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，代理模型在众多科学领域中受到越来越多的关注，且通常是开展敏感性研究、参数优化等工作的必要手段。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，需在输入空间中生成空间填充设计以定义训练点，并在此类点上对计算模型进行评估。为合理应用空间填充训练流程，物理参数空间常被转换为独立同分布的均匀输入空间。然而，由于这种变换，代理建模技术在预测精度上往往受到影响。为此，本文提出一种新方法，将输入参数变换应用于通用克里金法的基函数中。为了加速通用克里金法的超参数优化，本文推导了适用于高效梯度优化的表达式。通过多个基准函数对所述方法进行验证，并将其与传统方法进行了比较。