Project description
Digital twins are computer models representing some physical entity, and are widely used in industry. They are starting to be used in the health care setting to monitor patients, and to guide treatment. This PhD project is part of CVD-Net, a large EPSRC funded project with Imperial College, the Alan Turing Institute, and the University of Sheffield. Our aim is to create an exemplar digital twin of pulmonary hypertension patients (a serious medical condition affecting ~8000 people in the UK). There will be a cohort of 8 PhD students (three of whom will be working on statistical/machine learning methods) starting in autumn 2025 to complement the core work done by the postdoctoral researchers working on the project. There will be opportunities to collaborate across the project, and you will be exposed to a range of methods and data.
This particular PhD project will focus on developing methods for fast Bayesian inference of parameters in differential equation models. We use differential equations to model blood flow through the heart, but these models contain many unknown parameters. We will have clinical observations of patients, in the form of MRI scans and pressure readings from sensors embedded in each patient, and from these data, we need to estimate the unknown parameters. Standard methods for Bayesian inference, such as MCMC and particle filters are slow and computationally expensive, and need to be rerun for each new dataset.
Amortized inference is a new and emerging field of machine learning, where we learn an inference network (typically an invertible neural network) that learns the posterior distribution for any given dataset. Training this network is typically computationally expensive, but the benefits are that models can then be fitted almost instantly, making it feasible to deploy this technology in the clinic for 1000s of patients. These methods have only come to prominence in the last few years, and so much remains to be done, both theoretically and methodologically.