I have two main research interests: The first is in the application of methods from the calculus of variations to analyse large data limits of problems that arise from machine learning and statistics. The second is in the application and development of optimal transport distances to signal and image analysis.
Currently I am a co-organiser for the One World Seminar Series on the Mathematics of Machine Learning and an editor for the journal Foundations of Data Science.
I am also a part of the Cambridge led project on AI assisted diagnosis and prognostication in Covid-19, and the European Union's Horizon 2020 program NoMADS (grant agreement number 777826).
I would be happy to discuss potential PhD projects, particularly in the area of connecting differential equations with neural networks (both for the analysis of nueral networks and to design better neural network architectures). The ideal background for this work would include (at least some of) metric spaces, measure theory, functional analysis and calculus of variations. Coding experience is a positive but not necessary. Please reach out if you would like to talk more.
I can be contacted at matthew[dot]thorpe[dash]2@manchester[dot]ac[dot]uk.
Between the 1st July 2021 and 17th December I will be visiting the Isaac Newton Institute programme on the Mathematics of Deep Learning. Most days I can be found in office F2 in the INI building.