PhD Projects
Contact: info@mathrad.ac.ukMaThRad will offer PhD studentships at either the University of Warwick, University of Bath or the University of Cambridge. The PhD projects will be supported by our academic and industrial partners.
Opportunities will be posted here when they are available.
PhD Studentship: Computational Methods for Uncertainty Quantification in Nuclear Fusion
Deadline – Sunday, August 24, 2025
Host Institution: Newcastle University – School of Mathematics, Statistics and Physics
Supervision: Dr Jere Koskela (Newcastle) in collaboration with the UK Atomic Energy Authority
Research Network: Member of the MaThRad research network (Universities of Warwick, Bath, and Cambridge)
Project Overview
Nuclear fusion has the potential to deliver sustainable power to the electricity grid, but current simulation methods for predicting yields in tritium fuel cycles face significant challenges. Large engineering tolerances are required due to the lack of scalable uncertainty quantification tools, increasing reactor costs.
Physical experiments are costly, while simulations are affected by uncertainty in nuclear data and unresolved processes such as thermal expansion and fine-scale inhomogeneities. Generating independent simulation replicates that capture all relevant uncertainties is currently infeasible.
This PhD project will:
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Deliver a rigorous understanding of industry-standard simulation and variance reduction techniques, particularly importance sampling variants.
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Connect these techniques to modern Monte Carlo algorithm frameworks to improve accuracy, scalability, and cost-efficiency.
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Contribute fundamental methodologies critical to the sustainable delivery of fusion power.
The project is based at Newcastle University and will be co-supervised by the UK Atomic Energy Authority, with additional collaboration and networking opportunities through the MaThRad research network.
Research Areas
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Applied Mathematics
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Computational Mathematics
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Engineering Mathematics
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Machine Learning
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Mathematical Modelling
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Probability & Statistics
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Stochastic Processes
Funding
This studentship provides:
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Annual stipend: £21,470
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Full tuition fees (Home fee level only)
How to Apply / Enquire
To register your interest click here
To ask questions about the project, funding, or eligibility, please contact:
Dr Jere Koskela , Director of Statistics and Data Science, Reader in Statistics
Interacting particle methods for improved simulation algorithms in the nuclear energy industry
Funded Studentship at the University of Bath
This project is offered by the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa), for entry in September 2025.
Nuclear energy is and will be an important part of the future energy mix. Whilst the physical laws which underpin different stages of the nuclear energy cycle are generally well understood, solving the systems accurately and quickly remains challenging, and is an important challenge in the design, operation and safety of modern generation processes.
The ”gold standard” of numerical methods in the nuclear industry is Monte Carlo, since Monte Carlo methods are able to handle sophisticated designs and accurately incorporate complex nuclear data. Methods used in different applications include power iteration (for eigenvalue problems) and adaptive multi-level splitting for rare event problems. Both of these algorithms rely on the simulation of many particles which are simulated largely independently, but with times at which actions are performed which depend on the whole population. Such systems of particles are an example of interacting particle systems.
The aim of this project is to understand probabilistic properties of these algorithms, and how they feed into error analysis and other properties of the system, such as analysis of sensitivities of the answers to small changes in properties of the underlying system, such as fuel concentration, or rod positions.
Hybrid numerical algorithms for radiation transport
Funded Studentship at the University of Bath
This project is offered by the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa), for entry in September 2025.
Radiation transport plays a crucial role in numerous scientific and industrial domains, including nuclear engineering, medical physics and space technologies. These fields often require the simulation of complex systems where accurate and efficient numerical methods are essential. While both deterministic and stochastic methods have been developed for this purpose, each comes with its own advantages and limitations.
Deterministic methods, such as finite element discrete ordinates methods, are often preferred for their efficiency and accuracy in structured geometries but can struggle with handling uncertainties and highly heterogeneous environments. On the other hand, stochastic methods, Monte Carlo techniques, are the gold standard in representing random phenomena and complex geometries but can be computationally expensive and very slow to converge in certain cases. Hybrid algorithms seek to combine the strengths of both approaches, leveraging the deterministic framework where appropriate while incorporating stochastic components to handle the complexities of real-world applications.
The aim of this project is to develop, analyse and implement these hybrid numerical algorithms, assessing their performance in important applications. We will explore how to optimise these methods, focusing on error analysis, computational efficiency and adaptability to different physical settings. This work will contribute to improved simulation accuracy and reliability in critical areas of technology and science.
