Accurately estimating high-dimensional permeability (k) fields through data assimilation is critical for minimizing uncertainties in groundwater flow and solute transport simulations. However, designing an effective monitoring network to obtain diverse system responses in heterogeneous aquifers for data assimilation presents significant challenges. To investigate the influence of different measurement types (hydraulic heads, solute concentrations, and permeability) and monitoring strategies on the accuracy of permeability characterization, this study integrates a deep learning-based surrogate modeling approach and the entropy-based maximum information minimum redundancy (MIMR) monitoring design criterion into a data assimilation framework. An ensemble MIMR-optimized method is developed to provide more comprehensive monitoring information and avoid missing key information due to the randomness of stochastic response datasets in entropy analysis. A numerical case of solute transport with log-Gaussian permeability fields is presented, with twelve scenarios designed by combining different measurement types and monitoring strategies. The results demonstrated that the proposed ensemble MIMR-optimized method significantly improved the k-field estimates compared to the conventional MIMR method. Additionally, high prediction accuracy in forward modeling is essential for ensuring reliable inversion results, especially for observation data with strong nonlinearity. The findings of this study enhance our understanding and management of k-field estimation in heterogeneous aquifers, contributing to the development of more robust inversion frameworks for general data assimilation tasks.

中文翻译：

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深度学习和熵理论的集成框架，用于增强非均质含水层中高维渗透场识别


通过数据同化准确估计高维渗透率 （k） 场对于最大限度地减少地下水流和溶质运移模拟中的不确定性至关重要。然而，设计一个有效的监测网络以获得非均质含水层中的不同系统响应以进行数据同化带来了重大挑战。为了研究不同测量类型 （水力水头、溶质浓度和渗透率） 和监测策略对渗透率表征精度的影响，本研究将基于深度学习的代理建模方法和基于熵的最大信息最小冗余 （MIMR） 监测设计标准集成到数据同化框架中。开发了一种集成 MIMR 优化方法，以提供更全面的监测信息，并避免由于熵分析中随机响应数据集的随机性而丢失关键信息。提出了一个具有对数高斯渗透率场的溶质传输的数值案例，通过结合不同的测量类型和监测策略设计了 12 种场景。结果表明，与传统的 MIMR 方法相比，所提出的集成 MIMR 优化方法显着提高了 k 场估计。此外，正演建模中的高预测精度对于确保可靠的反演结果至关重要，尤其是对于具有强非线性的观测数据。这项研究的结果增强了我们对非均质含水层中 k 场估计的理解和管理，有助于为一般数据同化任务开发更强大的反演框架。