Boundary-to-Solution Mapping for Groundwater Flows in a Toth Basin
Boundary-to-Solution Mapping for Groundwater Flows in a Toth Basin
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DOI：
10.1016/j.advwatres.2023.104448
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发表时间：
2023-03
期刊：
影响因子：
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通讯作者：
Jin-Jin Sun-Jin;Jun Li;Y. Hao;Cuiting Qi;Chunmei Ma;Huazhi Sun;N. Begashaw;Gurcan Comet;Yi-mei Sun;Qi Wang
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文献类型：
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作者：
Jin-Jin Sun-Jin;Jun Li;Y. Hao;Cuiting Qi;Chunmei Ma;Huazhi Sun;N. Begashaw;Gurcan Comet;Yi-mei Sun;Qi Wang
在本文中，作者提出了一种新的方法来解决地下水流动方程在托特盆地的任意顶部和底部地形使用深度学习。他们没有使用传统的数值求解器，而是使用DeepONet来生成边界到解决方案的映射。该映射将物理域的几何形状沿着边界条件作为输入，以输出地下水流方程的稳态解。为了实现DeepONet，作者使用截断傅立叶级数或分段线性表示来近似顶部和底部边界。他们提出了DeepONet的两种不同实现：一种是将Toth盆地嵌入矩形计算域，另一种是将具有任意顶部和底部边界的Toth盆地通过非线性变换映射到矩形计算域。它们分别针对顶部的Dirichlet和Robin边界条件以及不透水底部边界的Neumann边界条件实现DeepONet。使用这种支持深度学习的工具，作者通过具有任意几何形状的顶部表面和底部不透水边界来研究表面地形对流型的影响。他们发现，顶面的平均坡度促进了长距离传输，而局部曲率控制着局部环流。此外，他们发现，底部不透水边界的坡度会严重影响地下水流的长距离输送。总的来说，本文提出了一种使用深度学习求解地下水流方程的创新方法，可以调查地表地形对地下水流模式的影响。
In this paper, the authors propose a new approach to solving the groundwater flow equation in the Toth basin of arbitrary top and bottom topographies using deep learning. Instead of using traditional numerical solvers, they use a DeepONet to produce the boundary-to-solution mapping. This mapping takes the geometry of the physical domain along with the boundary conditions as inputs to output the steady state solution of the groundwater flow equation. To implement the DeepONet, the authors approximate the top and bottom boundaries using truncated Fourier series or piecewise linear representations. They present two different implementations of the DeepONet: one where the Toth basin is embedded in a rectangular computational domain, and another where the Toth basin with arbitrary top and bottom boundaries is mapped into a rectangular computational domain via a nonlinear transformation. They implement the DeepONet with respect to the Dirichlet and Robin boundary condition at the top and the Neumann boundary condition at the impervious bottom boundary, respectively. Using this deep-learning enabled tool, the authors investigate the impact of surface topography on the flow pattern by both the top surface and the bottom impervious boundary with arbitrary geometries. They discover that the average slope of the top surface promotes long-distance transport, while the local curvature controls localized circulations. Additionally, they find that the slope of the bottom impervious boundary can seriously impact the long-distance transport of groundwater flows. Overall, this paper presents a new and innovative approach to solving the groundwater flow equation using deep learning, which allows for the investigation of the impact of surface topography on groundwater flow patterns.