Differentiable Physics in Scientific Machine Learning

This project would first require the student to become familiar with some simple concepts and techniques in Scientific Machine Learning (SML) and in algorithmic differentiation (AD). As an initial vehicle towards this a numerical model will be selected that it is straightforward to apply AD to. This will be used to generate labelled data to train a simple ML surrogate for predicting a quantity of interest (QoI) for prescribed input values. The training data will then be enhanced with gradient information at additional data points and modifications of the surrogate model will be investigated to assess ways of incorporating this gradient data most effectively into the training. Once this initial objective has been met then the work will be developed further based upon the outcome of a contemporary literature review. These developments are expected to involve the inclusion of greater complexity in the numerical model and research into different approaches to incorporate the numerical models within fully differentiable SML algorithms.