History Matching and Gaussian Process Emulation in High Dimensions

When calibrating mathematical models to match data, it is of huge practical interest to quantify our uncertainty; how confident are we in our predictions? in practice, however, many models are too computationally demanding for traditional inference methods such as MCMC.

History matching is an alternative algorithm that allows us to calibrate models with uncertainty much more cost-effectively, the result being a set of 'plausible' parameters.

History matching usually employs Gaussian process emulation as a method of surrogate modelling, which can quickly become an efficiency bottle-neck for expensive models in high dimensions.

Our work draws upon methods in scattered data approximation and high-dimensional numerical integration to construct more efficient emulators, potentially allowing for an arbitrarily large input-parameter dimension under anisotropy conditions. From here we can design history matching algorithms for models which would otherwise be difficult to calibrate.