Postdoctoral Research Associate in Applied and Computational Mathematics

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

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