Gradient-Enhanced Kriging

Build surrogate models of data that includes gradient information.

In Uncertainty Quantification and in Optimization we often use surrogate models (a.k.a. emulators, response surfaces, etc.), which are in fact interpolations (a.k.a. regression, reconstruction) of the output of an expensive computer code, conditional on a limited number of sample runs of the code.
The general objective is to be efficient, i.e. to obtain a highly accurate surrogate model from only a small number of samples.
A promising option is to use Gradient-Enhanced Kriging (GEK) for codes where gradient information is available at relatively low cost (such as from an adjoint solve). We find that it is vital to incorporate error information in the GEK analysis. The present code builds a GEK surrogate conditional on the output (values and gradients of the QoI), while incorporating error information.