PhD: Advanced Mathematical Optimisation in Materials Chemistry

University of Liverpool, UK

Project: The global optimisation of properties such as energy as a function of atomic positions is prevalent in materials chemistry. Its application is perhaps most evident in the field of crystal structure prediction, in which the global minimum of the energy of a system of periodically repeating atoms is sought. Crystal structure prediction is integral to many modern approaches of materials design and discovery, and under active development within the research team.

Until now, this global optimisation problem has been approached using heuristic algorithms such as simulated annealing, Monte-Carlo sampling / basin hopping or evolutionary algorithms. These algorithms have varying performance and provide limited information about the global optimum. There are, however, non-heuristic algorithms for specific types of optimisation problems that are more efficient and provide approximation guarantees on the solution with respect to the optimum. In this project we propose to apply such mathematical optimisation approaches to global optimisation problems in materials chemistry, such as crystal structure prediction, self-assembly of molecules into ordered structures as well as determination of ordered magnetic structures.

The student will work in the interface between Computer Science and Chemistry to apply advanced mathematical optimisation tools, such as semidefinite programming, to challenging problems in material discovery. During the project the student will have the opportunity to learn necessary topics from Materials Chemistry, Optimisation and Software Engineering. The acquired skills will be highly relevant not only for a future in materials science, but also in the areas of logistics, finance, operations research, and machine learning.

Research Environment: The successful applicant will join a cohort of students studying within the Leverhulme Research Centre for Functional Materials Design (LRC). The LRC aims to drive a design revolution for functional materials at the atomic scale by fusing chemical knowledge with state-of the-art computer science and robotics. The LRC is based within the Materials Innovation Factory (MIF) at the University of Liverpool. Opened in 2017, the MIF is a state of the art research building which is designed to enable the discovery of new materials through collaborative and interdisciplinary research.

Supervision: The studentship will be supervised by Dr Matthew Dyer and Dr Vladimir Gusev. Dr Dyer is a lecturer in the Department of Chemistry. His research interests lie in the field of computational materials chemistry and he has extensive experience in the development of new approaches to crystal structure prediction [1,2]. Dr Gusev is a theme lead of the LRC with background in theoretical computer science involving discrete mathematics, matrix algebras, algorithms, etc. as well as applied mathematics.

Qualifications: Applications are welcomed from students with a 2:1 or higher masters degree or equivalent in Chemistry, Computer Science, Applied Mathematics or Physics. Applications with some of the skills directly relevant to the project outlined above will be preferred. 

Teaching: Successful applicants will be enrolled as Graduate Teaching Assistants and required to teach undergraduate students.

Please apply by completing the online postgraduate research application form here.

Informal enquiries should be addressed to Matthew Dyer ([email protected])

Availability

Open to students worldwide

Funding information

Funded studentship

The award is available to international and UK/EU residents and will pay full tuition fees and a maintenance grant for 3.5years (£15,009 pa in 2019/2020).

References

[1] M S Dyer, C Collins, D Hodgeman, P A Chater, A Demont, S Romani, R Sayers, M F Thomas, J B Claridge, G R Darling, & M J Rosseinsky, “Computationally Assisted Identification of Functional Inorganic Materials”, Science 340 (2013) 847–852

[2] C Collins, M S Dyer, M J Pitcher, G F S Whitehead, M Zanella, P Mandal, J B Claridge, G R Darling & M J Rosseinsky, “Accelerated discovery of two crystal structure types in a complex inorganic phase field”, Nature 546 (2017) 280–284