Bayesian-Evolutionary Discovery of Functional Regimes in Adaptive Matter

alternative mechanisms, regime boundaries and robustness. The project will therefore combine evolutionary computation and Bayesian modelling to discover, characterise and synthesise functional regimes in adaptive matter.

The hypothesis is that functionality is organised around robust dynamical regimes in a design-dependent attractor landscape. Inexpensive response tests, such as relaxation times, damping ratios and transient spectra, may reveal regime-level similarity more reliably than parameter or topology similarity. Alignment should support selective knowledge reuse; divergence should raise uncertainty and trigger re-evaluation. Transferability will be tested, not assumed.

RQ1 asks how functional regimes can be discovered in large adaptive-material design spaces. Quality-diversity and multi-objective algorithms will use behavioural descriptors and MAP-Elites-style archives to expose diverse mechanisms and boundaries. RQ2 asks how uncertainty about functional regimes can be represented. Probabilistic models will predict functionality, robustness and regime membership, distinguish uncertainty types and estimate transfer reliability. RQ3 asks which experiments most efficiently improve system understanding. Cost-aware Bayesian experimental design will select between short response tests and full evaluations to maximise information gain about regimes, boundaries and transfer reliability. RQ4 asks how transitions between functional and non-functional regimes can be characterised. Evolutionary perturbation analysis and Bayesian boundary estimation will identify robustness margins, phase transitions and adaptation pathways. RQ5 asks how desired functionality can be synthesised through inverse design. Bayesian surrogates and evolutionary search will infer microscopic rules and structures from target functions under practical constraints.

The methodology forms a closed Bayesian-evolutionary loop. Evolutionary search proposes diverse candidate designs; ensembles of simulations evaluate performance under varied initial conditions and perturbations and generate short dynamical response traces; Bayesian surrogates learn functionality, robustness and regime membership with calibrated uncertainty; and active-learning policies select the next evaluations.

Three integrated components structure the work. First, evolutionary discovery will encode plausible designs, apply quality-diversity and multi-objective search, and cluster outcomes into regimes. Second, Bayesian region modelling will compare Gaussian processes, Bayesian neural networks, physics-informed and multi-fidelity models, combining design and response features to score knowledge reuse. Third, active exploration and inverse design will use acquisition functions balancing expected improvement, uncertainty and information gain with explicit evaluation costs. For each modification, policies will decide whether to reuse predictions, run a short response test or perform a full evaluation.

Validation will assess regime coverage, diversity, predictive accuracy, calibration, transfer prediction, evaluation cost and inverse-design performance against evolutionary, gradient-based, random, space-filling and greedy baselines. Outputs include regime archives, calibrated surrogates, transferability maps, probabilistic boundaries, cost-aware policies and an inverse-design pipeline.

Desirable Student Background

Applicants should have a strong quantitative degree, with experience in Python, optimisation and probabilistic modelling. Knowledge of evolutionary computation, Bayesian methods, dynamical systems, simulation or materials modelling is desirable but not essential.

How to apply

Please apply under the University of Manchester application portal and select 'PhD in Artificial Intelligence' (OAA Applicant 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 2026.

This project is with Honda Research Institute.

References

• Mouret, J.-B. and Clune, J. Quality Diversity Algorithms. https://members.loria.fr/jbmouret/qd.html
• Dai, Z. et al. (2025). pied: physics-informed experimental design. ICLR.
• Illuminating the property space in crystal structure prediction using Quality-Diversity algorithms (2024). Digital Discovery. https://pubs.rsc.org/en/content/articlehtml/2024/dd/d4dd00054d
• A physics-informed Bayesian optimization approach (2023). npj Computational Materials. https://www.nature.com/articles/s41524-023-01173-7
• A Bayesian neural network approach to multi-fidelity surrogate modelling (2024). International Journal for Uncertainty Quantification. https://hal.science/hal-03608580/document
• Surrogate-Based Bayesian Inference: Uncertainty Quantification and Active Learning (2026). arXiv. https://ar5iv.labs.arxiv.org/html/2603.13646
• AI-Driven Approaches for Materials Design and Discovery. OSTI. https://www.osti.gov/pages/servlets/purl/3030140
• Discovery and Optimization of Materials Using Evolutionary Approaches (2016). Chemical Reviews. https://pubs.acs.org/doi/abs/10.1021/acs.chemrev.5b00691