A neighbour-aware LSTM-PINN model for simultaneous soil moisture forecasting and retention function estimation

Predicting soil water retention functions (SWRFs) and forecasting soil moisture from field observations remain challenging under heterogeneous soils and uncertain boundary forcing. Existing approaches often treat forecasting and hydraulic parameter estimation separately and may rely on synthetic data or strong prior assumptions. We propose a hybrid framework that couples neighbour-aware Long Short-Term Memory (LSTM) networks with a physics-informed neural network (PINN) constrained by minimising the Richards equation residual under the van Genuchten–Mualem (VGM) parameterisation. Using hourly multi-depth soil moisture measurements (5, 15, and 25 cm) together with rainfall and evapotranspiration from three Tasmanian sites representing contrasting soil textures, the model jointly forecasts soil moisture and infers bounded hydraulic parameters without predefined initial guesses. With 9 months for training and 3 months for independent testing at each site, the model achieved an average RMSE of 0.005 cm 3 /cm 3 ( R 2 = 0.94) for soil moisture forecasting and 0.045 cm 3 /cm 3 for SWRF estimation. Compared to a purely data-driven LSTM, it maintains competitive predictive accuracy while providing physically interpretable hydraulic parameters, supporting sensor-based applications that require physically consistent, data-driven prediction.