Graph-based automated discovery of concise soil hydraulic functions from data: beyond the Mualem - van Genuchten model

2026-05-19

AI Summary

This study addresses the limitations of traditional soil hydraulic functions, such as the Mualem–van Genuchten (MvG) model, which rely on predefined empirical forms and struggle to simultaneously achieve accuracy, simplicity, and robustness across diverse soil types. To overcome this, the authors propose a graph-based automated model discovery framework that directly derives explicit hydraulic functions—including the soil water retention curve and unsaturated hydraulic conductivity—from experimental data. This approach, for the first time, enables data-driven discovery of novel yet concise functional forms, circumventing the constraints imposed by manual specification. Evaluations on the original MvG dataset and 249 real soil samples demonstrate that the discovered functions outperform the classical MvG model in predicting unsaturated hydraulic conductivity, while their fitted parameters exhibit strong correlations with underlying soil physical properties.

Abstract

Soil hydraulic functions are fundamental to modelling water flow and transport in vadose-zone hydrology and are central to a wide range of hydrological and geoscientific applications. Yet in practice, these functions are still predominantly specified through expert-designed empirical formulations, such as the Mualem-van Genuchten (MvG) model. Although such models have proved highly influential, their derivation relies on predefined functional assumptions that make it difficult to simultaneously achieve accuracy, compactness, and robustness across diverse soil textures. Here we present a graph-based automated model discovery framework for discovering explicit soil hydraulic functions directly from experimental data. Applied to the original datasets used in the development of the MvG model, the method identifies a concise soil water retention function and its associated unsaturated hydraulic conductivity function whose mathematical structure differs fundamentally from classical empirical forms. Across 249 real soil samples spanning diverse textural classes, the discovered functions achieve more accurate predictions of unsaturated hydraulic conductivity than the MvG model. The fitted parameters also exhibit correlations with soil physical properties. This work demonstrates that data-driven model discovery can move beyond traditional empirical derivation and provide a promising route for developing accurate and explicit constitutive models.

Problem

• soil hydraulic functions
• Mualem-van Genuchten model
• model discovery
• unsaturated hydraulic conductivity
• data-driven modeling

Innovation

• graph-based model discovery
• soil hydraulic functions
• data-driven modeling
• unsaturated hydraulic conductivity
• automated equation discovery