Physics-Informed Neural Networks for Estimating a Continuous Form of the Soil Water Retention Curve From Basic Soil Properties

Abstract

This paper presents a novel physics-informed neural network (PINN) approach for developing pedotransfer functions (PTFs) to predict continuous soil water retention curves (SWRCs) based on soil textural fractions, organic carbon content, and bulk density. In contrast to conventional parametric PTFs developed for specific SWRC models, the PINN learns a non-specific form of the SWRC from both measurements and physical constraints imposed during the training process. This approach allows the estimated SWRC to maintain its physical integrity from saturation to oven-dry conditions, even in scenarios with sparse data. The new approach is particularly effective for tackling the challenges encountered in developing PTFs on large SWRC data sets, which often have an imbalance toward the wet-end ($pF\mathit{\le }4.2$) and include numerous samples with limited and unevenly distributed measurements, many of which do not meet the requirements to fit traditional SWRC models. We compared the performance of the PINN with that of a conventional physics-agnostic neural network using a data set of 4,200 soil samples. While both networks performed similarly at the wet-end where data are abundant, with RMSE values of around 0.041 m³ m⁻³, the PINN excelled at the dry-end () where data are sparse and unevenly distributed, achieving a normalized RMSE of 0.172 (RMSE = 0.0045 m³ m⁻³) compared to a normalized RMSE of 0.522 (RMSE = 0.0136 m³ m⁻³) for the conventional neural network. The SWRC derived from the PINN is differentiable with respect to matric potential, making it well-suited for integration into models of water flow in the unsaturated zone.