Supervisors: Dr Arezoo Zakeri, Prof Alejandro Frangi, Dr Sam Coveney
Application deadline: Friday, December 04, 2026
Funding: Competition Funded PhD Project (Students Worldwide)
About the Project
AI_CDT_DecisionMaking
Details
Challenge
Conditional generative models can create virtual anatomical populations from imaging data, but their uncertainty remains poorly understood. This project will develop methods to distinguish sources of variation and provide reliable uncertainty estimates for applications such as in silico trials.
Objectives
Building on our recent work on 4D Cardiosynth [1] and HeartVolMesh [2], this project will develop interpretable and calibrated UQ methods for conditional geometry generator models by estimating uncertainty in learned population distributions, quantifying the effects of uncertainty in training data and conditioning variables, enabling uncertainty-aware conditional generation and rare anatomy synthesis, and establishing calibration methodologies for uncertainty estimates with guaranteed bounds for geometry generators.
Innovation
Most UQ methods are designed for classification, regression or prediction tasks where a unique ground truth exists. More recent UQ approaches for generative models estimate uncertainty associated with model parameters or generated samples [3-5]. This project addresses a different challenge: calibration and interpretation of uncertainty in learned anatomical population distributions. The key innovation is developing uncertainty representations and calibration methodologies for high-dimensional conditional geometry generators where uncertainty is treated as a property of the learned population distribution.
Approach and Methodology
We will develop uncertainty-aware conditional geometry generators for anatomical population modelling using compact latent shape representations derived from our graph Gaussian anatomical digital twins [2]. The project may investigate various model families: conditional variational autoencoders, normalising flows and diffusion models combined with conformal calibration strategies.
The generator will learn a conditional anatomical distribution from shape representations and demographic, anatomical and clinical descriptors. Conditioning variables will be represented probabilistically, enabling uncertainty propagation through latent representations and generated populations.
To quantify uncertainty, we will investigate Bayesian inference, deep ensembles and latent-space uncertainty representations. We will develop uncertainty metrics defined on learned population distributions and compare them with existing sample-level uncertainty measures [4], realism scores [6] and rarity scores [7].
A major focus is uncertainty calibration. Since generated anatomies have no unique ground truth, we will investigate calibration using distributional coverage, population-level anatomical statistics and latent-space consistency. Controlled perturbation experiments will quantify the effects of uncertainty in training geometries, measurements and conditioning variables. We will also investigate conformal prediction-inspired approaches to derive calibrated bounds on generative uncertainty.
Experiments will use large cardiac mesh datasets previously derived by our team from UK Biobank together with associated demographic and clinical information. The project will establish an AI framework for uncertainty estimation, calibration and sensitivity analysis in conditional geometry generators, providing foundations for trustworthy virtual populations for interpretable, uncertainty-aware AI in healthcare.
Desirable Student Background:
A background in Computer Science, Artificial Intelligence, Mathematics, or Statistics is desirable, together with strong Python programming skills and experience in machine learning or deep learning. An interest in uncertainty quantification, probabilistic modelling and generative AI is essential. Prior experience with generative models (e.g., VAEs, diffusion models or normalising flows), Bayesian methods, computer vision or medical image analysis would be advantageous but is not required.
How to apply:
Please apply under the University of Manchester application portal and select 'PhD in Artificial Intelligence' (OAA Application portal).
When applying, you’ll need to specify the full name of this project, the name of your supervisor, if you already having funding or if you wish to be considered for available funding through the university, details of your previous study, and names and contact details of two referees.
Your application will not be processed without all of the required documents submitted at the time of application, and we cannot accept responsibility for late or missed deadlines. Incomplete applications will not be considered.
You will be asked to upload the following supporting documents:
- Final Transcript and certificates of all awarded university level qualifications
- Interim Transcript of any university level qualifications in progress
- CV
- Supporting statement: A one or two page statement outlining your motivation to pursue postgraduate research and why you want to undertake postgraduate research at Manchester, any relevant research or work experience, the key findings of your previous research experience, and techniques and skills you’ve developed. (This is mandatory for all applicants and the application will be put on hold without it).
- Contact details for two referees (Please ensure referee email addresses are official university or workplace accounts, as we may need to verify the references.)
- English Language Certificate (if applicable)
We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status.
We also support applications from those returning from a career break or other roles. We are dedicated to supporting work-life balance and offer flexible working arrangements to accommodate individual needs. Our selection process is free from bias, and we are committed to ensuring fair and equal opportunities for all applicants.
We are dedicated to supporting work-life balance and offer flexible working arrangements to accommodate individual needs, including a part-time study option.
Join us and help grow the UK’s national capability in artificial intelligence, part of the UK’s modern industrial strategy. Everyone is welcome if you are passionate about uncertainty quantification, decision making with humans in the loop and decision making for machine learning systems and their applications in Science and Engineering, and looking to develop your research and innovation skills at the doctoral level to further your career in the AI sector.
Equality, diversity and inclusion is fundamental to the success of The University of Manchester, and is at the heart of all of our activities. We know that diversity strengthens our research community, leading to enhanced research creativity, productivity and quality, and societal and economic impact. (Equality, diversity and inclusion | The University of Manchester)
We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status.
Funding Notes
Fully funded AI UKRI CDT 4 year program; The Project will be based in University of Manchester.
The UKRI AI CDT in Decision Making for Complex Systems is part of the TechFirst offering stipends of £30,000 for students eligible for home fee status. The start date is September 2027.
References
- Dou, H., Huang, J., Zakeri, A., Zhou, Z., Mu, T., Duan, J., & Frangi, A. F. (2025, September). 4D cardiosynth: Synthesising dynamic virtual heart populations through spatiotemporal disentanglement. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 3-12). Cham: Springer Nature Switzerland. https://papers.miccai.org/miccai-2025/0004-Paper2701.html
- Lin, F., Zakeri, A., Dou, H., Zhou, Z., Lan, S., Duan, J., & Frangi, A. (2026). HeartVolMesh: Cardiac Volumetric Mesh Reconstruction via Covariance-Guided Graph Deformation. MICCAI 2026, https://papers.miccai.org/miccai-2026/paper/3675_paper.pdf
- Berry, Lucas, Axel Brando, and David Meger. "Shedding light on large generative networks: Estimating epistemic uncertainty in diffusion models." The 40th Conference on Uncertainty in Artificial Intelligence. 2024. https://openreview.net/forum?id=512IkGDqA8
- Jazbec, Metod, et al. "Generative uncertainty in diffusion models." arXiv preprint arXiv:[contact details available in the full listing]). https://arxiv.org/abs/[contact details available in the full listing]
- Lakara, Kumud, and Matias Valdenegro-Toro. "Disentangled uncertainty and out of distribution detection in medical generative models." arXiv preprint arXiv:[contact details available in the full listing]). https://arxiv.org/pdf/[contact details available in the full listing]
- Kynkäänniemi, Tuomas, et al. "Improved precision and recall metric for assessing generative models." Advances in neural information processing systems 32 (2019). https://proceedings.neurips.cc/paper_files/paper/2019/file/0234c510bc6d908b28c70ff[contact details available in the full listing]-Paper.pdf
- Han, Jiyeon, et al. "Rarity score: A new metric to evaluate the uncommonness of synthesized images." arXiv preprint arXiv:[contact details available in the full listing]). https://arxiv.org/abs/[contact details available in the full listing]
