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.
Four attention areas have been identified: (1) Reference priors for the probabilistic solution of differential equations. (2) Heavy-tailed stable distributions for robust uncertainty quantification. (3) Statistical estimation with multi-resolution operator decompositions. (4) Probabilistic numerical methods as Bayesian inversion methods. http://oates.work/samsi/
Part of The Alan Turing Institute-Lloyd’s Register Foundation Programme for Data-Centric Engineering