Application of Physics-Informed Neural Networks (PINNs) for Simulating Water Movement in Unsaturated Soils based on Richards’ Equation
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Abstract
Understanding unsaturated soil water flow is essential for precision agriculture and water resources management. Traditional numerical methods for solving the Richards’ equation often encounter instability at the wetting front and computational burdens due to grid discretization. This study evaluates the performance of Physics-Informed Neural Networks (PINNs) in simulating one-dimensional soil-water flow under irrigation conditions, using HYDRUS-1D data for loamy soil as a reference. The PINN architecture features four hidden layers with 64 neurons each, incorporating a sinusoidal activation function and a soft-clipping technique to enhance automatic differentiation efficiency and ensure mathematical stability near saturation limits. Results indicate exceptionally high performance, with a correlation coefficient (r) exceeding 0.99 and a Root Mean Square Difference below 0.004 for both training and testing datasets. The model accurately captured the highly non-linear movement of steep wetting fronts and daily irrigation-induced dynamics without numerical oscillations. Despite minor initial oscillations at t = 0, PINNs demonstrated a robust ability to learn physical laws and mass conservation. This research confirms the potential of PINNs as reliable surrogate models, offering a mesh-free alternative for analyzing soil water dynamics.
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