The Lloyds-Turing programme on data-centric engineering has partnered with the Statistical and Applied Mathematical Sciences Institute (SAMSI) to deliver ground-breaking research into uncertainty quantification for numerical methods. Activities are coordinated under a SAMSI “working group” as part of their year-long programme on Quasi Monte Carlo and High-Dimensional Sampling Methods for Applied Mathematics. The working group consists of 22 researchers from around the world, listed in the opposite panel. The group is co-led by Dr Chris Oates (Newcastle University and Lloyds-Turing) and Dr Tim Sullivan (Free University of Berlin).
The accuracy and robustness of numerical predictions that are based on mathematical models depend critically upon the construction of accurate discrete approximations to key quantities. The exact error due to approximation will be unknown to the analyst, but worst-case upper bounds can often be obtained. This working group aims, instead, to develop Probabilistic Numerical Methods, which provide the analyst with a richer, probabilistic quantification of the numerical error in their output. The goal is to provide engineers with tools to mitigate the “numerical risk” associated with unreliable numerical calculations based on physical models of interest.
In particular, the working group aims to address 4 main themes:
- Reference priors for the probabilistic solution of differential equations.
- Heavy-tailed stable distributions for robust uncertainty quantification.
- Statistical estimation with multi-resolution operator decompositions.
- Probabilistic numerical methods as Bayesian inversion methods.
As part of the project, a series of research visits have been undertaken and are planned:
- July and August, 2017: F Schaefer to visit M Girolami and F-X Briol @ Alan Turing Institute and Imperial College London.
- August and September, 2017: F-X Briol to visit H Owhadi, A Stuart and F Schaefer @ Caltech.
- April 11-13, 2018: Meeting of the working group at the Alan Turing Institute, London.
In addition, the working group conducts regular discussions, an up-to-date schedule for which can be found at: http://oates.work/samsi/
Part of The Alan Turing Institute-Lloyd’s Register Foundation Programme for Data-Centric Engineering
As an example of our research output, here you can watch a short video explainer for the paper “Probabilistic Models for Integration Error in Assessment of Functional Cardiac Models” at NIPS 2017.