Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of model evaluations remains a challenging task. We address this problem by suggesting a novel adaptive sampling criterion called VIGF (variance of improvement for global fit). The improvement function at any point is a measure of the deviation of the GP emulator from the nearest observed model output. At each iteration of the proposed algorithm, a new run is performed where the VIGF criterion is the largest. Then, the new sample is added to the design and the emulator is updated accordingly. A batch version of VIGF is also proposed which can save the user time when parallel computing is available. Additionally, VIGF is extended to the multi-fidelity case where the expensive high-fidelity model is predicted with the assistance of a lower fidelity simulator. This is performed via hierarchical kriging. The applicability of our method is assessed on a bunch of test functions and its performance is compared with several sequential sampling strategies. The results suggest that our method has a superior performance in predicting the benchmark functions in most cases.

翻译：高斯过程通常被视为以最小模型评估次数尽可能高精度训练代理模型的黄金标准，但这仍具挑战性。本文提出一种新型自适应采样准则VIGF（全局拟合改进方差）。任意点处的改进函数衡量高斯过程仿真器与最近观测模型输出之间的偏差。在算法每次迭代中，VIGF准则最大的位置执行新运行，随后将该样本加入设计并更新仿真器。本文还提出了VIGF的批量版本，可在并行计算可用时节省用户时间。此外，VIGF被扩展至多保真度情形，通过分层克里金法借助低保真度模拟器预测昂贵的高保真度模型。通过一系列测试函数评估方法适用性，并与其他序贯采样策略进行性能比较。结果表明，本方法在多数基准函数预测中具有更优性能。