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Abstract Accurately estimating water flux in variably saturated soils is crucial, yet traditional methods, such as the Richardson‐Richards equation, often suffer from some limitations. As an advancement of Physics‐Informed Neural Networks (PINNs), we introduce the Adaptive Constrained Neural Network (ACNN), designed to estimate variably saturated soil water flux using sparse volumetric water content (VWC) data alone, without requiring initial conditions (ICs), boundary conditions (BCs), or soil hydraulic constitutive relationships. The framework integrates domain decomposition methods and adaptive constraints within a sequential training framework. Testing on synthetic cases and soil column experiments demonstrates its capability to achieve unified modeling of variably saturated flow, seamlessly linking the unsaturated and saturated zones. It effectively addresses issues of incomplete knowledge and noisy data, not only mitigating ill‐conditioning compared to traditional PINNs, but also reducing flux estimation errors caused by uncertainties in ICs and BCs compared to numerical methods. Notably, under conditions of rapid moisture content change, ACNN successfully captures instantaneous flux changes at the boundary with an accuracy of approximately R 2 = 0.9, highlighting its potential in applications such as estimating surface infiltration, evapotranspiration, and groundwater recharge.
Wang et al. (Mon,) studied this question.