Stochastic kriging (SK) offers an explicit way to characterize heterogeneous noise variance in stochastic computer simulations and has gained considerable traction recently as a surrogate model. Nevertheless, SK relies on tedious Monte Carlo (MC) method to estimate the intrinsic variance at each design input. For computationally expensive simulations, the substantial replication effort has essentially rendered SK intractable. To this end, we develop generalized polynomial chaos (gPC)-informed efficient stochastic kriging (gPC-SK) to ameliorate the computational cost. At its core, gPC supplants the tedious repetitive MC simulations, instead resting on a much smaller set of sampling points to estimate the intrinsic uncertainty, thus applicable to those prohibitively expensive simulations. We present the gPC-SK in sequential optimal design on the borehole function and stability of time-delay dynamic systems.

随机克里金法 (SK) 提供了一种在随机计算机模拟中表征异质噪声方差的明确方法，并且最近作为替代模型获得了相当大的吸引力。然而，SK 依赖于繁琐的蒙特卡罗 (MC) 方法来估计每个设计输入的内在方差。对于计算成本高昂的模拟，大量的复制工作基本上使 SK 变得难以处理。为此，我们开发了基于广义多项式混沌 (gPC) 的高效随机克里金法 (gPC-SK) 以降低计算成本。从本质上讲，gPC 取代了繁琐的重复 MC 模拟，而是依靠一组小得多的采样点来估计内在不确定性，因此适用于那些昂贵得令人望而却步的模拟。