Development of numerical methods using evolutionary computation techniques

About the Project

Advances in AI-based techniques, including differential evolution, mimetic, and other evolutionary algorithms, facilitate the design of new sophisticated optimisation algorithms to develop novel numerical methods for the efficient solution of differential equations (DEs) more efficiently and rapidly than existing numerical approaches. This can have a significant impact in diverse areas such as infectious disease spread, weather prediction, and population dynamics. DEs are fundamental for investigating these phenomena, yet solving them computationally, as exact solutions in real-life conditions are usually impossible, is time and energy-intensive. The project focuses on optimising Runge-Kutta, Runge-Kutta-Nyström, and Linear Multistep methods, but can also include other types of numerical methods.

Objectives include constructing more efficient versions of these methods, targeting specific types of DEs they solve. The goal is to achieve a significant increase in efficiency compared to classical methods, ensuring faster and more accurate results. The objective function is set based on the global error norm, subject to a number of constraints. Tasks include selecting optimisation techniques, constructing efficient methods, and testing on real-life problems. This iterative process enhances method performance while minimising computation time. The research's potential impact is substantial, as improved numerical methods can lead to more precise weather forecasts, better disease modelling, and enhanced decision-making in various fields. By significantly reducing computational time while maintaining accuracy, these methods can save lives, aid emergency management, and mitigate economic losses caused by high-impact weather events and infectious disease outbreaks. This project addresses a critical need for highly efficient numerical methods, advancing the capabilities of solving DEs and contributing to various scientific and practical applications.

The PhD Programme

The DMU PhD provides a solid education for a research career, whether you stay in academic research or move to industry. There is a well-developed Researcher Development Programme which you will undertake alongside your research, supporting you through each year of your PhD. Working closely with your supervisors, you will undertake open-ended research. As part of a vibrant PhD community in the Faculty, you will have training opportunities which lead to presentations at international conferences and in writing papers in leading academic journals as the research progresses into the later stages of the PhD. The student will graduate with skills and knowledge at the forefront of academic and industrial expectations.

Entry Requirements

You must have achieved or be close to achieving a UK Honours Degree with at least an upper second class (2:1) or a Master's Degree or an academic or professional qualification with relevant experience in the sector or industry, which is deemed to be equivalent, or an international equivalent

Closing date: 1 year from the date of uploading. Applications will be considered in the order that they are received. The position will be considered filled when a suitable candidate has been identified.

Starting date: There are three intakes a year at DMU, and it is expected that the successful candidate will start either in January 2026, April 2026 or October 2026.

Funding Notes

This is a self-funded project and you will need to have sufficient funds in place (e.g., through a scholarship, personal funds and or other sources) to meet the tuition fees and living expenses for the duration of the degree programme.

DMU has information on scholarships and other funding opportunities at View Website