The Kennedy and O'Hagan (KOH) calibration framework uses coupled Gaussian processes (GPs) to meta-model an expensive simulator (first GP), tune its ``knobs" (calibration inputs) to best match observations from a real physical/field experiment and correct for any modeling bias (second GP) when predicting under new field conditions (design inputs). There are well-established methods for placement of design inputs for data-efficient planning of a simulation campaign in isolation, i.e., without field data: space-filling, or via criterion like minimum integrated mean-squared prediction error (IMSPE). Analogues within the coupled GP KOH framework are mostly absent from the literature. Here we derive a closed form IMSPE criterion for sequentially acquiring new simulator data for KOH. We illustrate how acquisitions space-fill in design space, but concentrate in calibration space. Closed form IMSPE precipitates a closed-form gradient for efficient numerical optimization. We demonstrate that our KOH-IMSPE strategy leads to a more efficient simulation campaign on benchmark problems, and conclude with a showcase on an application to equilibrium concentrations of rare earth elements for a liquid-liquid extraction reaction.

翻译：Kennedy与O'Hagan（KOH）校准框架采用耦合高斯过程（GPs）构建昂贵仿真器的元模型（首个GP），通过调整其“旋钮”（校准输入）以最佳匹配真实物理/现场实验的观测数据，并在预测新现场条件（设计输入）时修正建模偏差（第二个GP）。对于独立仿真实验设计（即无现场数据）的数据高效规划，存在成熟的设计输入布局方法：空间填充法，或通过最小化积分均方预测误差（IMSPE）等准则实现。而在耦合GP的KOH框架内，类似方法在文献中几乎空白。本文推导出适用于KOH框架下顺序获取新仿真器数据的闭式IMSPE准则。我们展示了该方法如何在设计空间中进行空间填充，而在校准空间中进行集中采样。闭式IMSPE准则进一步推导出闭式梯度，可实现高效数值优化。通过在基准问题上的验证，我们证明所提出的KOH-IMSPE策略能实现更高效的仿真实验设计，最后以液-液萃取反应中稀土元素平衡浓度的应用案例作为展示。