Physics‐Informed Neural Networks With Monotonicity Constraints for Richardson‐Richards Equation: Estimation of Constitutive Relationships and Soil Water Flux Density From Volumetric Water Content Measurements

Water retention curves (WRCs) and hydraulic conductivity functions (HCFs) are critical soil-specific characteristics necessary for modeling the movement of water in soils using Richardson-Richards equation (RRE). Well-established laboratory measurement methods WRCs HCFs not usually suitable simulating field-scale soil moisture dynamics because scale mismatch. Hence, inverse solution RRE must be used to estimate from field measured data. Here, we propose a physics-informed neural network (PINN) framework estimation only volumetric content (VWC) measurements. The proposed does need initial boundary conditions, which rarely available real applications. PINNs consist three linked feedforward networks, two were constrained monotonic reflect monotonicity HCFs. Alternatively, also tested without constraints. We trained synthetic VWC data with artificial noise, derived by numerical textures. constraints regularized problem. able reconstruct true dynamics. demonstrated that could recover underlying nonparametric form. However, reconstructed at wet dry ends unsatisfactory strong nonlinearity. additionally showed flux density broader range than currently methods.