Data from: Surrogate modelling for the prediction of spatial fields based on simultaneous dimensionality reduction of high-dimensional input/output spaces

Time-consuming numerical simulators for solving groundwater flow and
dissolution models of physico-chemical processes in deep aquifers normally
require some of the model inputs to be defined in high-dimensional spaces
in order to return realistic results. Sometimes, the outputs of interest
are spatial fields leading also to high-dimensional output spaces.
Although Gaussian process emulation has been satisfactorily used for
computing faithful and inexpensive approximations of complex simulators,
these have been mostly applied to problems defined in low-dimensional
input spaces. In this paper, we propose a method for simultaneously
reducing the dimensionality of very high-dimensional input and output
spaces in Gaussian process emulators for stochastic partial differential
equation models while retaining the qualitative features of the original
models. This allows us to build a surrogate model for the prediction of
spatial fields in such time-consuming simulators. We apply the methodology
to a model of convection and dissolution processes occurring during carbon
capture and storage.