Physics-informed neural network vs finite element method for modeling coupled water and solute flow in unsaturated soils

Accurate modeling of water infiltration and solute transport in unsaturated soils is critical for various applications. These include optimizing irrigation practices to conserve water and minimize environmental impact, as well as predicting the fate of contaminants in soil and groundwater. This study explores the application of the vanilla physicsinformed neural network (PINN) approach for modeling the coupled system of water flow and solute transport in unsaturated soils. We compare the performance of PINN with the Galerkin finite element method (FEM) to evaluate their effectiveness. Various techniques are implemented to improve the PINN solver, including adaptive activation functions. Numerical tests were carried out to evaluate the efficiency of the PINN solver in comparison to the FEM. The findings reveal that PINN can achieve accuracy comparable to FEM, albeit at a significantly higher computational cost during training, while maintaining fast inference times.

Citation: Kamil, H., Soulaïmani, A., & Beljadid, A. (2024, July). Physics-informed neural networks vs finite element method for modeling coupled water and solute flow in unsaturated soils. In 16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics, 21-26 July, Vancouver, Canada.
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