University of Warwick

What you'll study

This PhD is a research-led programme in which you will pursue an original project under the guidance of an academic supervisory team. Research topics commonly include multi-scale and multi-physics modelling, stochastic and deterministic descriptions of heterogeneous media, agent-based and hybrid models, network dynamics, parameter estimation and uncertainty quantification, and coupling between discrete and continuum representations.

Taught components are limited and focused on advanced training, typically including seminars and short courses in topics such as numerical methods for heterogeneous systems, stochastic processes, statistical inference for models, high-performance computing and model validation. You will also take training in research skills and professional development, including scientific communication, reproducible computing and project management.

Projects integrate mathematical analysis, algorithm development and computational experiments. You can expect to work with tools and methods such as partial differential equations, cellular automata and agent-based frameworks, Monte Carlo and particle methods, multi-scale asymptotics, Bayesian calibration and data assimilation. Access to department HPC facilities and software environments supports large-scale simulations and data integration.

Typical structure

• Initial period of intensive literature review and research planning, followed by development of methods and experiments.
• Regular meetings with supervisors, participation in research group seminars and relevant postgraduate training modules.
• Interim progress reviews with research proposals and milestones; preparation of papers for peer-reviewed journals and conferences during the candidature.
• Final submission of a thesis presenting original research and an oral examination (viva voce).

Entry requirements

Applicants are normally expected to hold a strong undergraduate degree in mathematics, physics, engineering, computer science or a closely related quantitative discipline. A taught postgraduate qualification (such as an MSc, MRes or equivalent) with substantial research or modelling content is highly desirable and may be required for some projects.

Admissions committees look for demonstrable skills in mathematical modelling, programming and numerical computation, together with evidence of independent research potential (such as a dissertation, publications, technical reports or relevant project work). Applicants should supply a research proposal or statement of research interests that aligns with available supervisory expertise.

International applicants must meet the University of Warwick's English language requirements; details and acceptable qualifications are published by the university. Applicants are also asked to provide academic references and transcripts; additional information or interviews may be requested as part of the selection process.

Career prospects

Graduates from PhDs in Modelling Heterogeneous Systems move into a wide range of research-intensive careers. Many continue in academia as postdoctoral researchers and lecturers, contributing to interdisciplinary research in applied mathematics, computational science and systems biology.

Outside academia, career paths include R&D roles in engineering and manufacturing, software and algorithm development for simulation and optimisation, quantitative research in finance and insurance, data science and machine learning positions that require complex-system modelling, and modelling roles in environmental science, energy, healthcare and biotechnology. Graduates are also well suited to roles in government research labs, consultancy and technology transfer where the ability to bridge theory, computation and data is valued.

Why study at University of Warwick

Warwick provides a strong interdisciplinary environment for modelling heterogeneous systems, with established research groups in applied mathematics, computational science and computer science, and close links to centres studying complex systems. The department offers access to experienced supervisors whose expertise spans theoretical analysis, numerical methods and large-scale simulation.

The university supports doctoral researchers with structured training opportunities, regular seminars, and facilities for high-performance computing. There are active collaborations with industry, national research institutes and other universities, which can offer opportunities for applied case studies, placements and co‑supervision. The campus research culture emphasises transferable skills, publication, and engagement with the broader scientific community, helping prepare graduates for diverse research and professional careers.