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PhD Studentship: Accelerating Uncertainty Quantification with Deep Learning

University of Exeter - College of Engineering, Mathematics and Physical Sciences

Qualification Type: PhD
Location: Exeter
Funding for: UK Students
Funding amount: For eligible students the studentship will cover Home tuition fees plus an annual tax-free stipend of at least £15,609 for 3.5 years full-time, or pro rata for part-time study
Hours: Full Time
Placed On: 3rd November 2021
Closes: 10th January 2022
Reference: 4313

Uncertainty Quantification (UQ) for engineering models is a rapidly growing field with numerous exciting applications. However, the current best-performing algorithms for quantifying the uncertainty through Markov Chain Monte Carlo (MCMC) rely on computing a gradient that is typically not readily available for complex engineering models. This project is concerned with investigating the potential of emerging methods from Machine Learning and Artificial Intelligence to construct efficient MCMC proposals that do not require this gradient. 

The MCMC methodology at large targets a broad class of problems known Bayesian inverse problems which are ubiquitous to many areas of engineering. There are various apparent ways that the MCMC methodology could be improved by exploiting other established methods borrowed from e.g. Reinforcement Learning and Artificial Neural Networks, but it is currently not clear exactly how to do this, and how such an algorithm will perform in real-world engineering problems. We can provide various relevant benchmark problems for testing, but you are free to explore other applications once you have familiarised yourself with the topic at large. Aside from developing and testing viable methods, this project also involves writing reusable computer code implementing these methods. There are opportunities to contribute to existing open-source code, but no requirement to do so. 

Since this is a broad topic with many promising avenues of research, we strongly encourage independent thought and creativity. There are numerous open questions and research opportunities within the current state-of-the-art algorithms, in particular within the subtopics of Delayed Acceptance (DA) and Multi-level MCMC (MLMCMC), around which the MCMC research in our group mainly revolves. While we encourage you to nestle your research within this frame of reference, you will have the freedom to explore other feasible approaches. 

The successful applicant will have a high level of numeracy and be proficient with computer programming since this project involves converting complex mathematical concepts to reusable computer code. Your programming language of choice is not essential, but knowledge of Python or C++ would be advantageous. 

Entry Requirements 

This studentship is open to UK and Irish nationals, who if successful in their application will receive a full studentship including payment of university tuition fees at the home fees rate. 

Applicants for this studentship must have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK, in an appropriate area of science or technology.

Candidates should have a strong mathematical background, preferably in probability and statistics. Experience of coding in Python and the use of deep learning libraries, such as PyTorch or TensorFlow, is desirable. 

If English is not your first language you will need to have achieved at least 6.0 in IELTS and no less than 6.0 in any section by the start of the project.  

Alternative tests may be acceptable (see http://www.exeter.ac.uk/postgraduate/apply/english/). 

Funding:

The University of Exeter’s College of Engineering, Mathematics and Physical Sciences is inviting applications for a fully-funded PhD studentship to commence in January 2022 or as soon as possible thereafter.  For eligible students the studentship will cover Home tuition fees plus an annual tax-free stipend of at least £15,609 for 3.5 years full-time, or pro rata for part-time study. 

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