Chris Oates is organising a workshop on extrapolation methods on 21 November 2024 in Newcastle, supported by funding from the Heilbronn Institute.

For over a century, extrapolation methods have provided a powerful tool to improve the convergence order of (deterministic) numerical methods. However, these tools are becoming increasingly ill-suited to modern computer codes, where multiple continua are discretised and convergence orders are not easily analysed. At the same time, there is increasing interest in statistical and machine learning aspects of extrapolation, where the concept is intimately connected to the generalisation error of an algorithm when applied in a context for which it was not explicitly trained. 

Our vision is that the next generation of extrapolation methods ought to be sufficiently general to meet the needs of these diverse communities. Our aim is to develop mathematical foundations for extrapolation methods that are capable of handling uncertain data, are accompanied by interpretable error estimators, and are applicable in scenarios where multiple sources of discretisation are simultaneously present. These desiderata are motivated by both applications in statistics and machine learning, where data are typically noisy and high-dimensional meaning that regression-based methods for extrapolation are required, and by scientific applications where complex mathematical models are discretised for simulation, often at considerable computational cost.

An improved understanding of extrapolation will help to bridge the gap between the limited applicability of classical extrapolation methods and the increasingly important practical problem of extrapolation in areas such as machine learning and scientific AI. The confirmed participants include experts in computational statistics, numerical analysis and mathematical modelling, who have a strong collaborative track record and are well-placed to make a meaningful contribution on this research front.

Confirmed Participants: Toni Karvonen (Postdoctoral Fellow, University of Helsinki), Chris Oates (Professor of Statistics, Newcastle University), Marina Riabiz (Lecturer in Statistics, King’s College London), Zheyang Shen (Postdoctoral Fellow, Newcastle University), Marina Strocchi (Postdoctoral Fellow, Imperial College London), Tim Sullivan (Associate Professor of Predictive Modelling, University of Warwick), Aretha Teckentrup (Reader in Mathematics of Data Science, University of Edinburgh), Mengxin Xi (PhD candidate, King’s College London)