Enhanced Universal Kriging for Transformed Input Parameter Spaces

TL;DR

This paper introduces an enhanced universal kriging method that incorporates input parameter transformations into basis functions, improving prediction accuracy in surrogate modeling for complex computational models.

Contribution

The paper proposes a novel universal kriging approach that integrates input transformations into basis functions and develops efficient gradient-based hyperparameter optimization techniques.

Findings

Improved prediction accuracy over conventional methods

Effective handling of transformed input spaces in surrogate models

Validated on several benchmark functions

Abstract

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.