  With computational models becoming more expensive and complex, surrogate
models have gained increasing attention in many scientific disciplines and are
often necessary to conduct sensitivity studies, parameter optimization etc. In
the scientific discipline of uncertainty quantification (UQ), model input
quantities are often described by probability distributions. For the
construction of surrogate models, space-filling designs are generated in the
input space to define training points, and evaluations of the computational
model at these points are then conducted. The physical parameter space is often
transformed into an i.i.d. uniform input space in order to apply space-filling
training procedures in a sensible way. Due to this transformation surrogate
modeling techniques tend to suffer with regard to their prediction accuracy.
Therefore, a new method is proposed in this paper where input parameter
transformations are applied to basis functions for universal kriging. To speed
up hyperparameter optimization for universal kriging, suitable expressions for
efficient gradient-based optimization are developed. Several benchmark
functions are investigated and the proposed method is compared with
conventional methods.
