A Two-Stage Physics-Informed Neural Network Framework for Estimating Soil Hydraulic Properties

Accurately characterizing soil hydraulic properties—specifically water retention and conductivity—is essential for modeling hydrological risks such as flooding, drought, and solute transport. However, direct measurement of these properties in heterogeneous field conditions remains a significant challenge. This study proposes a novel framework for estimating hydraulic parameters using Physics-Informed Neural Networks (PINNs), which constrain deep learning architectures with the fundamental physical laws of subsurface flow. To address the inherent noise and sparsity of field-collected data, we developed a two-stage training strategy: We first introduce a specialized neural network designed to preprocess raw sensor data and capture the complex spatio-temporal dynamics of soil moisture, an the PINN is subsequently refined to map these dynamics back to the underlying hydraulic properties. Furthermore, we enhanced the model’s robustness by integrating empirical soil-water characteristic models into the Activation function ensuring stability across the full moisture spectrum, from desiccation to saturation. Results indicate that this hybrid approach significantly improves parameter estimation accuracy compared to traditional inverse modeling and standard machine learning techniques. This methodology provides a scalable and robust tool for enhancing the predictive reliability of environmental water management models.