imperial Mathematics

Principal advisor: Prof Colin Cotter

Re-griding the TROVE nuclear motion program

UCL Physics and Astronomy

Principal advisor: Prof Jonathan Tennyson

Data-driven multi-scale modelling of bacterial biofilms

UCL Mathematics

Principal advisor: Dr. Philip Pearce

Time Reversal Imaging and Learned Physics with Neural ODEs

UCL Medical Physics and Biomedical Engineering

Principal advisor: Prof Ben Cox

Drift detection in graph streams and its applications in healthcare

UCL Computer Science and Advanced Research Computing Centre

Principal advisor: Dr. Yevgeniya Kovalchuk

Inference of gene regulatory networks from single cell data

Imperial Mathematics

Principal advisor: Prof Vahid Shahrezaei and Dr. Philipp Thomas

Optimal transport for probabilistic machine learning

Imperial Mathematics

Principal advisor: Dr.Felipe Tobar

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

UCL Advanced Research Computing Centre

Principal advisor: Dr Matt Graham

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

UCL Computer Science

Principal advisor: Prof Marta Betcke

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

UCL Statistics

Principal advisor: Prof Alexandros Beskos

A differentiable Gillespie algorithm for exact gradients through discrete stochastic systems

Imperial Mathematics

Principal advisor: Dr.Cristopher Salvi

Computational solution of inverse problems using large datasets of low rank

Backpropagation through rough differential equations

Large-scale high-performance solver for therapeutic ultrasound applications

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

Optimization methods for high-dimensional reinforcement learning

Data-driven preconditioning for parallel-in-time PDE solvers

AI code generation and numerical codes

Model correlation and the version control tree

Accelerating parabolic Stochastic PDE solver via a weak adversarial network approach

Improving impaired hearing through sound reconstruction from neural activity patterns

A machine learning-informed computational model of cancer-immune interactions

Developing Quasi-Geostrophic Coupled Ocean–Atmosphere Model

A Unified Form Language for PDEs in non-divergence form

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

Agent-based simulations of tissue dynamics

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

Automated Bayesian inference in stochastic differential equation models

Numerical methods for PDEs in fractal domains

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

Efficient Computation of Transition States in Molecular Dynamics

Fast Multipole Methods on modern architectures

Inference and inverse problems for stochastic interacting particle systems

Robust Bayesian Inference at Scale

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

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

Transfer Learning for Monte Carlo

A computational framework for heterogeneous coupling in large scale computations

Simulation-based Inference for Expensive Scientific Simulators

Koopman operator learning of nonlinear PDEs

Machine Learning for Low-Cost Data Assimilation

PARALIFT – A PARAllel framework for LIFTed training of neural networks

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

Re-griding the TROVE nuclear motion program

Data-driven multi-scale modelling of bacterial biofilms

Time Reversal Imaging and Learned Physics with Neural ODEs

Drift detection in graph streams and its applications in healthcare

Inference of gene regulatory networks from single cell data

Optimal transport for probabilistic machine learning

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

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

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

A differentiable Gillespie algorithm for exact gradients through discrete stochastic systems

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

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