This paper introduces an efficient surrogate model with the aim of accelerating joint estimation of subsurface geological properties and relative permeability parameters for high-dimensional inversion problems. We fully replace the high-fidelity model with a set of subdomain linear models through integrating model linearization with smooth local parameterization where the Gaussian geological parameters and non-Gaussian facies indicators are locally parameterized. These subdomain linear models with smooth local parameterization, referred to as SLM-SLP, are constructed in each subdomain individually using only a few high-fidelity model simulations. An adaptive scheme, that is, weighting smooth local parameterization (WSLP), is introduced as well to mitigate the negative effects of inappropriate domain decomposition schemes by adaptively optimizing the domain decomposition strategy. The computational advantages of the proposed algorithm are demonstrated on a synthetic non-Gaussian facies model and a real-world high-dimensional Gaussian model. The amount of computational cost has been drastically reduced while reasonable accuracy remains. Specifically, SLM-SLP only needs 220 fidelity simulations to optimize 302 parameters. Compared to ensemble smoother with multiple data assimilation (ES-MDA), SLM-SLP effectively and efficiently mitigates the ensemble collapse problem in the course of uncertain quantification.

中文翻译：

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使用平滑局部参数化对高维反问题的地下地质参数和相对渗透率参数进行基于代理的联合估计

本文介绍了一种有效的替代模型，旨在加速对高维反演问题的地下地质性质和相对渗透率参数的联合估计。我们通过将模型线性化与平滑局部参数化相结合，用一组子域线性模型完全替代高保真模型，其中高斯地质参数和非高斯相指标局部参数化。这些具有平滑局部参数化的子域线性模型，称为 SLM-SLP，仅使用少量高保真模型模拟在每个子域中单独构建。一种自适应方案，即加权平滑局部参数化（WSLP），还引入了通过自适应优化域分解策略来减轻不适当域分解方案的负面影响。在合成的非高斯相模型和现实世界的高维高斯模型上证明了所提出算法的计算优势。在保持合理的准确性的同时，计算成本已大大降低。具体来说，SLM-SLP 只需要 220 次保真度模拟就可以优化 302 个参数。与具有多重数据同化（ES-MDA）的集成平滑器相比，SLM-SLP有效地缓解了不确定量化过程中的集成崩溃问题。在合成的非高斯相模型和现实世界的高维高斯模型上证明了所提出算法的计算优势。在保持合理的准确性的同时，计算成本已大大降低。具体来说，SLM-SLP 只需要 220 次保真度模拟就可以优化 302 个参数。与具有多重数据同化（ES-MDA）的集成平滑器相比，SLM-SLP有效地缓解了不确定量化过程中的集成崩溃问题。在合成的非高斯相模型和现实世界的高维高斯模型上证明了所提出算法的计算优势。在保持合理的准确性的同时，计算成本已大大降低。具体来说，SLM-SLP 只需要 220 次保真度模拟就可以优化 302 个参数。与具有多重数据同化（ES-MDA）的集成平滑器相比，SLM-SLP有效地缓解了不确定量化过程中的集成崩溃问题。