Scientific Machine Learning

The overarching objective of Stuart's research in this area is to establish new theory and methodology at the interfaces of numerical analysis, statistics and machine learning. The theory and methodology will underpin the merging of model-centric and data-centric approaches to computational science and engineering, one of the defining research challenges in this century; the goal is to develop efficient, trusted, readily explainable algorithms that solve problems previously beyond reach. The technical approach is to develop theory and methodology for machine learning, and supervised learning in particular, for input-output maps between separable Banach spaces of (spatially and/or temporally varying) functions. The work is aimed at systematic development of the foundations required to understand the effects of discretization, finite data and their interactions with learning. Mathematical structure and physical insight are used to inform novel interpretable designs for learned maps, alongside theory elucidating efficiency and robustness, and new methodologies for optimized data acquisition.