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 novel 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 criteria 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 novel, closed from IMSPE criteria for sequentially acquiring new simulator data in an active learning setting 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 such acquisitions lead to a more efficient simulation campaign on benchmark problems, and conclude with a showcase on a motivating problem involving prediction of equilibrium concentrations of rare earth elements for a liquid-liquid extraction reaction.
翻译:肯尼迪和O'Hagan(KOH)校准框架在预测新的实地条件(设计投入)时,使用同步的GP(GP)程序来模拟一个昂贵的模拟器(第一次GP),调整其“口号”(校准投入),以最佳匹配实际物理/实地试验的观测,纠正任何模型偏差(第二次GP),在预测新的实地条件(设计投入)时,采用完善的方法将设计投入用于单独进行模拟活动的数据高效规划,即没有实地数据:空间填充,或通过最低集成平均和平均预测错误(IMSPE)等标准来模拟。在与GPG KOH相结合的框架中,大多没有进行“口号”(校准投入)校正。这里我们从IMDE标准中得出了一个新颖的,在KOH的积极学习环境中按顺序获取新的模拟数据(第二次GPME)标准(第二次GPMDE),我们说明了在设计空间中如何获取空间填充料,但集中于校准空间。封闭式IMSPE为高效的数字优化而采用封闭式梯度加速度。我们证明,这种购定能够更高效地模拟模拟测测测测测测测测到稀有的液态的土壤浓度问题,并结束。