Scientific Machine Learning for Fluid Dynamics and Hydraulics

Artificial Intelligence (AI) has become deeply integrated into modern society, offering immense benefits that often eclipse its limitations. Neural Networks (NNs), the most prevalent form of AI, typically demand vast training datasets and substantial computational power—resulting in high energy consumption and a considerable carbon footprint. Additionally, collecting and preparing data remains a major challenge that limits AI accessibility. However, many problems in physics and engineering are governed by well-established laws, often expressed as partial differential equations (PDEs). By incorporating this physical knowledge into neural networks, the need for large datasets can be greatly reduced—or even eliminated—along with much of the computational cost. These specialised networks are known as Physics-Informed Neural Networks (PINNs).

In this project, building on previous research by the host team, you will work towards the development and optimisation of PINNs for applications in various problems associated with fluid mechanics and hydraulics. Examples of applications include fast modelling of floods, alternative Navier-Stokes solvers and simulations of various fluid-structure interactions.

You will join a diverse, vibrant and growing PINNs research group at the University of Southampton, with access to one of the UK’s most powerful supercomputers, and support from a community of PhD students working in various aspects of Computational Fluid Dynamics and AI. You will also be part of a growing network of international collaborators.

You will receive comprehensive training to ensure the successful completion of your PhD. This includes access to dedicated support at Southampton for High Performance Computing and Computational Fluid Dynamics.

Additionally, the host research team—comprising several research students working on PINNs—will provide further guidance and collaboration opportunities

Entry requirements

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

• mechanical engineering
• aerospace engineering
• civil engineering
• computer science
• physics
• mathematics
• or related disciplines

Essential skills:

• basic programming skills

Desirable skills:

• a strong foundation in fluid mechanics, hydraulics and/or neural networks

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.

Competition-based studentships offered by our schools typically cover UK-level tuition fees and a stipend for living costs 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:

• 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

Applications should include:

• your CV (resumé)
• 2 academic references
• degree transcripts and certificates to date
• English language qualification (if applicable)

Contact us

Faculty of Engineering and Physical Sciences

For questions about applying, doctoralcollege-admissions@soton.ac.uk.

Project leader

For an initial conversation, s.maldonado@soton.ac.uk

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.