A multi-objective physics-informed machine learning framework for landslide susceptibility mapping

Landslide susceptibility mapping (LSM) is essential for regional geohazard assessment. However, conventional data-driven models often fail to capture slope-failure mechanisms and produce scientifically inconsistent predictions, particularly in regions with complex geology or limited data. This study proposes a novel physics-informed machine learning (PIML) framework that formulates LSM as a multi-objective optimisation problem. A positive-unlabelled (PU) bagging strategy identifies reliable non-landslide samples, and model training jointly minimises three complementary losses: a supervised loss ensuring predictive accuracy, a physical-consistency loss constraining monotonic relationships with the factor of safety (FoS), and a risk-consistency loss constraining monotonic relationships with the probability of failure (PoF). The FoS and PoF, derived from the simplified transient infiltration model (STIM) and the first-order reliability method (FORM), are incorporated into model training to enforce scientific consistency. A case study of rainfall-induced landslides in Gansu Province, China, shows that the proposed framework achieves Pareto-optimal trade-offs between accuracy and scientific consistency. Compared with the baseline, the optimal PIML model improved average AUC (0.882 vs. 0.870) under spatial cross-validation, reduced inconsistency by 73%, and outperformed the physically based probabilistic model. These results highlight that embedding geotechnical knowledge into ML produces susceptibility maps that are both accurate and scientifically meaningful.