A Neighbour-Aware LSTM-PINN Model for Physically Consistent Prediction of Soil Moisture and Water Retention Curves

Accurately modelling unsaturated water flow and predicting soil water retention functions (SWRFs) remain pivotal challenges in hydrologic science. Conventional numerical methods often struggle with the nonlinearities of the Richards equation, high computational demands, and sensitivity to uncertain initial parameters, particularly under heterogeneous soils and dynamic boundary conditions. This study presents a hybrid deep learning framework that integrates multiple Long Short-Term Memory (LSTM) networks with a Physics-Informed Neural Network (PINN). The architecture features parallel LSTM networks with neighbour-aware gating mechanisms to process time-sequenced soil moisture and meteorological inputs across multiple depths. A decoding module maps these outputs into volumetric water content and five van Genuchten–Mualem (VGM) parameters, while the PINN enforces physical consistency by minimising residuals of the Richards equation. This model eliminates the need for predefined parameter initialisation and enables simultaneous forecasting of soil moisture dynamics and estimation of physically consistent SWRFs. The framework is evaluated using three field datasets representing varied soil textures and boundary conditions. Results show the model achieves forecasting accuracy with average coefficients of determination (R²) of 0.94 and produces retention curves that closely match laboratory measurements. Comparisons with standard LSTM and Rosetta pedotransfer function models demonstrated improved physical consistency, interpretability, and generalisation. This framework provides a data-efficient, physically constrained modelling strategy for inverse estimation and real-time forecasting in heterogeneous unsaturated soils, supporting broader efforts to integrate process-based understanding into data-driven prediction.