Uniform designs seek to distribute design points uniformly in the experimental domain. Some discrepancies have been developed to measure the uniformity by treating all factors equally. It is reasonable when there exists no prior information about the system or when the potential model is completely unclear. However, in the situation of sequential designs, experimental information, such as the importance of each factor, would be obtained from previous stage experiments. With this fact, the weighted $L_2$-discrepancy is more suitable than the original discrepancy for choosing follow-up designs. In this paper, the sequentially weighted uniform design is proposed, which is obtained by minimizing the weighted $L_2$-discrepancy. The weights, indicating the relative importance of each factor, are estimated through a Bayesian hierarchical Gaussian process method based on serial experimental data. Results from several classic computer simulator examples, as well as a real application in circuit design, demonstrate that the performance of our new method surpasses that of its counterparts.

均匀设计寻求在实验域中均匀分布设计点。通过平等对待所有因素，已经开发出一些差异来衡量均匀性。当不存在有关系统的先验信息或潜在模型完全不清楚时，这是合理的。然而，在序贯设计的情况下，实验信息，例如每个因素的重要性，将从前阶段的实验中获得。考虑到这一事实，加权$L_2$- 差异比原始差异更适合选择后续设计。本文提出了顺序加权均匀设计，通过最小化加权得到$L_2$-差异。权重表示每个因素的相对重要性，通过基于系列实验数据的贝叶斯分层高斯过程方法进行估计。几个经典计算机模拟器示例的结果以及电路设计中的实际应用表明，我们的新方法的性能优于同类方法。