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 challenging. 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 VIGF 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（Gaussian processes, GPs）通常被视为模拟计算密集型计算机仿真器的黄金标准代理模型。然而，如何在最少模型评估次数下尽可能精确地训练高斯过程仍具挑战性。针对该问题，本文提出一种新型自适应采样准则——全局拟合改进方差（Variance of Improvement for Global Fit, VIGF）。任意点的改进函数衡量了GP仿真器与最近观测模型输出之间的偏差。在每次算法迭代中，选择VIGF值最大的位置执行新运行，随后将该新样本加入设计并相应更新仿真器。本文进一步提出批量版VIGF，可在具备并行计算条件时节省用户时间。此外，VIGF被拓展至多保真度场景，即利用低保真度仿真器辅助预测昂贵的高保真模型，并通过分层克里金方法实现这一过程。通过多组测试函数评估所提方法的适用性，并将其性能与多种序贯采样策略进行对比。结果表明，大多数情况下，本方法在基准函数预测中展现更优性能。