Bridge Designs for Modeling Systems With Low Noise

For deterministic computer simulations, Gaussian process models are a standard procedure for fitting data. These models can be used only when the study design avoids having replicated points. This characteristic is also desirable for one-dimensional projections of the design, since it may happen that one of the design factors has a strongly nonlinear effect on the response. Latin hypercube designs have uniform one-dimensional projections, but are not efficient for fitting low-order polynomials when there is a small error variance. <i>D</i>-optimal designs are very efficient for polynomial fitting but have substantial replication in projections. We propose a new class of designs that bridge the gap between <i>D</i>-optimal designs and <i>D</i>-optimal Latin hypercube designs. These designs guarantee a minimum distance between points in any one-dimensional projection allowing for the fit of either polynomial or Gaussian process models. Subject to this constraint they are <i>D</i>-optimal for a prespecified model.

在确定性计算机仿真场景中，高斯过程（Gaussian process）模型是拟合数据的标准方法。该类模型仅可在试验设计避免重复采样点的前提下使用。此特性对于设计的一维投影而言同样是必要的，因为若某一设计因子对响应变量存在显著非线性影响，则往往需要开展一维投影分析。拉丁超立方设计（Latin hypercube design）的一维投影具备均匀性，但在误差方差较小时，其对低阶多项式的拟合效率并不理想。D最优设计（D-optimal design）在多项式拟合方面效率极高，但在投影过程中存在大量重复采样点。本文提出一类全新的试验设计方案，可弥合D最优设计与D最优拉丁超立方设计之间的性能鸿沟。此类设计可确保任意一维投影内的采样点间均具备最小间距，从而可同时适配多项式模型与高斯过程模型的拟合需求。在满足该约束条件的前提下，针对预设模型而言，此类设计即为D最优设计。