We present the implementation and use of the Kriging methodology, i.e., surrogate models based on Kriging interpolation, in uncertainty quantification (UQ) in computational electromagnetics (CEM). We provide consistent, unified, and comprehensive description, derivation, implementation, use, validation, and comparative study of accuracy and convergence of several advanced Kriging approaches, namely, the universal Kriging, Taylor Kriging, and gradient-enhanced Kriging methods, for reconstruction of probability-density function in UQ CEM problems. We also propose, derive, and demonstrate the gradient-enhanced Taylor Kriging (GETK) methodology, novel to science and engineering in general. Numerical results using higher-order finite-element scattering modeling show that Kriging methods for UQ in CEM are able to accurately output probability-density function prediction for a quantity of interest (e.g., radar cross-section) given the probability density of stochastic input parameters (e.g., material uncertainties), as very efficient alternatives to Monte Carlo simulations. The novel GETK method shows dramatic enhancement over all other tested approaches, Kriging and non-Kriging, in terms of surrogate function accuracy and convergence with increasing the number of sample (training) points in all examples.

中文翻译：

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计算电磁学中不确定性量化的克里金方法

我们介绍了克里金方法（即基于克里金插值的代理模型）在计算电磁学 (CEM) 不确定性量化 (UQ) 中的实现和使用。我们对几种先进克里金方法（即通用克里金、泰勒克里金和梯度增强克里金方法）的准确性和收敛性进行了一致、统一和全面的描述、推导、实现、使用、验证和比较研究，用于重建UQ CEM 问题中的概率密度函数。我们还提出、推导并演示了梯度增强泰勒克里金法 (GETK) 方法，这对于科学和工程来说是新颖的。使用高阶有限元散射建模的数值结果表明，在给定随机输入参数的概率密度的情况下，CEM 中 UQ 的克里金方法能够准确输出感兴趣量（例如雷达截面）的概率密度函数预测（例如，材料不确定性），作为蒙特卡罗模拟的非常有效的替代方案。随着所有示例中样本（训练）点数量的增加，新颖的 GETK 方法在代理函数准确性和收敛性方面比所有其他测试方法（克里金法和非克里金法）有了显着增强。