Computer experiments have become an indispensable alternative to complex physical and engineering experiments. The Kriging model is the most widely used surrogate model, with the core goal of minimizing the discrepancy between the surrogate and true models across the entire experimental domain. However, existing sequential design methods have critical limitations: observation-based batch sequential designs are rarely studied, while one-point sequential designs have insufficient information utilization and suffer from inefficient resource utilization -- they require numerous repeated observation rounds to accumulate sufficient points, leading to prolonged experimental cycles. To address these gaps, this paper proposes two novel one-point sequential design criteria and a general batch sequential design framework. Moreover, the batch sequential design framework solves the inherent point clustering problem in naive batch selection, enabling efficient extension of any sequential criterion to batch scenarios. Simulations on some test functions demonstrate that the proposed methods outperform existing approaches in terms of fitting accuracy in most cases.

翻译：计算机实验已成为复杂物理与工程实验不可或缺的替代方案。克里金模型作为应用最广泛的代理模型，其核心目标在于最小化代理模型与真实模型在整个实验域上的差异。然而，现有序列设计方法存在关键局限：基于观测的批量序列设计研究甚少，而单点序列设计存在信息利用不足与资源效率低下的问题——这类方法需要通过大量重复观测轮次积累足够样本点，导致实验周期显著延长。为填补上述研究空白，本文提出了两种新颖的单点序列设计准则与一个通用的批量序列设计框架。此外，该批量序列设计框架解决了朴素批量选择中固有的样本点聚集问题，使得任意序列准则都能高效扩展至批量场景。通过对若干测试函数的仿真实验表明，所提方法在多数情况下相较于现有方法具有更高的拟合精度。