MARS offers expert supervision in a range of different research areas for our Applied Mathematics and Mathematical AI PhD programmes.
Find out more about our academic staff and their supervision interests below.
We are currently accepting applications from UK fees status students for October 2027 entry.
Please ensure that you contact the relevant supervisor to discuss your potential PhD project before you apply.
Apply to MARS
I am an applied mathematician working at the interface of applied modelling, statistical inference and machine learning. My research has two strands. In quantum fluids, I study the dynamics of quantised vortices and turbulence in superfluid helium, Bose–Einstein condensates and neutron stars, current work involves combining simulations with differentiable models to infer physical parameters such as mutual friction. In mathematical epidemiology and ecology, I develop models and inference methods for the spread of plant pests and pathogens, from reaction–diffusion PDEs and Bayesian inference for stochastic epidemic models to generative diffusion models that reconstruct spatial transmission maps from sparse outbreak data. A unifying theme is an interest in applying modern computational and AI tools to solve inverse problems in real-world systems. I have published over 70 refereed articles, and my work has been supported by EPSRC, Leverhulme, STFC, DEFRA and NERC.
Much of my research focusses on the behaviour of dynamical systems with network structure, which arise naturally in chemistry and biology. Techniques from algebra, geometry, and combinatorics can be used alongside traditional approaches from dynamical systems and bifurcation theory to understand how network structure influences the allowed dynamics of such systems. A particularly exciting application is "chemical reaction network theory", the abstract study of dynamical systems (deterministic or stochastic) arising from reaction networks.
My research focuses on modelling complex systems. These are often stochastic dynamical systems that are only partially observed, such as infection transmission in hospitals, human mobility, or disease spread through livestock movement networks. I am particularly interested in scalable Bayesian inference for calibrating these models to data in real time, with the aim of providing decision-time evidence. My main application is currently hospital infection control, where models can help identify the drivers of transmission and inform where control measures should be targeted.
I work at the intersection of applied and computational mathematics and mathematical analysis, on problems inspired by materials science, physics, data science and AI. Most are variational: an energy, its minimisers and critical points, and how these change with a parameter. My current themes are: energy landscapes of atomistic systems, where I develop numerical continuation and deflation methods that scale to large simulations with machine-learned interatomic potentials; rigorous discrete-to-continuum analysis of cracks, dislocations and plasticity; learning compact geometric models of the microstructure of metals such as steel from image data, using optimal transport and GPU computing, in collaboration with Tata Steel; and the theory and algorithms of unbalanced optimal transport, a tool for comparing distributions that is central to modern machine learning. I aim for results that are rigorous where possible and computable at scale, and release them as open-source software. See https://mbuze.github.io for details and publications.
My main research interests are in the dynamics of quantum fluids. Unlike classical fluids, these "superfluids" have the remarkable property that they can flow without viscous effects. Far from science fiction, they have been realised in state-of-the-art laboratories around the world, and are predicted to play a key role in the dynamics of neutron stars. While quantum fluids are a perfect testbed for many-body quantum physics, I am particularly interested in using quantum fluids to study turbulence, one of the most important and yet least understood phenomena in physics. They offer a route to study turbulence as they behave as an ideal fluid, they are amenable to mathematical modelling, and they can be studied in highly controllable experimental settings. In addition to this, I am part of a group within MARS who are developing machine learning tools to design, control, and interpret ultra-cold atomic devices for sensing applications.
I'm interested in understanding how perturbations propagate through complex systems, particularly those arising in mathematical biology and neuroscience. My research combines computational spectral theory, network science and dynamical systems to study how interactions and structural changes influence collective behaviour and stability.
I was awarded an EPSRC Postdoctoral Fellowship for my project "The Mathematics of Depression", which investigates mechanisms underlying Major Depressive Disorder (MDD). The project brings together brain networks and hormonal systems, which interact through many pathways and are measured in different ways.
Understanding these coupled systems requires lots of interesting ideas and advances in mathematical theory: how time delays shape oscillations and stability, how spectral properties relate to control, and how model parameters can be identified and constrained using different types of data. These questions motivate my interest in delay differential equations and the mathematical challenges of combining modalities.
I work at the interface of epidemiology, computing, and statistics, creating methods for training and prediction using probabilistic state-transition models. In particular, I focus on Bayesian stochastic epidemic models, using Monte Carlo methods for training and prediction. I am highly interested in computer science and research software engineering, and support an amazing team of PhD students, postdocs, and RSEs.
I work on probabilistic machine learning for scientific discovery and engineering design, in settings where every experiment is slow, costly, or both. My group, Mathematical AI for Decision and Discovery, builds models that decide what to measure next and that can absorb what scientists already know about a system.
Much of our current work develops Gaussian process flows, which recast Gaussian process sampling as a generative flow. This gives a general mechanism for incorporating the full richness of real-world knowledge as conditioning information, from governing physics and hard constraints to descriptions in natural language, rather than relying on measurements alone. Alongside this we work on Bayesian optimisation, active learning and experimental design.
We work closely with industry on problems ranging from drug discovery to fusion reactor design, climate modelling and materials discovery. I hold a UKRI Future Leaders Fellowship. See my website for more info (https://henrymoss.github.io/)
My research lies at the interface of computational statistics and probabilistic machine learning, with a focus on developing scalable, reliable algorithms for Bayesian inference and generative modelling. A central theme is Monte Carlo methodology – Markov chain Monte Carlo, sequential Monte Carlo and stochastic gradient samplers – designed for large datasets and complex, high-dimensional models. I am particularly interested in the interplay between sampling and optimisation, including learning-rate-free algorithms, and in combining classical Monte Carlo with modern generative models such as normalising flows, flow matching and diffusion models, for example to accelerate MCMC or to solve inverse problems through guided diffusion. A growing strand of my work concerns probabilistic models for structured data, including generative models for graphs and hypergraphs and statistical models for populations of networks. Applications include environmental science, such as locating gas emission sources and modelling soil moisture dynamics.
My research lies at the intersection of mathematical biology, numerical analysis and scientific computing. I develop mathematical and computational models to understand and investigate cell-tissue interactions, with applications including wound healing, tissue contraction, cell deformation during migration, cancer invasion, and ultrasound-assisted drug delivery in the brain. A central theme of my research is bridging and comparing models at different scales via Dirac delta distributions: from agent-based models to continuum-based models in the form of partial differential equations. Recent work combines experimental imaging data with information on cell proliferation and migration to study wound closure. Moreover, I investigate travelling waves and numerical methods for modelling wildfire propagation. Techniques including agent-based modelling, dynamical systems, numerical analysis, finite-element method, and scientific programming.
My research interests span sequential decision making, including reinforcement learning, Bayesian optimisation, and active learning, data-driven modelling of dynamical systems, and generative modelling. I am particularly interested in developing mathematically principled methods for learning and decision making, as well as new approaches motivated by emerging real-world/AI problems (e.g., language model, RLHF, drifting model etc).
My work is in computational applied mathematics, focusing on developing and analysing numerical and probabilistic machine-learning methods for challenging problems in science and engineering. I am particularly interested in Bayesian sampling, active learning, generative modelling, and high-performance computing, often in the context of atomistic/molecular modelling and simulation. A unifying thread here is that most of the systems I work with are governed by stochastic dynamics.
I am also interested in geometric machine learning, in particular the development of equivariant machine-learning models whose predictions transform consistently under symmetry operations.
I work closely with domain specialists — in chemistry, physics, materials science and statistics — to tackle real-world problems in the simulation of molecules and materials, while developing mathematically well-founded machine-learning approaches.
My research lies at the interface of optimization, statistical learning, and machine learning, with a focus on the theory and design of efficient algorithms for large-scale problems. I am particularly interested in understanding how computational, memory, and communication constraints shape optimization and statistical performance. My work covers stochastic and non-convex optimization, distributed and federated learning, communication compression, adaptive and second-order methods, and model compression through sparsity, quantization, and low-rank structure. A recurring theme is to develop algorithms with rigorous convergence and complexity guarantees while accounting for constraints that arise in modern large-scale learning systems. More broadly, I aim to connect mathematical foundations in optimization with practical questions of scalability, robustness, and resource efficiency.
