Uncertainty quantification for black box models

Project aims

Our aim is to extend the methodology for uncertainty quantification in complex numerical models. One major part of our work is the development of a new library for computer programmes that will bring the most modern methods of computation, exploiting GPUs and such like, in an easy to use set of computer code. if at the end of the project we have a well validated computer code that is easy to use and is being used in a variety of applications we will regard that as a success. On the methodological side we have four workpackages. The first aims to improve the quantification in cases where we have a hierarchy of models at different resolutions/fidelities. Such models are common across all application areas. The second  investigates whether we can improve on the calibration of models (estimate the model parameters using data on the outputs), taking into account the fact that ‘all our models are wrong’, so called model discrepancy. The third concentrates on models whose properties change as we move around parameter space, so called non-stationary models. The final workpackage will investigate the relationship between uncertainty quantification and machine learning and deep learning. In particular can we use our methods for understanding how numerical models based on partial differential equations to investigate deep learning models and bring some transparency to such models.