A U-Net architecture as a surrogate model combined with a geostatistical spectral algorithm for transient groundwater flow inverse problems

IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES
Dany Lauzon
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引用次数: 0

Abstract

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.

Abstract Image

Abstract Image

作为代用模型的 U-Net 架构与地质统计谱算法相结合,用于解决瞬态地下水流反问题
确定地下水流参数对于了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重要作用。然而,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,它可以取代瞬态地下水流模型,缩短运行时间,并能快速量化与关键参数相关的不确定性,包括异质水力传导性、边界条件、比储量和抽水速率。代用模型通过对前导模型的有限评估来学习水力传导场与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、比储量和源项,也被绘制成图并作为输入引入模型,以增强其对瞬态地下水流控制方程的理解。为了加快使用图像-图像回归的学习速度,先前预测的瞬态水头也可作为预测当前时间步的瞬态水头的输入。模型训练完成后,我们使用频谱地质统计方法来解决反问题,即使用代用模型代替前向模型进行 12 小时的抽水测试。我们的研究表明,训练有素的 U-Net 能准确地再现特定参数场对应的状态变量,而在计算需求方面,使用 U-Net 作为代用模型可将所需的计算时间减少约一个数量级。所提出的方法为复杂含水层系统的地下水流参数特征描述和不确定性量化提供了一种高效、准确的方法。
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来源期刊
Advances in Water Resources
Advances in Water Resources 环境科学-水资源
CiteScore
9.40
自引率
6.40%
发文量
171
审稿时长
36 days
期刊介绍: Advances in Water Resources provides a forum for the presentation of fundamental scientific advances in the understanding of water resources systems. The scope of Advances in Water Resources includes any combination of theoretical, computational, and experimental approaches used to advance fundamental understanding of surface or subsurface water resources systems or the interaction of these systems with the atmosphere, geosphere, biosphere, and human societies. Manuscripts involving case studies that do not attempt to reach broader conclusions, research on engineering design, applied hydraulics, or water quality and treatment, as well as applications of existing knowledge that do not advance fundamental understanding of hydrological processes, are not appropriate for Advances in Water Resources. Examples of appropriate topical areas that will be considered include the following: • Surface and subsurface hydrology • Hydrometeorology • Environmental fluid dynamics • Ecohydrology and ecohydrodynamics • Multiphase transport phenomena in porous media • Fluid flow and species transport and reaction processes
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