Importance Weighting in Hybrid Iterative Ensemble Smoothers for Data Assimilation

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Yuming Ba, Dean S. Oliver
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Abstract

Because it is generally impossible to completely characterize the uncertainty in complex model variables after assimilation of data, it is common to approximate the uncertainty by sampling from approximations of the posterior distribution for model variables. When minimization methods are used for the sampling, the weights on each of the samples depend on the magnitude of the data mismatch at the critical points and on the Jacobian of the transformation from the prior density to the sample proposal density. For standard iterative ensemble smoothers, the Jacobian is identical for all samples, and the weights depend only on the data mismatch. In this paper, a hybrid data assimilation method is proposed which makes it possible for each ensemble member to have a distinct Jacobian and for the approximation to the posterior density to be multimodal. For the proposed hybrid iterative ensemble smoother, it is necessary that a part of the mapping from the prior Gaussian random variable to the data be analytic. Examples might include analytic transformation from a latent Gaussian random variable to permeability followed by a black-box transformation from permeability to state variables in porous media flow, or a Gaussian hierarchical model for variables followed by a similar black-box transformation from permeability to state variables. In this paper, the application of weighting to both hybrid and standard iterative ensemble smoothers is investigated using a two-dimensional, two-phase flow problem in porous media with various degrees of nonlinearity. As expected, the weights in a standard iterative ensemble smoother become degenerate for problems with large amounts of data. In the examples, however, the weights for the hybrid iterative ensemble smoother were useful for improving forecast reliability.

Abstract Image

用于数据同化的混合迭代集合平滑器中的重要性加权
由于在数据同化后一般不可能完全确定复杂模型变量的不确定性,因此通常通过从模型变量的后验分布近似值中采样来近似确定不确定性。当使用最小化方法进行采样时,每个样本的权重取决于临界点数据不匹配的程度,以及从先验密度到样本提议密度的变换的雅各布。对于标准迭代集合平滑器来说,所有样本的雅各比是相同的,权重只取决于数据错配。本文提出了一种混合数据同化方法,使每个集合成员都有一个不同的雅各比,并使后验密度的近似具有多模态性。对于所提出的混合迭代集合平滑器来说,从先验高斯随机变量到数据的部分映射必须是解析的。例如,从潜在高斯随机变量到渗透率的解析变换,再从渗透率到多孔介质流状态变量的黑箱变换,或从渗透率到状态变量的类似黑箱变换的高斯分层变量模型。本文使用具有不同非线性程度的多孔介质中的二维两相流问题,研究了权重在混合迭代集合平滑器和标准迭代集合平滑器中的应用。不出所料,对于数据量较大的问题,标准迭代集合平滑器中的权重会退化。然而,在实例中,混合迭代集合平滑器的权重有助于提高预测可靠性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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