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Surrogate modeling for unsaturated infiltration via the physics and equality-constrained artificial neural networks

Journal of Rock Mechanics and Geotechnical Engineering 2024年第6期16卷 2282-2295页

作者： Peng Lan Jingjing Su Sheng Zhang School of Civil Engineering Central South UniversityChangsha410075China Discipline of Civil Surveying and Environmental EngineeringPriority Research Centre for Geotechnical Science and EngineeringThe University of NewcastleCallaghanNSW2308Australia Qinghai University Qinghai810016China

Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated *** pure data-driven methods(*** neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the *** this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary *** takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(*** equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary *** unsaturated infiltration cases are designed to test the training performance of PECANN,***-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and *** predicted results of PECANN are compared with the finite difference solutions or analytical *** results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and *** is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training ***,we investigate the effect of the hyperparameters of PECANN on solving RE *** provides an effective tool for simulating unsaturated infiltration.

关键词： Richards equation(RE) unsaturated infiltration Data-driven solutions Numerical modeling Machine learning(ML)

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