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.

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.

Cardio-vascular disease is the biggest cause of death worldwide. It is usually caused by the rupture of plaque that builds up inside arteries. The mechanisms of plaque formation are not well understood, partly because it is difficult to measure the velocity fields inside arteries.

The aim of this combined experimental/theoretical project is to measure the velocity field in arteries with unprecedented accuracy. We will combine advanced adjoint-based data assimilation methods with Magnetic Resonance Images. This project has recently become possible due to developments in data acquisition, algorithms, and computational power.

This project will suit a student with strong skills in mathematics, numerical analysis, or programming.

We are looking for a PhD student to work with Prof. Matthew Juniper and Dr. Lloyd Fung (Peterhouse College Cambridge) on Bayesian Inference (BI) for the sparse identification of nonlinear dynamical systems (SINDy). We will re-formulate the well-known SINDy algorithm within a Bayesian framework, which a scoping study has shown to be more robust to noise and more able to cope with sparse data. This project would suit a student with strong skills in mathematics, numerical analysis, or programming.