Physics-informed neural networks enhanced by data augmentation: a novel framework for robust soil moisture estimation using multi-source data fusion - Hu, Jinhui; Deng, Changtao; Zhang, Qiuwen; Pang, Aoxuan (Journal of hydrology (Amsterdam), 2025)
•Novel PINN + TVAE framework proposed for robust soil moisture estimation.•Physics (WCM, Oh) integrated into end-to-end differentiable PINN structure.•TVAE data augmentation effectively overcomes data scarcity for PIML models.•PINN-Aug outperforms baselines (RF, MLP) and non-augmented PINN model.•Predicted intermediate parameters show physically realistic spatial–temporal patterns. Accurate soil moisture (SM) monitoring is crucial for hydrology, agriculture, and climate studies, yet challenging due to factors like vegetation and roughness, compounded by data scarcity. This study aims to develop a robust, high-resolution, and physically interpretable framework for soil moisture retrieval by integrating multi-source remote sensing data. We propose a novel hybrid model, potentially the first of its kind for SM retrieval, which integrates Deep Learning (DL) techniques to dynamically predict key physical parameters within an end-to-end differentiable physics-informed structure built upon the complete WCM and Oh models. This Physics-Informed Neural Network (PINN) is further enhanced by Tabular Variational Autoencoder (TVAE)-based data augmentation to overcome data limitations. Results demonstrate the superior performance of the TVAE-enhanced PINN (PINN-Aug), achieving the highest accuracy on the test set with a Pearson Correlation Coefficient (PCC) of 0.7706, Root Mean Squared Error (RMSE) of 0.0349 m3/m3, Mean Absolute Error (MAE) of 0.0277 m3/m3, and Unbiased Root Mean Squared Error (ubRMSE) of 0.0348 m3/m3, significantly outperforming baseline models and the PINN without augmentation. Furthermore, the analysis confirmed that the intermediate physical parameters predicted by the PINN align with expected physical ranges and seasonal patterns, enhancing model interpretability. This study concludes that the proposed framework offers a powerful and promising approach for accurate, interpretable, high-resolution SM estimation, providing valuable theoretical insights into hybrid modeling and practical tools for water resource management and precision agriculture, especially in data-scarce environments.