Ensemble learning of soil–water characteristic curve for unsaturated seepage using physics-informed neural networks

The determination of the soil–water characteristic curve (SWCC) is crucial for hydro-mechanical modelling and analysis of soil slopes. Conventional inverse analysis often relies on a predetermined SWCC model for parameter estimation. However, the selection of SWCC functions heavily relies on engineering judgement, which may be subjective and biased. Moreover, the estimation of multiple governing parameters for a preselected function form from limited site-specific data is a nontrivial task, particularly for inexperienced engineering practitioners. To explicitly address this challenge, this study proposes an ensemble learning framework that leverages physics-informed neural networks (PINN) for parameter estimation. Multiple representative SWCCs following different function forms are compiled, providing flexible learning bases to construct arbitrary SWCC. For a specific slope, the most compatible basis combination is adaptively selected based on limited site-specific measurements before being mobilized for forward predictions of hydraulic behavior. The proposed method is illustrated through a hypothetical example and a real slope project at Jalan Kukoh, Singapore. Results indicate that the ensemble learning framework can accurately estimate SWCC functions and the associated pore pressure distributions from limited measurements in a data-driven and physics-informed manner. The robustness of the method has also been demonstrated through a series of sensitivity analyses, showcasing the capability of PINN for unsaturated hydraulic seepage modelling and SWCC estimation during rainfall conditions.