Active learning in computer experiments aims at allocating resources in an intelligent manner based on the already observed data to satisfy certain objectives such as emulating or optimizing a computationally expensive function. There are two main ingredients for active learning: an initial experimental design, which helps to approximately learn the function, and a surrogate modeling technique, which provides a prediction of the output along with its uncertainty estimates. Space-filling designs are commonly used as initial design and Gaussian processes for surrogate modeling. This article aims at improving the active learning procedure by proposing a new type of initial design and a new correlation function for the Gaussian process. The ideas behind them are known in other fields such as in sensitivity analysis or in kernel theory, but they never seem to have been used for active learning in computer experiments. We show that they provide substantial improvement to the state-of-the-art methods for both emulation and optimization. We support our findings through theory and simulations, and a real experiment on the vapor-phase infiltration process.

翻译：计算机实验中的主动学习旨在基于已观测数据以智能方式分配资源，以满足特定目标，例如模拟或优化计算代价高昂的函数。主动学习包含两个核心要素：初始实验设计（用于近似学习目标函数）和代理建模技术（提供输出预测及其不确定性估计）。空间填充设计通常作为初始设计方法，而高斯过程则常用于代理建模。本文通过提出新型初始设计方法及高斯过程的新型相关函数，致力于改进主动学习流程。这些方法背后的思想在敏感性分析或核理论等其他领域已有应用，但此前似乎从未被用于计算机实验的主动学习。我们通过理论与仿真验证，并结合气相渗透过程的真实实验，证明所提方法在仿真与优化任务上均能对现有先进技术带来显著提升。