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.

翻译：随着计算模型日益昂贵和复杂，代理模型在许多科学学科中受到越来越多的关注，并且通常对于进行敏感性研究、参数优化等来说是必要的。在不确定性量化（UQ）这一科学学科中，模型输入量通常由概率分布描述。为了构建代理模型，在输入空间中生成空间填充设计以定义训练点，然后在这些点上对计算模型进行评估。为了以合理的方式应用空间填充训练程序，物理参数空间通常被转换为独立同分布的均匀输入空间。由于这种转换，代理建模技术在其预测精度方面往往会受到影响。因此，本文提出了一种新方法，即对通用克里金法的基函数应用输入参数变换。为了加速通用克里金法的超参数优化，开发了适用于高效基于梯度优化的表达式。研究了几种基准函数，并将所提出的方法与常规方法进行了比较。