Characterizing groundwater flow parameters is crucial for understanding complex aquifer systems, and inverse techniques play a fundamental role in modeling hydrogeological parameters and assessing their uncertainties. Nonetheless, the use of a forward model in these methods can be highly time-consuming, especially with an increasing number of model parameters. To address this issue, we propose a surrogate model based on a U-Net architecture that replaces the transient groundwater flow model, reducing runtime and enabling a fast quantification of uncertainties related to key parameters, including heterogeneous hydraulic conductivity, boundary conditions, specific storage, and pumping rate. The surrogate is trained using limited evaluations of the forward model to learn the physical relationship between hydraulic conductivity fields and transient hydraulic heads measured on-site. The physical principles of the studied problem, including boundary conditions, specific storage, and source terms, are also mapped and introduced as inputs to the model to enhance its understanding of the governing equation of transient groundwater flow. To speed up learning using image–image regression, the previously predicted transient hydraulic heads also serve as an input to predict the transient heads at the current time step. Once the model is trained, we use a spectral geostatistical method to solve the inverse problem, a pumping test of 12 h, using the surrogate model in place of the forward model. Our study demonstrates that the trained U-Net accurately reproduces the state variables corresponding to a specific parameter field, and in terms of computational demand, using U-Net as a surrogate model reduces the required computational time by approximately an order of magnitude for the defined problem. The proposed approach offers an efficient and accurate method for groundwater flow parameter characterization and uncertainty quantification in complex aquifer systems.

中文翻译：

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U-Net 架构作为代理模型与地质统计谱算法相结合，用于解决瞬态地下水流反问题


表征地下水流参数对于理解复杂的含水层系统至关重要，而反演技术在水文地质参数建模和评估其不确定性方面发挥着基础作用。尽管如此，在这些方法中使用正演模型可能非常耗时，尤其是在模型参数数量不断增加的情况下。为了解决这个问题，我们提出了一种基于 U-Net 架构的替代模型，取代了瞬态地下水流模型，减少了运行时间，并能够快速量化与关键参数相关的不确定性，包括异质水力传导率、边界条件、特定存储、和泵送速率。使用正演模型的有限评估来训练代理，以了解水力传导率场和现场测量的瞬态水头之间的物理关系。研究问题的物理原理，包括边界条件、特定存储和源项，也被映射并作为模型的输入引入，以增强对瞬态地下水流控制方程的理解。为了使用图像-图像回归加速学习，之前预测的瞬态水头也作为输入来预测当前时间步的瞬态水头。模型训练完成后，我们使用谱地统计方法来解决反演问题，即 12 小时的抽水测试，使用替代模型代替正演模型。 我们的研究表明，经过训练的 U-Net 准确地再现了特定参数场对应的状态变量，并且在计算需求方面，使用 U-Net 作为代理模型将所需的计算时间减少了大约一个数量级。问题。该方法为复杂含水层系统中的地下水流参数表征和不确定性量化提供了一种有效且准确的方法。