Sakar et al. (2025) A physics-informed neural network workflow for forward and inverse modeling of unsaturated flow and root water uptake from hydrogeophysical data

Identification

• Journal: Journal of Hydrology
• Year: 2025
• Date: 2025-11-26
• Authors: Caner Sakar, Kuzma Tsukanov, Nimrod Schwartz, Ziv Moreno
• DOI: 10.1016/j.jhydrol.2025.134675

Research Groups

• The Robert H. Smith Faculty of Agriculture, Food and Environment, The Hebrew University of Jerusalem, Rehovot, Israel
• Institute of Soil, Water and Environmental Sciences, Agricultural Research Organization (ARO), Volcani Institute, Rishon LeZion, Israel

Short Summary

This study introduces a Physics-Informed Neural Network (PINN) to infer the spatiotemporal dynamics of root water uptake (RWU) directly from hydrogeophysical data. The PINN successfully reconstructs high-resolution soil saturation fields and predicts unknown RWU distributions, with significant accuracy improvements when constrained by total daily transpiration.

Objective

• To determine if a Physics-Informed Neural Network (PINN), constrained by imperfect hydrogeophysical data (Electrical Resistivity Tomography and sparse point-sensor measurements) and Richards' equation, can reconstruct the underlying root water uptake (RWU) distribution without any prior assumptions about its mathematical form.

Study Configuration

• Spatial Scale: A 9 meter (m) × 6 m soil domain, modeled as a vertical cross-section, with root water uptake concentrated in the upper 1.5 m of the soil profile. The Electrical Resistivity Tomography (ERT) survey domain was extended to 27 m × 6 m.
• Temporal Scale: A 28-day (2.419 × 10^6 seconds) simulation period, with daily snapshots of soil water dynamics.

Methodology and Data

• Models used:
  • Physics-Informed Neural Network (PINN) with a dual-output architecture.
  • HYDRUS-2D (finite element model) for generating synthetic "ground truth" data.
  • Richards’ equation for water flow in variably saturated porous media.
  • Van Genuchten–Mualem model for soil hydraulic properties.
  • Feddes model for root water uptake (used in HYDRUS-2D for ground truth, inferred by PINN).
  • Waxman–Smits petrophysical model for converting saturation to electrical conductivity.
• Data sources:
  • Synthetic Electrical Resistivity Tomography (ERT) images (smoothed and inverted to mimic real-world data).
  • Synthetic sparse point-sensor measurements (volumetric water content, mimicking TDR sensors) at three locations within the root zone.

Main Results

• PINN accurately reconstructed the soil saturation field with high fidelity (R² = 0.98, Root Mean Squared Error (RMSE) = 0.035), consistently outperforming the ERT-derived saturation data used as input.
• The unconstrained PINN qualitatively recovered the spatiotemporal distribution of the unknown RWU term.
• Incorporating a physically measurable total daily transpiration constraint significantly improved RWU inference, reducing the daily transpiration RMSE by approximately 88 % (from 1.227 × 10^-8 m²/s to 1.516 × 10^-9 m²/s) and lowering local RWU errors to below 5 %.
• PINN successfully recovered the underlying functional relationship between water stress and uptake, estimating key Feddes stress-response parameters with approximately 2 % error in corresponding effective saturations.
• The method demonstrated robustness, maintaining high accuracy (R² = 0.97, RMSE = 0.044) when provided with perturbed hydraulic parameters and noisy data (3 % multiplicative Gaussian noise in TDR measurements).

Contributions

• Introduces a novel PINN-based inverse modeling framework capable of inferring spatiotemporal root water uptake (RWU) dynamics directly from hydrogeophysical observations without prior assumptions about the mathematical form of RWU.
• Demonstrates that integrating Richards' equation as a physics-based regularizer allows PINN to "denoise" and improve upon imperfect geophysical images, yielding hydrologically consistent soil state reconstructions.
• Highlights the significant value of incorporating a simple, measurable integral constraint (total daily transpiration) to enhance the accuracy of RWU inference.
• Shows the ability of PINN to recover functional relationships between soil moisture and RWU from indirect observational data, moving beyond traditional parameter fitting.
• Establishes the robustness of the PINN framework to uncertainties in model parameters and observational noise, suggesting its potential for real-world field applications.
• Offers a pathway to bridge the scale gap between point-scale soil sensors and plot- or field-scale hydrological models for improved water management.

Funding

• Binational Agricultural Research and Development Fund (BARD), Grant IS-5698–24.

Citation

@article{Sakar2025physicsinformed,
  author = {Sakar, Caner and Tsukanov, Kuzma and Schwartz, Nimrod and Moreno, Ziv},
  title = {A physics-informed neural network workflow for forward and inverse modeling of unsaturated flow and root water uptake from hydrogeophysical data},
  journal = {Journal of Hydrology},
  year = {2025},
  doi = {10.1016/j.jhydrol.2025.134675},
  url = {https://doi.org/10.1016/j.jhydrol.2025.134675}
}