Graph-based Automated Discovery of Concise Soil Hydraulic Functions from Data: Beyond Empirical Formulations
Abstract
Soil hydraulic functions underpin water flow and transport modeling in the vadose zone, yet they are commonly represented by expert-designed formulations such as the Mualem-van Genuchten (MvG) model. Because these formulations rest on predefined functional assumptions, balancing predictive accuracy and parametric compactness across soil textures remains challenging. Here we introduce a graph-based equation discovery framework that distills soil hydraulic functions from experimental data. Reapplied to the original datasets that motivated the MvG parameterization, the framework recovers a concise water retention function together with an analytical unsaturated hydraulic conductivity expression whose mathematical structure departs from classical empirical forms. Evaluated across soils of contrasting texture, the discovered model predicts unsaturated hydraulic conductivity more accurately than MvG and its common variants, while its fitted parameters retain interpretable correlations with measurable soil physical properties. These findings suggest that data-driven discovery can yield compact, analytically tractable constitutive relations that move beyond fixed empirical formulations.
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BibTeX
@misc{xu2026graphbased,
title = {{Graph-based Automated Discovery of Concise Soil Hydraulic Functions from Data: Beyond Empirical Formulations}},
author = {Hao Xu and Jinshen Sun and Yuntian Chen and Dongxiao Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.19379},
eprint = {2605.19379},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.19379},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Graph-based Automated Discovery of Concise Soil Hydraulic Functions from Data: Beyond Empirical Formulations
AU - Hao Xu
AU - Jinshen Sun
AU - Yuntian Chen
AU - Dongxiao Zhang
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2605.19379
UR - https://arxiv.org/abs/2605.19379
AB - Soil hydraulic functions underpin water flow and transport modeling in the vadose zone, yet they are commonly represented by expert-designed formulations such as the Mualem-van Genuchten (MvG) model. Because these formulations rest on predefined functional assumptions, balancing predictive accuracy and parametric compactness across soil textures remains challenging. Here we introduce a graph-based equation discovery framework that distills soil hydraulic functions from experimental data. Reapplied to the original datasets that motivated the MvG parameterization, the framework recovers a concise water retention function together with an analytical unsaturated hydraulic conductivity expression whose mathematical structure departs from classical empirical forms. Evaluated across soils of contrasting texture, the discovered model predicts unsaturated hydraulic conductivity more accurately than MvG and its common variants, while its fitted parameters retain interpretable correlations with measurable soil physical properties. These findings suggest that data-driven discovery can yield compact, analytically tractable constitutive relations that move beyond fixed empirical formulations.
ER -