Every year, G-Research runs a number of different PhD prizes in Maths and Data Science at universities in the UK, Europe and beyond.
Each prize is worth up to £10,000 and is open to final or penultimate year PhD students at specific universities, working across areas including Machine Learning, Quantitative Finance and Mathematics.
We’re pleased to announce the winners of this PhD prize, run in conjunction with the University of Cambridge.
“I am a final-year PhD student in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. My research looks at machine learning and analysis, with a focus on infinite-dimensional formulations of machine learning algorithms. In particular, I study graph-based semi-supervised learning methods and their mathematical analysis.
“My work uses tools from calculus of variations and optimal transport to understand the behaviour of these algorithms in the large-data regime. In particular, I am interested in questions of asymptotic consistency, examining how these methods perform as the number of samples grows and approaches infinity. This involves analysing continuum limits and establishing connections between discrete graph-based models and their limiting counterparts.
“Alongside theoretical work, I am interested in applying these state-of-the-art ML algorithms to problems in health data science. I have used graph-based learning approaches to study the cost-effectiveness of interventions for the elimination of neglected tropical diseases in low- and middle-income countries. More broadly, I am motivated by the potential of mathematically grounded machine learning techniques to inform public health decision-making.”
“I am currently a final-year PhD Student at the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. My research interests lie in the analysis of partial differential equations, specifically in relation to fluid mechanics.
“I have worked on the rigorous analysis of mathematical models from sea-ice and oceanic dynamics. Some of my work concerns the existence and regularity theory for (weak) solutions for geophysical models and the analysis of their dynamical behaviour. In addition, part of my research focuses on the mathematical analysis of wall-bounded turbulence, in particular the role played by the hydrodynamic pressure in incompressible flow and its behaviour in boundary layers.”
“I am a PhD student and a Trinity Henry Barlow Scholar in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge.
“The artificial intelligence revolution is currently driving a paradigm shift in sciences from knowledge-driven modeling (models from first principles) to data-driven modeling (models from data), promising to accelerate scientific progress. Yet, these models are fragile, biased and fail unpredictably, limiting their adoption in critical fields.
“My research confronts this problem by examining the theoretical limitations of current paradigms and using these insights to reshape our methods into ones with provable guarantees. Specifically, I focus on establishing the theoretical foundations for the use of machine learning in the sciences. This work spans various fields of applied mathematics, including non-smooth non-convex optimisation, inverse problems, imaging, scientific machine learning, geometric deep learning, and structure preservation.
For example, I introduced the concept of model collapse – a degenerative process in machine learning whereby training with synthetic data provably causes models to degrade, posing the critical and timely question of long-term generative AI improvement, given the widespread use of synthetic data in the industry.
Similarly, my work on discoverability illustrates the fundamental limitations of AI-driven “physics discovery,” providing a sobering answer for scientists asking if AI could be used to discover the governing laws of their systems. For many practical applications the answer is no, simply due to failure of an often unquestioned assumption: that systems dynamics can be uniquely identified from observations.”
