Song et al. (2026) From Soil Moisture Observations to Governing Flow Equations: What Data‐Driven Equation Discovery Reveals

⚠️ Warning: This summary was generated from the abstract only, as the full text was not available.

Identification

• Journal: Water Resources Research
• Year: 2026
• Date: 2026-11-01
• Authors: Wenxiang Song, Liangsheng Shi, Yujie Wang, Leilei He, Mehdi Rahmati, Harry Vereecken
• DOI: 10.1029/2026wr045026

Research Groups

Not specified in the abstract.

Short Summary

This study introduces Spline-SR, a spline-regularized sparse regression framework, to discover nonlinear soil moisture flow equations from sparse fixed-depth observations. It successfully identifies the three-term structure of the Richards equation from both numerical experiments and physical column measurements, demonstrating that sparse experimental data can reveal governing equation structures.

Objective

• To develop and apply Spline-SR, a spline-regularized sparse regression framework, for discovering nonlinear soil moisture flow equations from sparse fixed-depth observations.

Study Configuration

• Spatial Scale: Laboratory soil columns (sand and loamy-sand).
• Temporal Scale: Dynamic soil moisture processes under wetting, drying, and alternating conditions.

Methodology and Data

• Models used: Spline-SR (spline-regularized sparse regression framework), automatic differentiation for derivative evaluation.
• Data sources: Numerical experiments; measurements from laboratory sand and loamy-sand columns (sparse fixed-depth observations).

Main Results

• Spline-SR reliably recovers the known three-term structure of the water-content form of the Richards equation from sparse and noisy numerical sampling.
• Experimental analysis on sand and loamy-sand columns identifies a parsimonious structure containing the three terms expected from the water-content form of the Richards equation.
• The resulting discovered equations effectively reconstruct the main features of soil moisture dynamics.
• Inferred coefficient functions vary across different forcing conditions, indicating sensitivity to observational coverage and flow conditions.

Contributions

• Development of Spline-SR, a novel spline-regularized sparse regression framework for data-driven discovery of nonlinear soil moisture flow equations.
• Demonstration that sparse, fixed-depth experimental observations from soil columns contain sufficient information to identify the governing structure of soil moisture flow equations.
• Extension of data-driven equation discovery for soil moisture beyond numerical experiments to real-world experimental data.

Funding

Not specified in the abstract.

Citation

@article{Song2026From,
  author = {Song, Wenxiang and Shi, Liangsheng and Wang, Yujie and He, Leilei and Rahmati, Mehdi and Vereecken, Harry},
  title = {From Soil Moisture Observations to Governing Flow Equations: What Data‐Driven Equation Discovery Reveals},
  journal = {Water Resources Research},
  year = {2026},
  doi = {10.1029/2026wr045026},
  url = {https://doi.org/10.1029/2026wr045026}
}