The Department of Mathematical Sciences at the University of Bath is inviting applications from excellent candidates for a PhD studentship in the EPSRC Programme Grant EP/V026259/1 on the “Mathematics of Deep Learning” (Maths4DL). Maths4DL is a joint programme run by the University of Bath, the University of Cambridge and University College London.
Start date: 2 October 2023.
This is an exceptional opportunity to conduct ambitious research at the forefront of mathematics, statistics, and machine learning. The Vision and Ambition of Maths4DL is to develop a comprehensive mathematical, statistical and computational framework that addresses i) the foundational challenges on interpretability of the trained Deep Neural Networks (DNN), ii) robustness and generalisation of DNN on test data, iii) statistical confidence in DNN-outputs and iv) computational challenges with large-scale models and high-dimensional training data.
Project Overview:
The goal of this project is to study machine learning approaches in an infinite-dimensional setting. Lifting high-dimensional problems to an infinite-dimensional space and designing algorithms in that setting has been a fruitful idea in many areas of applied mathematics, including inverse problems, optimisation, and partial differential equations. This approach allows one to develop algorithms that are inherently dimension- and discretisation-independent and typically perform better in high-dimensional problems. In the context of machine learning, this approach has gained significant attention in the context of, e.g., operator learning. Within the general theme of the project, there will be possibilities to work on such topics as, for example, approximation properties of neural networks, training dynamics, semi-supervised learning, and applications in, e.g., mathematical imaging.
Project keywords: deep learning, machine learning, data science, mathematics.
Candidate Requirements:
Applicants should hold, or expect to receive, a First Class or good Upper Second Class Honours degree (or the equivalent) in mathematics or a closely-related discipline. A master’s level qualification would also be advantageous.
The ideal candidate will have experience in one or more of the following areas: inverse problems, machine learning, mathematical imaging, applied functional analysis, and/or optimisation. Experience in programming is desirable (e.g., MATLAB / Python, Tensorflow / PyTorch).
Non-UK applicants must meet our English language entry requirement.
Enquiries and Applications:
Informal enquiries are welcomed and should be directed to Dr Yury Korolev on email address [Email Address Removed]
Formal applications should be submitted via the University of Bath’s online application form for a PhD in Mathematics.
More information about applying for a PhD at Bath may be found on our website.
Note: Applications may close earlier than the advertised deadline if a suitable candidate is found. We recommend, therefore, that you contact Dr Korolev prior to applying and submit your formal application as early as possible.
Funding Eligibility:
To be eligible for funding, you must qualify as a Home student. The eligibility criteria for Home fee status are detailed and too complex to be summarised here in full; however, as a general guide, the following applicants will normally qualify subject to meeting residency requirements: UK and Irish nationals (living in the UK or EEA/Switzerland), those with Indefinite Leave to Remain and EU nationals with pre-settled or settled status in the UK under the EU Settlement Scheme. This is not intended to be an exhaustive list. Additional information may be found on our fee status guidance webpage, on the GOV.UK website and on the UKCISA website.
Equality, Diversity and Inclusion:
We value a diverse research environment and aim to be an inclusive university, where difference is celebrated and respected. We welcome and encourage applications from under-represented groups.
If you have circumstances that you feel we should be aware of that have affected your educational attainment, then please feel free to tell us about it in your application form. The best way to do this is a short paragraph at the end of your personal statement.
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