Physics-informed neural networks (PINNs) with unsaturated water flow models for inverse analysis of soil hydraulic parameters of layered soil profiles

Information about the spatial distribution of soil hydraulic parameters is necessary for the accurate prediction of soil water flow and coupled movement of chemicals and heat at the field scale using a process-based model. Physics-informed neural networks (PINNs), which can provide physical constraints in deep learning to obtain a mesh-free solution, can be used to inversely estimate the soil hydraulic parameters from less and noisy training data. Previous studies using PINNs have successfully estimated soil hydraulic parameters for homogeneous soil but estimating such parameters of layered soil profiles where the interface depth and the parameters are unknown still has some difficulties. The objective of this study was to develop PINNs to inversely estimate the distribution of soil hydraulic parameters, such as saturated hydraulic conductivity and α and n, of the Mualem-van Genuchten model directly within layered soil profiles by predicting changes in pressure head from training data b..., , , # Physics-Informed Neural Networks (PINNs) with Unsaturated Water Flow Models for Inverse Analysis of Soil Hydraulic Parameters of Layered Soil Profiles

[https://doi.org/10.5061/dryad.pc866t1z4](https://doi.org/10.5061/dryad.pc866t1z4)

This is a supplemental material for VZJ-2024-01-0001-OA.

## Description of the data and file structure

They consist of one python file and 10 datasets files. The dataset consists of pressure heads [cm] at 10, 20, 40, 60, 80, and 100 cm depth for each depth, volumetric water content [cm^3/cm^3] at 0, 30, and 70 cm depth for each depth, and time steps calculated by HYDRUS. Running this python file will train the accompanying dataset to predict saturated hydraulic conductivity Ks,α,n profiles for the soil hydraulic parameters.

## Sharing/Access information

A link to the original code is shown below. The python file for this dataset is a modified version of the following code.

[https://github.com/nanditadoloi/PINN](https://github.com/nanditadoloi/PINN)...