PINN‐SM: A Physics‐Informed Neural Networks Model for Vadose Zone Soil Moisture Profile Prediction

Accurate prediction and monitoring of soil water content in the vadose zone (VZSWC) is important, yet challenging, for sustainable management of water resources. Although machine learning algorithms have shown promise, given limited and noisy subsurface data, they often struggle with overfitting, poor generalization, and physical inconsistency. In this study, we explore the effectiveness of physics‐informed neural networks (PINNs) in addressing these challenges by presenting PINN‐SM, a physics‐informed neural network model tailored for predicting physically consistent VZSWC profiles by incorporating Richardson's equation as the governing partial differential equation. Our model extends a traditional PINN architecture by including process‐informed input variables and an attention mechanism that captures the time delay in the response of VZSWC to rainfall events. Using data from a monitoring station in Austin, Texas with soil moisture sensors at different depths, PINN‐SM demonstrated superior predictive performance compared to the traditional PINN model, reducing RMSE by 80% across all depths. Furthermore, PINN‐SM outperformed conventional artificial neural networks (ANNs), achieving an approximately 25% lower RMSE across all depths. This performance advantage was particularly pronounced in the prediction of peak events, where PINN‐SM achieved a RMSE of around 50% lower in all depths. The results indicate that, compared to conventional ANNs, PINN‐SM can more effectively capture the underlying patterns while avoiding overfitting and excel in the prediction of extreme events. By integrating physical constraints with meteorological inputs and modeling temporal dependencies through attention mechanisms, PINN‐SM represents a significant advancement in the prediction of VZSWC, with potential applications in improving subsurface hydrological monitoring and satellite‐based forecasting systems.