论文标题
混合迭代合奏对于层次模型的历史匹配而更加顺畅
Hybrid iterative ensemble smoother for history matching of hierarchical models
论文作者
论文摘要
先前模型的选择可能会对吸收数据的能力产生很大的影响。在基于合奏的数据同化的标准应用中，初始集合中的所有实现都是从相同的协方差矩阵生成的，并具有隐含的假设，即此协方差适合该问题。在层次方法中，协方差函数的参数，例如方差，各向异性的方向和两个主要方向的范围，可能都不确定。因此，分层方法对模型错误指定更为强大。在本文中，讨论了从后验中进行分层参数化的三种方法：一种基于优化的采样方法（RML），一种迭代的集合（IES）和前两种方法的新型混合物（杂种IES）。将三种近似采样方法应用于线性高斯反问题，可以将结果与精确的“边缘 - 条件”方法进行比较。此外，对IES和杂种方法进行了二维流问题测试，而先前的协方差不确定各向异性。标准IES方法在流动示例中的性能很差，因为通过基于合奏的方法对局部灵敏度矩阵的表示不佳。但是，混合方法的样品即使相对较小的整体尺寸也很好。
The choice of the prior model can have a large impact on the ability to assimilate data. In standard applications of ensemble-based data assimilation, all realizations in the initial ensemble are generated from the same covariance matrix with the implicit assumption that this covariance is appropriate for the problem. In a hierarchical approach, the parameters of the covariance function, for example the variance, the orientation of the anisotropy and the ranges in two principal directions, may all be uncertain. Thus, the hierarchical approach is much more robust against model misspecification. In this paper, three approaches to sampling from the posterior for hierarchical parameterizations are discussed: an optimization-based sampling approach (RML), an iterative ensemble smoother (IES), and a novel hybrid of the previous two approaches (hybrid IES). The three approximate sampling methods are applied to a linear-Gaussian inverse problem for which it is possible to compare results with an exact "marginal-then-conditional" approach. Additionally, the IES and the hybrid IES methods are tested on a two-dimensional flow problem with uncertain anisotropy in the prior covariance. The standard IES method is shown to perform poorly in the flow examples because of the poor representation of the local sensitivity matrix by the ensemble-based method. The hybrid method, however, samples well even with a relatively small ensemble size.
