Computer models of physical systems are often expensive to run, resulting in a small number of model evaluations, hence the use of statistical emulators (usually Gaussian process-based) to predict the model output at unseen inputs, and to search for plausible matches to real-world observations (calibration/history matching). Many such computer models have high-dimensional spatial and/or temporal outputs, all of which we may wish to emulate and calibrate rather than only considering summaries of the output, so that dimension reduction is an attractive option in terms of computational efficiency.

 

We consider a few scenarios, including spatial output (climate, engineering examples) and spatio-temporal inputs (boundary conditions for an ice sheet model), and demonstrate that basis methods have several desirable properties. We finally discuss the case when model discrepancy (missing processes in the model) is unknown, and how we might aim to fix this problem.