When applied to molecular dynamics simulations involving vast numbers of atoms, coarse-graining approaches seek to reduce the number of degrees of freedom in a material model. This significantly lowers computational costs and environmental impact while attempting to maintain simulation accuracy. Although coarse-graining techniques are widely utilized across computational science and engineering, substantial theoretical development is still required to rigorously assess their accuracy and efficiency.

This PhD research project aims to study the underlying mathematical theory behind coarse-graining approaches. By analyzing these methods, the project will provide new fundamental understanding regarding the magnitude and sources of errors introduced during coarse-graining. The research will combine the formal development of mathematical theory with careful, validating numerical experiments.

The PhD project is supervised by Dr. Thomas Hudson (Reference: HP-2026-017) and hosted within HetSys (Centre for Doctoral Training in Modelling of Heterogeneous Systems) at the University of Warwick. HetSys provides an innovative, fully funded, interdisciplinary PhD training environment that brings together applied mathematics, physics, engineering, and computer science to tackle complex real-world challenges through computational modelling and simulation.

Eligibility Criteria

• Open to UK students (funding specific to UK/home applicants).

• Applicants should hold or expect to obtain a strong undergraduate degree (1st Class or 2:1 honours) or Master’s degree in Applied Mathematics, Mathematics, Physics, Theoretical Chemistry, Engineering, or a related quantitative discipline.

Required expertise/skills

• Strong mathematical background, particularly in applied mathematics, analysis, probability, or mathematical physics.

• Keen interest in mathematical theory, multiscale modelling, and molecular dynamics simulations.

• Aptitude for conducting numerical experiments and algorithm implementation using programming languages such as Python, C++, or Fortran.

• Analytical thinking and problem-solving skills for quantifying errors and evaluating mathematical frameworks.

• Excellent technical communication and collaboration skills to engage effectively in an interdisciplinary cohort across mathematics, science, and engineering.

Salary details Fully funded PhD Studentship for UK applicants, covering full University tuition fees, a research training budget, and a tax-free stipend to cover living costs (standard UKRI rate of £21,805 per annum for 2026/2027, equivalent to the national living wage).

Application Deadline 28th August 2026

Application Link