Physics-informed neural networks for efficient probabilistic analysis of regional rainfall-induced landslides

Estimating the probability of regional rainfall-induced shallow landslides presents a significant challenge. Simplified or analytical solutions, such as the Green-Ampt model, are computationally efficient but often lack accuracy and generalization across diverse soil and rainfall conditions. The Richards equation provides a physically consistent representation of unsaturated flow, yet solving it for regional-scale, probabilistic assessments is computationally intensive due to repeated numerical evaluations. This gap underscores the need for methods that combine physical accuracy with computational efficiency for large-scale shallow landslide modeling. Conventional surrogate models, typically used as “black-box” tools, lack transparency in capturing the physical mechanisms of slope seepage. As a result, training these models often requires numerous physical simulations, and the trained models may not exhibit robust extrapolation capabilities for slopes with varying design parameters (e.g., slope angle, superficial layer thickness) or under different rainfall conditions. This paper proposes a method based on Physics-Informed Neural Networks (PINNs) to analyze rainfall infiltration and slope stability, addressing these challenges. The proposed method accommodates multiple input parameters, including rainfall intensity, soil thickness, slope angle, and soil properties. By embedding the governing equation and boundary conditions into the loss function as soft constraints, and incorporating the initial condition into the network’s output as a hard constraint, the method significantly improves both training efficiency and predictive accuracy. An infinite slope model is first used to demonstrate the method’s effectiveness under various rainfall conditions, showing that the PINN model’s predictions closely match numerical solutions in terms of accuracy. The approach is then applied to two large-scale regions (Xiaojiagou Basin and Provincial Road 303) to assess time-varying shallow failure probabilities under rainfall. The PINN model predicts results in less than 1 s, irrespective of region size, offering a significant reduction in computation time compared to similar studies.