PhD Studentship - Learning heat: Physics-Informed Fourier Neural Operators for High-Fidelity Thermal NDE

Learning heat: Physics-Informed Fourier Neural Operators for High-Fidelity Thermal NDE

Modern non-destructive evaluation (NDE) increasingly relies on AI models that can reason with physics, scale to complex geometries, and run in real time for digital-twin monitoring. This project will develop physics-informed Fourier Neural Operators (FNOs) for thermal NDE of curved and layered composite structures (e.g., wind-turbine blades, rails, laminates). Building on our recent “FNO-Kernel” work—embedding a physics-based convolutional kernel inside the Fourier operator—the PhD will deliver operator-learning methods that are data-efficient, reliable, and deployment-ready.

Aims

1. Advance operator-learning architectures for transient heat transfer in complex geometries, integrating physical priors (PDE structure, boundary conditions, material anisotropy) into FNO training.
2. Develop an end-to-end pipeline: synthetic and experimental data generation, physics-informed loss functions, uncertainty quantification, and fast inverse solvers for defect characterisation.
3. Validate against laboratory and partner case studies; produce reproducible benchmarks, open models, and demonstrators suitable for digital-twin integration and REF2029 impact.

Methods and workplan

• Data and simulation: curate multi-fidelity datasets that couple finite-element heat simulations with active thermography experiments.
• Model design: extend FNOs with learnable physical kernels, geometry encodings, and boundary-aware layers; compare to PINNs, U-Nets, graph operators, and transformer baselines.
• Learning strategy: physics-informed and multi-task losses, curriculum over geometry/BCs, calibration of predictive uncertainty, and robustness to sensor noise.
• Tasks: forward prediction (temperature fields), inverse reconstruction (defect size, depth, orientation), and few-shot generalisation to novel geometries and layups.
• Evaluation: accuracy–speed–stability trade-offs, ablations on priors, uncertainty coverage, and real-time feasibility for on-line inspection.

Partnerships and liaison

The student will liaise closely with existing Royal Society projects, in particular the ISPF UK–Brazil collaboration on thermographic reconstruction (e.g., UFRJ and industry partners). Liaison will include coordinated milestones, shared datasets and protocols, short secondments/exchanges, and co-authored outputs to accelerate translation and ensure alignment with partner needs.

Candidate profile

We welcome applicants with backgrounds in computer science, applied mathematics, or engineering. Essential: strong Python, deep learning experience (PyTorch), and foundations in calculus/linear algebra. Desirable: PDEs/numerics, thermofluids/heat transfer, uncertainty quantification, and hands-on lab skills. Prior publications or open-source contributions are a plus but not required.

Eligibility requirements:

• Academic excellence i.e. 2:1 (or equivalent GPA from non-UK universities with preference for 1st class honours); or a Masters (preference for Merit or above); or APEL evidence of substantial practitioner achievement.
• Appropriate IELTS score, if required.
• Applicants cannot apply if they are already a PhD holder or if currently engaged in Doctoral study at Northumbria or elsewhere.
• Must be able to commit to campus-based full-time or part-time study.

To be classed as a Home student, candidates must:

• Be a UK National (meeting residency requirements), or
• Have settled status, or
• Have pre-settled status (meeting residency requirements), or
• Have indefinite leave to remain or enter.

If a candidate does not meet the criteria above, they would be classed as an International student.

Applicants will need to be in the UK and fully enrolled before stipend payments can commence and be aware of the following additional costs that may be incurred, as these are not covered by the studentship.

• Immigration Health Surcharge www.gov.uk/healthcare-immigration-application
• If you need to apply for a Student Visa to enter the UK, please refer to www.gov.uk/student-visa. It is important that you read this information carefully as it is your responsibility to ensure that you hold the correct funds required for your visa application, otherwise your visa may be refused.
• Costs associated with English Language requirements which may be required for students not having completed a first degree in English, will not be paid by the University.
• International applicants (including EU) need to have their own valid immigration permissions to live and study in the UK if they wish to study on a part-time basis as Northumbria University does not sponsor part-time Student Visas.

For further details on how to apply see www.northumbria.ac.uk/research/postgraduate-research-degrees/how-to-apply

In your application, please include a research proposal of approximately 1,000 words and the advert reference (e.g. RDF26/…).

Deadline for applications: 23^rd January 2026

Start date of course: 1^st October 2026

Northumbria University is committed to creating an inclusive culture where we take pride in, and value, the diversity of our postgraduate research students. We encourage and welcome applications from all members of the community.

Academic enquiries

This project is supervised by Dr Qiuji Yi. For informal queries, please contact qiuji.yi@northumbria.ac.uk. For all other enquiries relating to eligibility or application process please use the email form below to contact Admissions.

This studentship is available to Home and International (including EU) students and includes a full stipend at UKRI rates (for 2025/26 FT study this is £20,780 per year) and full tuition fees. Studentships are also available for Home applicants who wish to study part-time over 5 years (0.6 FTE, stipend £12,542 per year and full tuition fees) in combination with work or personal responsibilities). Please note additional costs that may apply to international applicants.