Deep learning latent dynamics: uncovering hidden structure in complex dynamical systems

About the project

Can AI learn to understand, not just predict, complex engineering dynamical systems? In this PhD, you will combine deep learning with the mathematics of nonlinear dynamics to uncover the hidden structure behind vibrations, flutter and instabilities in aerospace systems, creating fast, interpretable models for safer, lighter and net-zero flight.

Modern aerospace systems, from aero-engine structures to flexible wings and electrified propulsion, are becoming lighter, smarter and more strongly coupled across physics. As a result, they show complex nonlinear dynamics: flutter and other limit cycle oscillations, multiple coexisting stable states, internal resonances and sudden bifurcations. High-fidelity simulations of these behaviours are too slow for design and control, while standard machine learning models act as black boxes that are hard to trust or interpret.

This project will develop interpretable, data-driven reduced order models by connecting deep learning of latent dynamics with invariant manifold theory, which shows that complex systems are often governed by hidden low-dimensional structures. The research works in both directions:

Expected outcomes include a new modelling framework, validated on nonlinear aero-engine structures, aeroelastic systems and electro-mechanical systems, and released as open-source software. The work will support faster, more reliable design of safer, lighter and more efficient aircraft for net-zero aviation.

You will join the Computational Engineering and Design group , with access to the University's high-performance computing facilities, a tailored doctoral training programme and opportunities to present at international conferences.

You will receive training in scientific machine learning, nonlinear dynamics and reduced order modelling through one-to-one supervision, group meetings and research seminars. You will gain hands-on experience with high-performance computing on the University’s Iridis supercomputer .

The University’s Doctoral College provides a researcher development programme covering research skills, academic writing, presentation and career development. You will also have opportunities to present at international conferences, publish in leading journals, and gain teaching experience as a demonstrator.

The School of Engineering is committed to promoting equality, diversity inclusivity as demonstrated by our Athena SWAN award. We welcome all applicants regardless of their gender, ethnicity, disability, sexual orientation or age, and will give full consideration to applicants seeking flexible working patterns and those who have taken a career break. The University has a generous maternity policy, onsite childcare facilities, and offers a range of benefits to help ensure employees’ well-being and work-life balance. The University of Southampton is committed to sustainability and has been awarded the Platinum EcoAward.

• theory to learning: embed invariant manifold and normal form theory into deep learning architectures, giving latent spaces physical meaning
• learning to theory: use deep learning to discover invariant manifolds and nonlinear dynamics directly from sparse, high-dimensional data
• uncertainty quantification: make predictions robust to noise, sparse sensing and real-world variability

Dr Jie Yuan FRAeS, FHEA, CEng

• Computational methods for large-scale nonlinear dynamical systems
• Dynamic control using novel functional material and interface
• Non-deterministic approaches for robust optimisation and identification

Professor David Toal

• Design optimisation & automation
• Machine learning & deep learning
• Computer aided design

Entry requirements

You must have a UK 2:1 honours degree or its international equivalent in one of the following:

Essential:

Desirable skills:

• engineering
• mathematics
• physics
• computer science
• a related discipline
• strong mathematical skills
• strong programming skills (e.g. Python)
• experience in machine learning, nonlinear dynamics or structural dynamics.

Fees and funding

We offer a range of funding opportunities for both UK and international students. Horizon Europe fee waivers automatically cover the difference between overseas and UK fees for qualifying students.

Competition-based Presidential Bursaries from the University cover the difference between overseas and UK fees for top-ranked applicants.

Funding will be awarded on a rolling basis, so apply early for the best opportunity to be considered.

For more information, please visit our postgraduate research funding pages.

How to apply

Apply now

You need to:

Applications should include:

• choose programme type (Research), 2027/28, Faculty of Engineering and Physical Sciences
• select Full time or Part time
• search for programme PhD Engineering & the Environment (7175)
• add name of the supervisor in section 2 of the application
• your CV (resumé)
• 2 academic references
• degree transcripts and certificates to date
• English language qualification (if applicable)

Faculty of Engineering and Physical Sciences

If you have a general question, email our Doctoral College (doctoralcollege-admissions@soton.ac.uk) .

Project leader

If you wish to discuss any details of the project informally, email Dr Jie Yuan (j.yuan@soton.ac.uk).

Research areas