Ensemble prediction intervals for reservoir landslide displacement with a novel cost function

Predicting landslide displacement with quantified uncertainty is essential for reliable early warning. However, most existing machine-learning approaches focus on point predictions and provide limited interpretability in terms of uncertainty quantification. This study develops a probabilistic ensemble framework for landslide displacement prediction by integrating Bootstrap and lower–upper bound estimation (LUBE) with a new prediction-interval (PI)-based lost function that penalizes deviations between the interval center and the observations. The proposed method is evaluated against conventional PI-based cost functions using data from two GPS monitoring points on the Shuping landslide in the Three Gorges Reservoir Area (TGRA), representing step-like and gradual displacement patterns. The results indicate that the proposed lost function improves the balance between interval width and coverage, with more pronounced improvements observed in the LUBE framework than in the Bootstrap framework. For the step-like deformation pattern, the ensemble strategy provides the most favorable trade-off between coverage and sharpness, whereas for smoother deformation, LUBE alone performs comparably well. Overall, the results demonstrate that the proposed framework can effectively capture uncertainty in landslide displacement prediction under different deformation behaviors and may support uncertainty-informed landslide early warning in reservoir environments.