Discovery of new materials for applications on glass using Mathematical Optimisation and Machine Learning methodologies (Ref NSGPVCS2023)


The functionalisation of flat glass is a multi-billion-dollar industry spanning applications including displays technology, energy saving windows and energy generation through photovoltaics. To maintain the rate of progress in these and other emerging fields new materials are required with performance beyond that of known materials.

The interplay of many considerations including structure, bonding, and defect chemistry makes for a challenging opportunity to develop a new material that is stable and has interesting functional properties that can be applied as a thin film on glass. Mathematical modelling and optimisation which are ubiquitous in machine learning and artificial intelligence, are also in the core of a multitude of complex problems in chemistry and material science, such as prediction of new functional materials with desirable properties, statistical characterisation of data, experimental design, production control and planning.

This PhD project will study and apply existing optimisation methods and propose methods and mechanisms for novel ones. In particular, focus will be given to black-box optimisation methods capable of handling difficult complex problems that are difficult or impossible to model directly. Examples include grid, coordinate and pattern searches, metaheuristics, model-based methods, surrogate models, evolutionary optimisation methods such as genetic algorithms or ones utilising natural gradient and information geometry, and Bayesian optimisation. Many of them relay heavily on the use of various machine learning and statistical mechanisms to adapt to the optimisation landscape and automatically collect data where applicable.

The student will work closely with computer scientists, inorganic chemists, physicists, and material scientists to develop tools to predict new materials that may exhibit desirable properties. The developed or improved optimisation algorithms will go far beyond classical approaches deployed by physical computational science researchers thus far in the literature.

Qualifications: Applications are welcomed from students with a preferably 1st or 2.1 class BSc or equivalent in Mathematics, Computer Science or Physics. Previous experience with optimisation and machine learning (or any knowledge in chemistry) is not a requirement, though successful candidates must have strong mathematical and programming skills.

Please apply by completing the online postgraduate research application form here: How to apply for a PhD - University of Liverpool  

Please ensure you quote the following reference on your application: Discovery of new materials for applications on glass using Mathematical Optimisation and Machine Learning methodologies (Reference NSGPVCS2023) and make the application to Computer Science


Open to students worldwide

Funding information

Funded studentship

The award is 50% funded by NSG Group and 50% funded by the University of Liverpool through an EPSRC Doctoral Training Partnership award and will pay full tuition fees and a maintenance grant for 3.5 years. Applications from candidates meeting the eligibility requirements of the EPSRC are welcome – please refer to the EPSRC website ( It provides full tuition fees and a stipend of approx. £17,668 (this is the rate from 01/10/2022) full time tax free per year for living costs. The stipend costs quoted are for students starting from 1st October 2022 and will rise slightly each year with inflation.

The funding for this studentship also comes with a budget for research and training expenses of £1000 per year, and for those that are eligible, a disabled students allowance to cover the costs of any additional support that is required.

Due to a change in UKRI policy, this is now available for Home, EU or international students to apply. However, please be aware there is a limit on the number of international students we can appoint to these studentships per year.

You will be encouraged to undertake some teaching duties for the department for which you will receive training and payment. You will have the option to work towards and apply for Associate Fellowship of the Higher Education Academy (via the Foundations in Learning & Teaching in Higher Education (FLTHE) programme or the University of Liverpool Teaching Recognition and Accreditation (ULTRA) Framework




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  • 3AlS3.3Cl0.7: A Sulfide–Chloride Lithium Ion Conductor with Highly Disordered Structure and Increased Conductivity. Chemistry of Materials, 33, 8733-8744 (2021);
  • Element selection for crystalline inorganic solid discovery guided by unsupervised machine learning of experimentally explored chemistry. Nature Communications 12, 5561 (2021);