A differentiable hybrid modeling approach for learning soil water retention mechanisms from partial knowledge and data

Soil physics models have long relied on simplifying assumptions to represent complex processes, yet such assumptions can strongly bias model predictions. Here, we propose differentiable hybrid modeling (DHM) as a paradigm-shifting framework that learns unobservable intrinsic processes from data and physical constraints, rather than simplifying them. As a proof of concept, we apply the DHM approach to the challenge of partitioning the soil water retention curve (SWRC) into capillary and adsorbed water components, a problem where traditional assumptions have led to divergent results. The hybrid framework derives this partitioning directly from data while remaining guided by simple physical constraints. Using basic soil physical properties as inputs, the DHM couples an analytical formula for the dry end of the SWRC with data-driven physics-informed neural networks that learn the wet end, the transition between the two ends, and key soil-specific parameters. The model was trained on a SWRC dataset from 482 undisturbed soil samples, spanning a broad range of texture classes and organic carbon contents. The hybrid model successfully learned both the overall shape and the capillary and adsorbed components of the SWRC. Notably, the learned patterns were consistent with pore-scale thermodynamic saturation behavior in angular pores, without relying on explicit assumptions about soil pore geometry or its distribution. Moreover, the model revealed a distinctly nonlinear transition between capillary and adsorbed domains, challenging the linear assumptions invoked in previous studies. The methodology introduced here provides a blueprint for learning other soil processes where high-quality datasets are available but mechanistic understanding is incomplete.