DOI: 10.6071/m3t376
title: Dataset for: Physics-informed neural networks with monotonicity constraints for Richardson-Richards equation: Estimation of constitutive relationships and soil water flux density from volumetric water content measurements by Toshiyuki Bandai and Teamrat A. Ghezzehei

description: Simulation of soil moisture dynamics is important for various fields, such
 as agriculture, hydrological modeling, and natural disasters. Such
 simulations are conducted by solving a partial differential equation (PDE)
 called the Richardson-Richards equation (RRE). Because the RRE is a highly
 non-linear PDE, we need to solve it numerically. Various numerical methods
 have been used to solve the RRE, such as the finite difference, finite
 element, and finite element volume method. In order for those numerical
 methods to produce correct solutions, they require precise information on
 initial and boundary conditions, as well as hydraulic properties of soils.
 In "Physics-informed neural networks with monotonicity constraints
 for Richardson-Richards equation: Estimation of constitutive relationships
 and soil water flux density from volumetric water content measurements by
 Toshiyuki Bandai and Teamrat A. Ghezzehei," we presented an
 alternative numerical method to infer hydraulic properties of soils from
 volumetric water content measurements withtout the initial and boudary
 conditions using physics-informed neural networks (PINNs). In this
 repository, we provide all the datasets that are needed to reproduce the
 analysis conducted in the paper.
description: The dataset was collected by computational simulations. The zip
 files
 (<strong>PINN_Monotonic.zip, NN_structure.zip, relative_errors.zip</strong>) were produced by running PINNs (physics informed neural networks) programs the authors developed. Please refer to Github page (https://github.com/ToshiyukiBandai/PINNs_RRE) for the PINNs programs. The other zip files (<strong>hydrus_run_files.zip and hydrus_nod_files.zip</strong>) were produced by running a software called HYDRUS-1D (https://www.pc-progress.com/en/Default.aspx?hydrus-1d).
description: The dataset contains 5 zip files. <strong>“PINN_Monotonic.zip”</strong> This zip file contains 6 files that have the results from the PINNs with monotonicity constraints for 3 soils and 2 upper boundary conditions. These files are used in Section 4.3. In each file, there is “data.csv,” which summarizes predicted values and training data. Also, trained WRCs and HCFs are “lookup.csv.”  Other data can be produced from “data.csv.” <strong>“NN_structure.zip”</strong> This zip file contains Excel files that contain the results from the PINNs with and without monotonicity constraints with different neural network architecture. These Excel files are used to generate ”relative_errors” files. <strong>“relative_errors.zip”</strong> This zip file contains relative error data used in Section 4.1 and 4.2. <strong>“hydrus_run_files.zip”</strong> This zip file contains files that are useful to run HYDRUS-1D and process the output data. “hydrus_condition.xlsx” summarizes the HYDRUS-1D settings. “HydrusProcess.ipynb” is a Jupyter notebook file that can be used to convert the HYDRUS data into the “{soil_name}_nod.csv” file, which is used to feed the training and validation data to the PINNs. “<strong>hydrus_nod_files.zip”</strong> This zip file contains synthetic data generated by HYDRUS-1D. Each file corresponds to each soil (sandy loam, loam, silt loam soil) and different upper boundary conditions (“ ": Scenario 1; “2”: Scenario 2). These files can be generated by “hydrus_run_files.zip.”