Developing Novel Machine Learning Methods for Equation of State Uncertainty Quantification


This PhD project aligns with the CDT in Distributed Algorithms: The What, How and where of Next-Generation Data Science.


The University of Liverpool’s Signal Processing group hosts the Centre for Doctoral Training in Distributed Algorithms (CDT) and together the team works in partnership with 30+ external partners from the manufacturing, defence and security sectors to provide a 4-year innovative PhD training programme that will equip its students with: the essential skills needed to become future leaders in distributed algorithms; the technical and professional networks needed to launch a career in next generation data science and future computing; and the confidence to make a positive difference in society, the economy and beyond.  This studentship is fully-funded by AWE – an organisation that supports the defence and security of the UK. 


The proposed aim of the PhD is to develop a highly parallelisable Sequential Monte Carlo Samplers capability and apply it to a high dimensional posterior distribution from an externally generated likelihood function. This capability must be applicable to AWE HPC platforms and utilise gradient-free proposal distributions. Whilst the aim is defined, the successful candidate can guide the research activities in a direction that fulfils this mission. The likelihood is costly to evaluate, cannot be sampled, and gradients of the likelihood are intractable. The likelihood function is calculated from the agreement between experiments and a bulk, thermodynamic equation of state (EoS) for a material of interest. By the multiphase nature of the EoS the likelihood will contain discontinuities and have high sensitivities to some input parameters. The software will be tested by the application of this method to the multiphase material model for Tin performed on the HPC platforms at AWE.


The successful student will be based at the University of Liverpool and be part of the CDT and Signal Processing Group  - a large, successful, social and creative research group that works together solving tough research problems.  Students have two academic supervisors and an industrial partner who provide co-supervision, placements and the opportunity to work on real world challenges. In addition, students attend technical and professional training to gain unparalleled expertise to make a difference now and in the future.


The research group is committed to providing an inclusive environment in which diverse students can thrive. The CDT particularly encourages applications from women, disabled and Black, Asian and Minority Ethnic candidates, who are currently under-represented in the sector.  We can also consider part time PhD students.  We also encourage talented individuals from various backgrounds, with either an UG or MSc in a numerate subject and people with ambition and an interest in making a difference. 


The studentship is open to: UK nationals who are willing and able to undergo security clearance.


Applicants please note: You must not submit a research proposal. The PhD project is defined. You must provide a supporting statement (no more than 700 words) that explains why you are interested in undertaking a PhD, this specific topic and joining the research group.


Open to UK applicants

Funding information

Funded studentship

This is a 4 year fully-funded PhD studentship starting 1 Oct 2024. The successful student will receive  funding for the UK tuition fees and a monthly maintenance at the UKRI Doctoral Stipend rate (£19,237 per annum, 2024/25 rate). In addition to fees and stipend, the student will receive a training grant of £4.5k/year for research-related expenses such as training and conferences.