Postdoctoral Research Associate in Applied and Computational Mathematics

Grade UE07: £40,247 to £47,874 per annum

School of Mathematics / College of Science & Engineering     

Full time: 35 hours per week

Fixed term: for 14 months

We are looking for a talented early career researcher in non-Newtonian fluid dynamics, with expertise in computational methods and machine learning, to work on the project “A new understanding of turbulence via a machine-learnt dynamical systems theory” (UKRI Frontier Research Guarantee for an ERC Starting Grant). 

The Opportunity:

The dynamical systems view of turbulence, in which the flow “pinballs” between exact coherent states (ECS), is a promising way to unify our statistical understanding of turbulence with a mechanistic understanding of the complex self-sustaining processes that underpin it. Historically, this approach has been restricted to weakly turbulent flows due to the difficulty of identifying and converging ECS, and this project will seek to use advances in machine learning and automatic differentiation to overcome these barriers. 

A core part of this project is the development and interpretation of state-of-the-art machine learning (ML) models to model and predict high Reynolds number fluid flows of Newtonian and non-Newtonian fluids. The post-holder will work on a combination of: (1) low order models for high-dimensional flows, e.g. generated via self-supervised learning, to parameterise the inertial manifold; (2) super-resolution/data-assimilation strategies incorporating flow solvers in the loss; (3) development of differentiable code for turbulent simulation of wall-bounded flow. 

There are significant computational resources set aside specifically for the post-holder, along with PI, to train large models (access to a dedicated GPU cluster with >200  A100/H100 cards).  There is scope for a strong candidate to shape the research direction. 

Relevant reading:

• Page, Norgaard, Brenner & Kerswell, “Recurrent flow patterns as a basis for turbulence: predicting statistics from structures”, Proceedings of the National Academy of Sciences 121 (2024)
• Page, “Super-resolution of turbulence with dynamics in the loss”, Journal of Fluid Mechanics 1002 (2025)
• Kochkov et al, “Machine learning-accelerated computational fluid dynamics”, Proc. Nat. Acad. Sci. 118 (2021)

Your skills and attributes for success:

• Excellent knowledge of fluid mechanics fundamentals 
• Experience with non-Newtonian fluid dynamics 
• Experience implementing machine learning approaches and/or high performance computing for flow simulations
• Strong coding skills in an object-oriented language
• Experience with machine learning libraries (e.g. one or more of JAX, TensorFlow, PyTorch) would be highly beneficial

Click to view a copy of the full job description (opens new browser tab) 

Applicants should upload a CV and a brief research statement (max two pages) when applying for the post online. In addition, they should arrange for at least two letters of reference to be sent direct to references@maths.ed.ac.uk quoting the reference number 12160.  For informal enquiries please contact Jacob Page – jacob.page@ed.ac.uk

As a valued member of our team you can expect: 

• A competitive salary.
• An exciting, positive, creative, challenging and rewarding place to work. 
• To be part of a diverse and vibrant international community.
• Comprehensive Staff Benefits, such as a generous holiday entitlement, a defined benefits pension scheme, staff discounts, family-friendly initiatives, and flexible work options. Check out the full list on our staff benefits page (opens in a new tab) and use our reward calculator to discover the total value of your pay and benefits. 
• Significant budget for international travel and computing resources, with opportunities to visit and collaborate with researchers and engineers from leading universities and technology companies. 

Championing equality, diversity and inclusion

The University of Edinburgh holds a Silver Athena SWAN award in recognition of our commitment to advance gender equality in higher education. We are members of the Race Equality Charter and we are also Stonewall Scotland Diversity Champions, actively promoting LGBT equality. 

Prior to any employment commencing with the University you will be required to evidence your right to work in the UK. Further information is available on our right to work webpages (opens new browser tab).

The University is able to sponsor the employment of international workers in this role.  If successful, an international applicant requiring sponsorship to work in the UK will need to satisfy the UK Home Office’s English Language requirements and apply for and secure a Skilled Worker Visa. 

Key dates to note

The closing date for applications is 10 March 2025.

Unless stated otherwise the closing time for applications is 11:59pm GMT. If you are applying outside the UK the closing time on our adverts automatically adjusts to your browsers local time zone. 

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