We are looking for a PhD student to work with Prof. Matthew Juniper and Dr. Alexandros Kontogiannis (EPSRC Fellow) on Physics-enhanced velocimetry of Flow-MRI images. We have proven the concept in steady flows and are searching for a PhD student to work with us to extend this method to periodic flows. In this project we will collaborate with the School of Clinical Medicine and the Chemical Engineering and Biotechnology Department at Cambridge. This project would suit a student with strong skills in mathematics, numerical analysis, or programming, and an interest in fluid mechanics.

We are looking for a PhD student to work with Prof. Matthew Juniper, Matthew Yoko, and an industrial partner on adjoint-accelerated Bayesian Inference for Combustion Instability. This approach involves (i) building physics-based models of thermoacoustic systems, (ii) designing and performing automated experiments to collect data, (iii) using Bayesian inference to train the physics-based models on the experimental data, (iv) scaling this up to a full-scale industrial test rig.

We have proven the concept on a laboratory scale thermoacoustic system. We are now looking to extend this to flames and combustion chambers which are more representative of aerospace engines. In this project we will focus on building more detailed models of the flame dynamics, into which we can assimilate data to produce digital-twins of the flames.

This project is a great opportunity for a student who would like to combine physics-based modeling, experiments, and machine learning. The project would suit a student with strong skills in mathematics, numerical analysis, or programming, and an interest in combustion, particularly for long distance air transport. Good experimental skills would be valuable, although not essential.

We are looking for a PhD student to work with Prof. Matthew Juniper and other group members on Adjoint-accelerated Inference and Optimization Methods (AXIOMs). These use adjoint methods to accelerate Bayesian Inference (BI) so that BI works on practical timescales for many real world problems. AXIOMs require a principled (e.g. physics-based) model that can be differentiated with respect to its parameters, which is often mathematically challenging. This model is then trained in much the same way as a neural network but, being orders of magnitude smaller, requires less data and less computational training effort. This project would suit a student with strong skills in functional analysis and an interest in applying Machine Learning to physics-based problems.

The aim of this project is to extend Programmable Inference to large non-self-adjoint PDE problems, such as the Navier–Stokes equations. These problems are challenging because: (i) their function evaluations are expensive, (ii) they can contain many variable parameters, (iii) the forward problem must be carefully formulated in order for the inverse problem to be well-posed.

This position will be advertised formally in early December. In the meantime, please contact me if you have any questions.