Featured research

Our research

MARS research spans a range of application areas. From predicting climate events and managing disease outbreaks to molecular modelling and personalised treatments for depression, we are delivering next-generation mathematics that has real-world impact.

Oak Processionary Caterpillars

Data-driven insights for invasive species control

Innovative research from MARS Professor Andrew Baggaley is using mathematical modelling tools to predict Oak Processionary Moth spread, reducing its negative ecological and public health impacts.

Oak Processionary Moth (OPM) is an invasive pest that damages oak trees and poses risks to human health. First identified in London in 2006, it has since spread to surrounding counties in South East England. Richmond Park, a protected site of ecological and public importance, has experienced particularly severe outbreaks. Effective control requires not only understanding current infestation locations but also anticipating future spread and severity.

This research involves the development of a modelling framework based on partial differential equations – a type of mathematical equation used to describe how things change over space and time – to simulate OPM’s population dynamics.

Richmond Park is represented as a grid, with each square corresponding to a specific area. The model tracks how suitable each location is for OPM infestation and how the population will grow and spread between areas. Real-world data, including past nest locations, tree density, and climate data, is used to inform the model. Advanced machine learning techniques are applied to fine-tune the model to ‘learn’ it’s free parameters, enabling greater understanding and prediction of OPM’s spatiotemporal spread.

The project’s culmination will be a forecasting tool, designed to support land managers and conservation teams in Richmond Park and beyond to target interventions and reduce the ecological and public health impacts of OPM.

Human Cell

Transforming systems biology through mathematical innovation

MARS Senior Lecturer, Dr Murad Banaji, is developing a powerful new toolkit for analysing the complex dynamics of biochemical networks.

Many biological processes are driven by networks of chemical reactions. These networks often control how cells behave - for example, by ‘switching’ from one state to another in response to a signal, or by generating oscillations where outputs change periodically. When these signalling process go wrong, they can lead to diseases such as cancer, Type 2 Diabetes and Alzheimer’s.

But how can we identify which reaction networks are capable of behaviours like switching and oscillation? Numerical simulation is helpful, but as networks get larger and more complex, simulations become harder to scale and interpret.

This research explores two promising alternatives. The first examines ‘bifurcations’ - sudden qualitative changes in dynamics that occur when certain inputs change. These shifts can lead to switching, oscillation and other complex cell behaviours. By combining mathematical analysis and computational algebra it is possible to detect bifurcations without running simulations.

The second approach involves developing theory on how networks ‘inherit’ behaviours from their smaller subnetworks. By understanding the dynamics of these smaller building blocks, it is possible to predict the behaviour of larger, more complicated systems.

Together, these methods offer a powerful new toolkit for analysing biochemical networks. The ultimate aim is to automate the process of identifying key behaviours in real-world biological networks – an advance that could significantly improve how we study and treat disease.

Norovirus

Model-based methods for hospital infection control

MARS Lecturer, Dr Jess Bridgen, is developing an innovative system to help hospitals detect and control infections before they spread.

Hospital-acquired infections are a significant burden to health systems world-wide, and are associated with increased morbidity and mortality. Effective hospital infection control requires a detailed understanding of the role of different transmission pathways, yet identifying exactly where and how infections spread within the complex structure of healthcare settings presents a unique statistical and computational challenge.

A model-based system can be used to rapidly detect at-risk areas of a hospital and quantify relative routes of transmission, providing actionable insights for infection control. This research focuses on developing a flexible mathematical modelling framework for bacterial and viral diseases, and novel statistical methodology to identify drivers of transmission.

This research began during the COVID-19 pandemic, working with NHS clinicians to develop a Bayesian framework to retrospectively identify infection times and disentangle hospital outbreak dynamics (Bridgen, 2024). This methodology is now being extended to assess the effectiveness of control measures, model a range of infectious diseases, and incorporate real-time data.

By providing hospitals with data-driven insights, this research could save lives and reduce the burden on healthcare systems.

Atoms

Advanced mathematical tools for developing stronger, more resilient materials

New research from MARS Lecturer, Dr Maciej Buze, is creating powerful mathematical tools to better predict how materials behave at the atomic level.

Understanding how tiny imperfections, or defects, form and move within materials is crucial for improving everything from electronics to structural integrity of materials. Defects can influence a material's strength, durability, and functionality, making this research particularly relevant for industries like aerospace, manufacturing, and technology. However, studying these defects at the atomic level is challenging because the energy landscapes involved are highly complex and full of twists and turns. Traditional simulation methods often struggle to navigate this complexity efficiently.

This research aims to bring advanced mathematical tools - called numerical continuation and deflation techniques - into the world of atomistic modelling. These methods have proven successful in other fields but are not yet widely used for studying materials at the atomic scale. To bridge this gap, a prototype tool has been developed that integrates these mathematical techniques with existing simulation software. This tool has already been used to explore how defects form in copper surfaces; how vacancies (missing atoms) move in multi-species systems; and how cracks propagate through silicon.

The ultimate goal is to make these powerful tools more accessible to researchers, helping them predict material behaviour more accurately. This could lead to the development of stronger, more resilient materials with practical applications in technology and industry.

Vortex

Mathematical simulations for stabilising complex vortex states

MARS Lecturer, Dr Ryan Doran, is developing new techniques that will pave the way for controlled studies of quantum turbulence.

Turbulence – the complex and seemingly chaotic motion of fluids – is one of the most important and least understood phenomena in physics. It plays a central role in systems ranging from atmospheric flows and ocean currents to industrial mixing and even the flow of blood in arteries. Despite its importance, turbulence remains difficult to predict because it involves many interacting structures across different length and time scales. Studying turbulence in simplified, highly controllable systems is therefore essential for uncovering the basic physical principles that govern it.

This research uses an ultra-cold quantum fluid as a model system in which turbulence can be broken down into its simplest building blocks: vortices. These are the quantum version of the whirlpool created when a sink is unplugged, but unlike that whirlpool, these vortices are discrete objects whose motion and interactions can be precisely controlled. The goal is to develop new techniques that allow vortices to be experimentally created at specific locations, with a chosen strength, and in a reproducible way. This can be achieved by mathematically modelling the quantum fluid and then simulating the resulting flow.

The ability to engineer and stabilise complex vortex states is a key step toward controlled studies of quantum turbulence. Beyond fundamental insight, this work lays foundations for future applications in precision sensing, quantum simulation, and the design of quantum fluid systems where flow and stability can be tailored with high accuracy.

Man with head in his hands

Creating personalised treatments for depression

MARS Lecturer, Dr Catherine Drysdale, is using cutting-edge mathematical techniques to model brain and hormone interactions improving treatment pathways for people with depression.

Depression affects one in six people in the UK and is the leading cause of ill-health and disability worldwide. Despite decades of research, accurately predicting treatment response to interventions, such as antidepressants or therapy, remains a significant challenge. Many endure a painful cycle of trial and error, waiting months or even years to find an approach that works.

This research uses mathematics to better understand this complex issue. Depression is deeply connected to hormone rhythms - especially cortisol, the primary stress hormone - and brain networks that control memory, emotion, and decision-making. These systems are interconnected through complex feedback loops, making it difficult to pinpoint where things go wrong.

Mathematical approaches offer a new way forward. Techniques such as pseudospectra, which measure how sensitive systems are to change, and graph theory, enable modelling of how brain and hormonal networks interact and respond to stress. These models can help explain why some people develop depression after events like bereavement or relationship breakdown, while others do not.

By revealing the underlying dynamics of depression, this research will ultimately support personalised mental health care. It will help to identify who is most at risk and which treatments are likely to work, offering faster and more effective support for those who need it most.

Advanced mathematical models for timely outbreak response

Head of MARS, Professor Chris Jewell, is developing state-of-the-art statistical and AI methods to improve real-time understanding of infectious disease outbreaks.

Disease outbreaks, such as seasonal flu, the COVID-19 pandemic, and measles affect people of all ages, genders, and nationalities. Health services must respond quickly and effectively to prioritise care for the most severe cases, manage the social and economic impacts, and ultimately save lives.

Yet, timely decision-making remains fraught with difficulty: case reports are often incomplete or delayed, and individuals typically only report symptoms several days after infection, meaning that the outbreak picture lags behind the true situation.

This research addresses these challenges by using stochastic dynamical models to improve real-time understanding of outbreaks, providing an accurate evidence base for timely public health decision making. A particular focus is on developing Monte Carlo methods (particularly Markov chain and Sequential Monte Carlo) to calibrate complex, high-dimensional models.

These models enable detailed analysis of how factors such as location, ethnicity, socioeconomic status, age and gender influence infection risk or how routine hygiene practices – such as handwashing and sanitation – affect the spread of antimicrobially-resistant bacteria.

The overarching goal is to translate these advanced statistical and AI methods into usable tools, including software that aids the rapid development of models, simplifies calibration, and lowers the entry barrier for those new to complex outbreak modelling.

An abstract image of a neural network

Accelerating scientific discovery with machine learning

MARS Lecturer, Dr Henry Moss, is revolutionising scientific experimentation with smarter machine learning models.

Machine learning (ML) has dramatically transformed how scientists approach experimentation, especially in domains like drug discovery, materials science, and engineering. Yet, there remains a need for smarter ML models to accelerate the pace of scientific innovation, particularly in areas where experimentation is technically and financially costly.

This research tackles a fundamental question: Given a trained ML model, what additional data should be collected to empower scientists to make more informed decisions?

It focuses on pioneering new ML methodologies to enable automated experimental design across a range of high-stakes settings.

Application of these new ML methodologies has already had real-world impact. It has contributed to scientific breakthroughs including the discovery of novel molecules, the development of innovative engineering solutions, and advances in climate model calibration to help scientists refine their predictions and simulations. It has even led to improvements in the ML systems themselves, for instance in Amazon Alexa.

Research partnerships with the British Antarctic Survey, AstraZeneca, and the UK Atomic Energy Authority are bringing these advanced ML tools into the experimental workflows of even more scientists. By enhancing the way experiments are designed and executed, this research is accelerating discovery and shaping the future of innovation.

Mountain landscape with water

AI-powered earth observation for rapid climate action

MARS Professor Chris Nemeth is converting raw satellite and sensor feeds into early-warning signals for a warming world.

As the impacts of climate change accelerate, the need for timely, accurate environmental data has become critical. To manage risk and make effective decisions - from preventing greenhouse gas leaks to forecasting sea-level rise - real-time, reliable information on the Earth’s rapidly changing systems is urgently needed.

This research blends physics-based and neural surrogate models to pinpoint methane leaks in seconds, harnesses satellite data to map daily ice melt across Greenland, and applies Bayesian learning to uncover hidden soil-nutrient loss from field samples. These tools plug into an open-source pipeline that updates as fresh data arrives, delivering a live picture of how land, ice and atmosphere are shifting.

With this faster more precise environmental intelligence, inspectors can shut faulty valves before large-scale methane emissions occur, farmers can treat soil degradation before crop yields crash, and glaciologists can refine sea-level forecasts in almost real-time.

By providing trustworthy, probabilistic snapshots of Earth’s vital signs, this research empowers industry and policy-makers to make confident, climate-smart decisions.

Doctors operating on a patient

Personalised wound healing with mathematical modelling

State-of-the-art research from MARS Lecturer, Dr Alice Peng, is pioneering a patient-centred approach to wound healing.

Despite extensive research into wound healing, many aspects remain poorly understood. Even when patients receive the same diagnosis, their healing processes can vary significantly. Subtle variations, often too small to detect manually, can have a major impact on recovery.

This is where mathematical modelling can make a difference. By adjusting patient-specific parameters, mathematical models can predict healing scenarios that may not be directly measurable. This enables clinicians to design and refine optimal treatment strategies tailored to each patient.

This research uses agent-based modelling, which treats individual cells as distinct entities, allowing precise tracking of their location and activity. This model has already successfully replicated key clinical and experimental findings, demonstrating that early-stage wound conditions are strongly linked to long-term healing outcomes, including wound contraction and overall recovery.

The long term goal of this research is to develop a patient-specific digital twin - a virtual model that continuously monitors a patient’s wound. This technology could provide early warnings when subtle, hard-to-detect changes occur. Additionally, by simulating different treatment approaches, clinicians can identify the most effective strategies for individual patients whilst minimising complications.

This innovative approach brings wound care closer to personalised treatment, improving outcomes and enhancing patient wellbeing.

Molecules in a network

Adaptive algorithms for targeted scientific modelling

MARS Lecturer, Dr Jixiang Qing, is developing mathematically rigorous methods to help scientists collect data more efficiently.

Running experiments costs time and money. In drug discovery, a single reaction can take days. In engineering, one simulation might run for hours. Scientists must decide carefully which experiments or conditions to investigate, but the most informative options are not always obvious at the start – they only become apparent after some initial results are obtained. Collecting the right data is essential, yet figuring out which data will be most useful is a major challenge.

This research tackles this problem using techniques from active learning, which focus on selecting the experiments that provide the most valuable information; and bandit optimisation, a method for exploring different possibilities while gradually focusing on the most promising ones. By developing new algorithms with mathematical guarantees, these techniques are proven to reliably identify the best options for scientists. They have already outperformed existing approaches on molecular modelling tasks, achieving accurate predictions with fewer experiments.

The ultimate aim is to accelerate scientific discovery across disciplines by reducing wasted experiments. By providing scientists with principled, reliable tools for deciding where to collect data next, this research could speed up progress in molecular science, materials design, engineering, and beyond.

*This work is being carried out in collaboration with Dr Matthias Sachs.

Molecules

Advancing technological development through symmetry-aware AI

New research from MARS Lecturer, Dr Matthias Sachs, is developing machine learning models to accelerate atomic-scale simulations for real-world application.

Machine learning (ML) is increasingly being used to predict and understand macroscopic properties of atomistic systems. This is especially impactful in fields such as materials science, computational chemistry and engineering, where it supports the development of new materials, drug discovery, and clean energy technologies.

In contrast to many other ML applications, training data on these systems is often scarce due to the high computational cost of generating it using quantum mechanical models. Additionally, many target properties typically follow strict symmetry rules which are not inherently known to standard ML models.

These challenges can be addressed by employing symmetry-adapted neural network architectures. These models are specifically designed to respect the physical symmetries of the system so that the model treats equivalent atomic arrangements in the same way. This leads to more accurate predictions and significantly reduces the amount of data required for training.

This research develops these symmetry-aware models to learn key atomic-scale quantities, including interatomic force fields and electronic friction tensors. The latter is essential for realistically simulating molecule-surface interactions, which play a crucial role in electrode-electrolyte interfaces in batteries and hydrogen fuel cells.

The long-term aim is to deploy these machine-learned representations in large-scale computer simulations, enabling faster and more cost-effective development of advanced technologies by reducing reliance on laboratory experiments.

Neural network with equations

Mathematical innovation for accessible, sustainable and trustworthy AI

MARS Lecturer, Dr Mher Safaryan, is developing new algorithms and theoretical tools to optimise the performance of modern AI systems.

From smartphone assistants and medical imaging to online translation and climate modelling, modern AI systems rely on training large models using vast amounts of data. While these systems can be highly accurate, they are also expensive to train and run, requiring large data centres that consume significant energy and memory. This limits where and how AI can be deployed, especially in settings such as hospitals or on mobile devices.

To address this challenge, this research focuses on the mathematics of optimisation: the process by which computer algorithms learn from data by gradually improving their predictions. Optimisation provides the mathematical backbone of modern machine learning, yet its growing scale raises new scientific and practical challenges.

This work develops new algorithms and theoretical tools that allow learning to happen using far less memory, computation, and communication, without sacrificing performance. In particular, the research explores ways to “compress” AI models so they become smaller and lighter, and to train models collaboratively across many devices without sharing sensitive data.

The long-term goal is to make advanced AI systems more accessible, sustainable, and trustworthy. By improving the efficiency of the algorithms behind AI, this research aims to reduce energy use and carbon emissions, support privacy-preserving technologies in healthcare, and enable intelligent systems to run directly on everyday devices - bringing powerful AI out of large data centres and into practical, responsible use across society.