Integrating multi-task learning with a differentiable physics constrained framework for hydrological forecasting

Abstract Accurate prediction of terrestrial water cycle variables like soil moisture (SM) and evapotranspiration (ET) is crucial, yet existing Deep Learning (DL) models face limitations. Many adopt Single-Task Learning (STL), ignoring inter-variable dependencies, while purely data-driven models lack physical consistency, compromising their generalization and robustness, especially with sparse data or during extreme events. To address these challenges, we propose a novel differentiable physics-constrained framework coupled with a Multi-Task Learning (MTL) model. Our approach embeds neural networks into hydrological water balance equations to dynamically learn and characterize the poorly-defined physical process components (such as snowmelt and groundwater exchange). This innovative design of directly integrating neural networks into the physical equations achieves a deep fusion of physical processes with a multi-task prediction model, thereby enabling simultaneous and synergistic predictions of multi-layer soil moisture and evapotranspiration. Validated on the LandBench 1.0 dataset, our framework demonstrates consistent and measurable improvements over baseline models. Notably, it achieves enhanced generalization under data-sparse conditions (e.g., KGE for the SM3 task improved from 0.675 to 0.730) and shows increased robustness for low extreme values (e.g., median KGE for low SM2 values increased from 0.434 to 0.504). Our work introduces a flexible and effective strategy to integrate physical knowledge into deep learning, suggesting a potential pathway toward developing more reliable and robust hydrological forecasting models.