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Theme 1: High dimensionality

Models typically have very many inputs and produce many outputs. Both inputs and outputs can comprise values over large spatial domains. Outputs are often both space- and time-varying. The Gaussian process methodology becomes itself more computer-intensive as the dimensionality of the input space increases, and there is a need to develop efficient methods of dimension reduction, or ways to exploit simple local structure within globally complex models. This theme will work with versions of some of the largest and most challenging models in areas such as earth systems science, protein modelling and particle physics. It seeks to extend the technology as far as possible in terms of being able to address seriously large and complex models.

Theme 1 is led by Dan Cornford

Theme 2: Using observational data

When confronting model predictions with observational data, it is crucial to recognise that discrepancies arise both because of observational error and from model error. Models are imperfect versions of the physical systems that they purport to represent. The sources of imperfection are of two kinds: (i) simplifications in modelling the laws governing the operation of the system and in representing the input and output structure (whether due to imperfect understanding of the system or in order to obtain a more tractable model); (ii) approximations in solving the equations in the simulator (e.g. we may need to discretise a continuous equation system, and to limit the level of iteration to the full solution). It is important to characterise the discrepancy between model outputs and reality, both in order to account for all sources of uncertainty when models are used to predict the real physical system, and in order to make use of observational data properly.

Observational data have the potential to improve our understanding of the behaviour of models and to reduce uncertainty, through calibration, data assimilation, model criticism or validation. However, in order to realise this potential we need to describe the data in terms of a statistical model. Much current work on calibration and data assimilation implicitly assumes that the data are observations of the model outputs with independent random errors, but this is fundamentally wrong. They are observations of functions of the true system with (usually) simple error structure, and it is essential to consider this discrepancy between the true system and the model outputs. The work packages in this theme address the link between models and reality, as well as specific topics in using observational data.

Theme 2 is led by Michael Goldstein

Theme 3: Realising the potential

This theme concerns bringing the various techniques together into a coherent collection of tools that can be routinely used by modellers, researchers and policy makers. To do so will mean addressing other challenges that are generic to all the techniques.

Theme 3 is led by Peter Challenor