Electronics and Electrical Engineering

In-situ optical spectroscopy during Laser Powder Bed Fusion (LPBF) captures high-resolution signals encoding the physical state of the melt pool. However, this data presents a formidable statistical challenge: observations are strongly non-i.i.d., exhibiting spatiotemporal autocorrelation, directional asymmetry from moving laser paths, and complex thermal dynamics. Because labeled defect data is rarely available at scale, this project bypasses supervised approaches to build principled, physics-informed unsupervised learning frameworks. 

This project will build on the supervisors’ research in stochastic modelling, statistical learning, numerical analysis, and mathematically grounded anomaly detection. The research will focus on formulating flexible, label-free statistical machine learning for real-time anomaly detection and defect classification. Depending on candidate interest and project evolution, potential methodological avenues include combining spatial modelling with non-parametric hypothesis testing to separate systematic process variation from distributional shifts. To account for complex spatiotemporal dependencies, you will investigate robust calibration schemes (such as block-permutation or wild-bootstrap methods), while exploring techniques ranging from sparse matrix decomposition to geometric clustering and manifold learning to isolate and classify physical anomaly regimes like porosity, lack of fusion, or keyhole collapse. 

Bridging spatial statistics, rough path theory, functional data analysis, and advanced process engineering, this project translates rigorous mathematical methodology into immediate industrial impact for metal additive manufacturing.

• a 1st Class undergraduate degree (or equivalent).
• the University’s English language requirements.

Applications are welcomed from self-funded students, or students who are applying for scholarships from the University of Edinburgh or elsewhere.

Further information and other funding options.

Reconstructing 3D gas concentration and temperature profiles within dynamic, turbulent plumes from sparse optical measurements is a classic ill-posed inverse problem. Positioned at the intersection of radiative transfer, fluid dynamics, and statistical physics, this project aims to push the boundaries of computational imaging in extreme, harsh environments. 

The research will focus on developing forward models governed by coupled radiative and heat transfer PDEs, while exploring alternative, more informative measurement modalities to significantly boost spatial resolution and noise robustness under severe data scarcity. To address the chaotic nature of dynamic flows, you will construct Bayesian inference frameworks and random media models to parameterise chaos and achieve data-consistent uncertainty quantification. Furthermore, the project offers scope to integrate scientific machine learning, such as neural operators and diffusion models, to efficiently represent complex, swirling fluid structures alongside classical physics-based inversions. Bridging deep mathematical theory with real-world applications in aerospace propulsion, combustion efficiency, and environmental monitoring, this project involves direct collaboration with specialists in gas metrology and aerospace engineering to validate computational models against experimental data. 

It is ideal for ambitious candidates in Engineering, Applied Mathematics, Computational Physics, or Signal Processing with a strong foundation in differential equations, linear algebra, inverse problems, or statistical learning.

• a 1st Class undergraduate degree (or equivalent).
• the University’s English language requirements.

Applications are welcomed from self-funded students, or students who are applying for scholarships from the University of Edinburgh or elsewhere.

Further information and other funding options.

We invite applications for a PhD focused on data-driven and digital solutions to accelerate the decarbonisation of electricity systems - in a way that yields benefits for the grid, end-users/communities, system resilience and beyond. The successful candidate will develop, test and validate methods that combine some of digital twins, AI/ML, optimisation, novel market mechanisms (e.g., peer-to-peer trading, flexibility markets) and enabling technologies (e.g., smart contracts) to coordinate distributed energy resources such as EVs, batteries, heat pumps and beyond. The project aims to bridge academic research and real-world implementation, delivering tools that enhance resilience, flexibility and affordability in smart, low‑carbon grids. The position sits within the Institute for Energy Systems (Electronics & Electrical Engineering) and builds on our recent work on: - community energy and local energy solutions that support Just Energy Transitions - demand-side response, energy flexibility assessment and smart coordination (via optimisation and AI decision-making) - smart contracts and transactive energy in local markets - virtual power plants (VPPs) of EVs and residential batteries, including extreme-weather resilience.

If a suitable candidate is found, this position may close earlier than the closing date.

The applicants should hold a first degree in Engineering, Physics, Informatics or similar.

Further information and other funding options.