A physics-informed neural network workflow for forward and inverse modeling of unsaturated flow and root water uptake from hydrogeophysical data

Understanding Root Water Uptake (RWU) is critical for sustainable agriculture, yet quantifying its spatiotemporal dynamics in the field remains a challenge. Conventional methods rely on either sparse point measurements, which miss spatial heterogeneity, or numerical models that require prescribing the mathematical form of RWU a priori, limiting the ability to characterize complex plant–soil interactions. This study introduces a Physics-Informed Neural Network (PINN) to infer RWU directly from hydrogeophysical data. We simulated a synthetic benchmark where a numerical model generated a high-resolution dataset of soil water dynamics. Realistic but imperfect field observations were simulated, including Electrical Resistivity Tomograms (ERT) and sparse point-sensor data. A dual-output PINN was trained on these data to simultaneously reconstruct the high-resolution soil saturation field and predict the unknown RWU function and spatial distribution, with no prior assumptions. Results demonstrate that PINN successfully reconstructed the soil saturation field with high accuracy (R²=0.98[jls-end-space/], RMSE =0.035[jls-end-space/]), outperforming the ERT data used as input. While the unconstrained PINN qualitatively recovered the spatiotemporal distribution of the unknown RWU term, incorporating a physically measurable total daily transpiration constraint improved the inference, reducing the daily transpiration RMSE by approximately 88 % and lowering local RWU errors to below 5 %. Furthermore, PINN successfully recovered the underlying functional relationship between water stress and uptake, estimating the key Feddes stress-response parameters with 2 % error. The method also proved robust, maintaining high accuracy (R²=0.97[jls-end-space/], RMSE =0.044[jls-end-space/]) when provided with perturbed hydraulic parameters and noisy data, highlighting its potential for real-world applications.