Physically Informed Machine Learning  

Project description

Applied mathematics and statistics traditionally use very different types of modelling framework. In applied maths, models tend to be based upon physical laws of nature and first principles: our ability to model relies upon having a sound scientific understanding of the phenomena being modelled. In contrast, statistical models tend to be based on data and observed correlations: our ability to build accurate models relies upon having enough high-quality data.

This project will focus on developing machine learning models that combine scientific knowledge and empirical learning. In the first instance we will focus on incorporating differential equations into Gaussian process models (which are a key non-parametric modelling framework widely used in statistics and machine learning).  This is an area of rapidly growing interest within machine learning, particularly as the tech companies (Google, Microsoft, Uber etc) realise that to make progress in some problems requires models that can meld data and expert knowledge.

The project will develop the underlying mathematics, using exemplar problems to guide this development.