Hybrid3D (integrated modeling): a 3D theory-guided machine learning algorithm for inverse modeling of variably saturated groundwater flow coupled with surface flow dynamics

Hybrid3D is a new fully modifiable code for inverse modeling of variably saturated groundwater flow coupled with surface flow dynamics.

Summary of what is new:
1) The idea of considering each component of the overall water system as a theory-guided model that exchanges information with other models that are themselves theory-guided.
2) First integrated theory-guided machine learning code for spatio-temporal groundwater level simulation.
3) First code for the simulation of aquifers with variable saturation.

Details:
The code is initially built for a real aquifer with an irregular geometry composed of 4 stratigraphic units, each one formed by different hydrogeological layers. In this aquifer, we have 4 hydrogeological layers: 3 layers of sands with variable granulometry and one layer of clay. The conceptual model of this aquifer can be found in Adombi et al (2022)*.

Since this is an integrated model, the new idea was to consider each component of the system (aquifer + surface water) as a model that exchanges information with the other model. For example, the aquifer was considered as a variably saturated medium and is represented by a theory-guided artificial neural network ("variably saturated flow equations") and the surface water by another theory-guided artificial neural network ("2D Saint Venant equations").

The code can also be modified to consider the pumping wells as a third model (theory-guided neural network) that interacts with the other two.

The retention and permeability laws used are those of Brooks & Corey (1964) but can be modified to use any retention and permeability laws.

In this code, the Saint Venant equations are incompletely constrained. The user has the choice, if data are available, to increase the constraint on these equations for the surface water system.

All code details are provided in the python files. A folder containing the data is also added. So the code can be executed directly after the download.

Requirements: TensorFlow version: 2.3 or less

References:

Adombi, A.V.D.P., Chesnaux, R., Boucher, M.-A., 2022. Comparing numerical modelling, traditional machine learning and theory-guided machine learning in inverse modeling of groundwater dynamics: A first study case application. Journal of Hydrology: 128600. DOI:https://doi.org/10.1016/j.jhydrol.2022.128600.

Brooks, R.H. and Corey, A.T., 1964. Hydraulic Properties of Porous Media. Hydrology Paper: Vol. 3, Colorado State University, Fort Collins.

Hybrid3D是一款可完全自定义修改的全新代码，用于耦合地表水流动力学的变饱和地下水流（variably saturated groundwater flow）反演模拟。

创新要点如下：
1) 提出将整体水系统的各组分视为理论指导模型（theory-guided model），并使其与其他同类理论指导模型实现信息交互的创新理念。
2) 首款面向时空地下水位模拟的理论指导机器学习（theory-guided machine learning）集成代码。
3) 首款支持变饱和含水层模拟的专用代码。

详细说明：
该代码最初针对由4个地层单元构成的不规则几何形态真实含水层开发，每个地层单元均由不同水文地质层（hydrogeological layers）组成。本次研究的含水层包含4层水文地质结构：3层粒度可变的砂层，以及1层黏土层。该含水层的概念模型可参见Adombi等人（2022）的研究*。

作为一款集成模型，本次开发的核心思路是将系统的各组分（含水层+地表水）均作为可相互交换信息的独立模型。例如，含水层被视为变饱和介质（variably saturated medium），通过理论指导人工神经网络（theory-guided artificial neural network）表征“变饱和流动方程（variably saturated flow equations）”；地表水则通过另一款理论指导人工神经网络，表征“二维圣维南方程组（Saint Venant equations）”。

用户还可对代码进行自定义修改，将抽水井作为第三个理论指导神经网络模型，使其与前述两个模型实现交互。

本次代码采用的持水率（retention）与渗透定律（permeability laws）为Brooks与Corey（1964）提出的公式，但也可修改为任意同类定律。

本代码中，圣维南方程组的约束条件并不完备。若用户拥有可用实测数据，可自行选择强化地表水流系统对应的该方程组约束条件。

所有代码细节均已在Python文件中给出，同时附带了包含数据集的文件夹，用户下载后即可直接运行代码。

运行要求：TensorFlow版本需不高于2.3

参考文献：
1. Adombi, A.V.D.P.、Chesnaux, R.、Boucher, M.-A., 2022. 地下水流动力学反演模拟中数值模拟、传统机器学习与理论指导机器学习的对比研究：首个案例应用. 水文学杂志（Journal of Hydrology）: 128600. DOI: https://doi.org/10.1016/j.jhydrol.2022.128600.
2. Brooks, R.H.与Corey, A.T., 1964. 多孔介质的水力特性. 水文学论文集（Hydrology Paper）: 第3卷, 科罗拉多州立大学, 柯林斯堡.