University: University of Cambridge (Department of Engineering)
Programme: PhD (Full-time)
Location: Cambridge, UK
Funding: EPSRC Industrial Doctoral Landscape Award (IDLA) — funding available for eligible UK students and a limited number of international students
Deadline: 14 May 2026
Reference: NM48594
Partner: IBM (industry collaboration)
Application fee: £20 (via the University Application Portal)
Contact: Professor Mark Girolami (mag92@cam.ac.uk) with copy to div-d@eng.cam.ac.uk
Early applications are encouraged. The position may be filled before the deadline if a suitable candidate is identified.
Author: Dr Niaz Chowdhury (LinkedIn)
Designation: Lecturer (Computer Science)
Affiliation: Ulster University, Birmingham, UK
Overview of the PhD project
This PhD studentship is part of an ongoing collaboration between IBM and the Department of Engineering at the University of Cambridge, focused on the mathematical and computational modelling of Earth and planetary systems.
The research will investigate Probabilistic Numerical Computation for large-scale inverse problems, with a particular emphasis on inverse problems governed by partial differential equations (PDEs).
In many modern workflows, inverse problems are approached using foundation-model (FM) surrogates. However, some real-world inverse problems are data-scarce, making FM training impractical. In those settings, one alternative is to generate synthetic data using direct PDE solvers. This studentship explores how probabilistic numerics can enhance, supplement, or replace current approaches, with a strong focus on:
- Principled uncertainty quantification in numerical computation
- Improved performance in large-scale inverse modelling
- Practical relevance to Earth and planetary modelling challenges faced in industry
Why this topic matters
Inverse problems are at the heart of many scientific and engineering applications: we observe limited or noisy measurements and try to infer underlying parameters, fields, or system states. When these systems are governed by PDEs (as many geophysical and planetary processes are), inference becomes computationally demanding.
Probabilistic numerics offers a powerful perspective: instead of treating numerical computation as exact, it models computation itself as uncertain and quantifies that uncertainty. This can lead to:
- More reliable decision-making in data-scarce contexts
- Better-calibrated models when observations are noisy or incomplete
- Transparent uncertainty estimates that support scientific interpretation
If your interests sit at the intersection of applied mathematics, scientific computing, machine learning, and physical modelling, this project is highly relevant.
Research themes you may encounter
While the exact direction will evolve during the PhD, the advert suggests the work may include themes such as:
- Probabilistic numerical methods for PDE solvers
- Uncertainty-aware computation for large-scale inverse problems
- Alternatives to surrogate modelling in limited-data regimes
- Synthetic data generation using direct PDE-based simulation
- Scalable computational strategies for inverse modelling in complex systems
Who should apply
This opportunity is best suited to applicants with strong foundations in quantitative and computational disciplines and an appetite for research ownership.
The advert states applicants should have (or expect to receive) a good UK Master’s degree (or overseas equivalent) in a relevant subject, such as:
- Engineering
- Physics
- Computer Science
- Mathematics
You will likely do well in this project if you enjoy some combination of:
- Mathematical modelling and numerical analysis
- Probability, statistics, and uncertainty quantification
- Scientific computing and computational methods
- PDEs and inverse problems
- Research writing and communicating technical ideas clearly
Funding notes (EPSRC IDLA)
This studentship sits under the EPSRC Industrial Doctoral Landscape Award (IDLA) framework. The advert indicates:
- Studentships are available for eligible home students
- A limited number of international students may be funded
The advert does not specify the exact stipend figure in the excerpt provided, so you should check the official funding page and application portal listing for the most up-to-date details.
What you must upload (application documents)
Applicants are asked to upload:
- Short research statement (maximum 1 page)
- Past research
- Future goals
- Why you are interested and suitable for this position
- Curriculum vitae (CV)
- Publication list (if applicable; include preprints, posters, and substantial technical reports where relevant)
- Contact details of two referees who can provide letters of recommendation
How to apply
Applications should be submitted via the University Application Portal (using the “Apply” button associated with the project listing).
Important: There is a £20 application fee.
Because the advert states the position may be filled early, it is sensible to apply well before the closing date if you are ready.
A strong 1-page research statement (structure you can follow)
A one-page statement is tight, so clarity matters more than length. Here is a structure that fits the project well:
1) Opening (2–3 sentences)
- Your current status (Master’s student / graduate / research role)
- Your core interests (probabilistic numerics, inverse problems, PDEs, uncertainty)
- One sentence linking your interests to Earth/planetary modelling or large-scale inverse modelling
2) Past research experience (4–6 sentences)
- One main project (your role, methods used, what you learned)
- Mention relevant tools (e.g., Python, MATLAB, Julia, C++, PyTorch/JAX, scientific computing libraries)
- Highlight any work involving PDEs, optimisation, Bayesian methods, simulation, or uncertainty
3) Why this project (4–6 sentences)
- Show you understand the challenge: data-scarce inverse problems, limits of FM training, use of PDE solvers
- Explain why probabilistic numerics is a meaningful direction here
- Mention your interest in uncertainty quantification that is principled and useful in practice
4) What you want to explore (3–5 sentences)
- A small set of research questions you’d like to explore
- Example areas: uncertainty-aware solvers, scalable inference for PDE-governed systems, probabilistic error modelling in numerical pipelines
- Keep this open-ended rather than over-committing to specifics
5) Closing (1–2 sentences)
- Your readiness for doctoral research
- Your motivation to work at the Cambridge–IBM interface and contribute to the wider research programme
Tips to improve your chances
- Make your fit obvious early: Use the terms probabilistic numerics, inverse problems, PDEs, and uncertainty quantification naturally and correctly.
- Show you can handle scale: Mention any experience with large datasets, HPC, numerical simulation, or computational constraints.
- Be honest about publications: If you don’t have formal papers, list strong alternatives (thesis, workshop reports, posters, arXiv preprints, open-source contributions).
- Choose referees strategically: Ideally, referees who can speak about your research ability and independence, not only your coursework performance.
- Apply early: The advert explicitly states the role may be filled before the deadline.
Contact details (queries)
If you have questions about the project, the advert advises you to contact:
- Professor Mark Girolami: mag92@cam.ac.uk
- Copy to: div-d@eng.cam.ac.uk
When emailing, include:
- The reference NM48594
- A short paragraph on your fit
- Your CV (optional but helpful if you’re asking a substantive question)
Key dates
- Placed on: 28 January 2026
- Deadline: 14 May 2026
- Note: Early applications encouraged; the position may be filled before the deadline.
Final checklist before you submit
- 1-page research statement (tailored to probabilistic numerics + inverse problems + PDEs)
- CV (clear, research-forward, includes relevant technical stack)
- Publication list (or equivalent scholarly outputs)
- Two referee contact details confirmed
- Ready to pay the £20 application fee
- Submission completed well before the deadline
