Salter James M, Williamson Daniel
College of Engineering, Mathematics and Physical Sciences University of Exeter Exeter U.K.
Environmetrics. 2016 Dec;27(8):507-523. doi: 10.1002/env.2405. Epub 2016 Sep 12.
Expensive computer codes, particularly those used for simulating environmental or geological processes, such as climate models, require calibration (sometimes called tuning). When calibrating expensive simulators using uncertainty quantification methods, it is usually necessary to use a statistical model called an emulator in place of the computer code when running the calibration algorithm. Though emulators based on Gaussian processes are typically many orders of magnitude faster to evaluate than the simulator they mimic, many applications have sought to speed up the computations by using regression-only emulators within the calculations instead, arguing that the extra sophistication brought using the Gaussian process is not worth the extra computational power. This was the case for the analysis that produced the UK climate projections in 2009. In this paper, we compare the effectiveness of both emulation approaches upon a multi-wave calibration framework that is becoming popular in the climate modeling community called "history matching." We find that Gaussian processes offer significant benefits to the reduction of parametric uncertainty over regression-only approaches. We find that in a multi-wave experiment, a combination of regression-only emulators initially, followed by Gaussian process emulators for refocussing experiments can be nearly as effective as using Gaussian processes throughout for a fraction of the computational cost. We also discover a number of design and emulator-dependent features of the multi-wave history matching approach that can cause apparent, yet premature, convergence of our estimates of parametric uncertainty. We compare these approaches to calibration in idealized examples and apply it to a well-known geological reservoir model.
昂贵的计算机代码，尤其是那些用于模拟环境或地质过程的代码，如气候模型，需要进行校准（有时也称为调优）。当使用不确定性量化方法校准昂贵的模拟器时，在运行校准算法时通常需要使用一种称为模拟器的统计模型来代替计算机代码。尽管基于高斯过程的模拟器通常比它们所模拟的模拟器评估速度快许多个数量级，但许多应用程序却试图通过在计算中仅使用回归模拟器来加快计算速度，他们认为使用高斯过程带来的额外复杂性不值得额外的计算能力。2009年英国气候预测分析就是这种情况。在本文中，我们在气候建模界日益流行的一种称为“历史匹配”的多波校准框架下，比较了两种模拟方法的有效性。我们发现，与仅使用回归的方法相比，高斯过程在降低参数不确定性方面具有显著优势。我们发现，在多波实验中，最初使用仅回归模拟器，然后使用高斯过程模拟器进行重新聚焦实验，其效果几乎与全程使用高斯过程相同，但计算成本仅为其一小部分。我们还发现了多波历史匹配方法中一些与设计和模拟器相关的特征，这些特征可能导致我们对参数不确定性的估计出现明显但过早的收敛。我们在理想化示例中比较了这些校准方法，并将其应用于一个著名的地质油藏模型。
