Learning Soil Water Retention Components through an End-to-End Differentiable Hybrid Model

Sarem Norouzi, Per Moldrup, Ben Moseley, David Robinson, Dani Or, Budiman Minasny, Morteza Sadeghi, Tobias L. Hohenbrink, Emmanuel Arthur, Mogens H. Greve, Lis W. de Jonge

Keywords: Differentiable modeling, Hybrid modeling, Soil hydraulic properties, Soil Physics

TL;DR: We combine physics and neural networks to discover capillary–adsorbed partitioning in soil water retention

Abstract: Soil physics is complex, and mechanistic models have traditionally used simplifying assumptions to represent complex processes, but these assumptions can bias predictions. However, the increasing availability of high-quality data offers an opportunity to both improve the predictive power of existing models and gain new fundamental physics insights. Here, we propose a hybrid soil physics framework that combines analytical formulations with flexible, data-driven components to learn uncertain parts directly from data. A key enabler is end-to-end differentiability via automatic differentiation, which allows the entire model, including physical and neural components, to be optimized jointly by minimizing a downstream loss function. We apply this approach to the challenge of partitioning the soil water retention curve (SWRC) into capillary and adsorbed water components. The hybrid model, trained on 483 undisturbed soils from Central Europe, produces smooth and physically consistent SWRC curves and automatically discovers the capillary and adsorptive branches of the curve. Notably, the model reveals 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.

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Submission Number: 38