Integrating machine learning and physics-based slope stability through Bayesian geostatistics: An uncertainty-aware framework for landslide prediction

Effective landslide susceptibility assessment requires a modelling framework that integrates heterogeneous geospatial information while explicitly accounting for predictive uncertainty. This study developed a Bayesian geostatistical approach that combined susceptibility prediction from a data-driven random forest (RF) classifier with factor of safety (Fs) output from a physics-based model — transient rainfall infiltration and grid-based regional slope-stability (TRIGRS) — using the integrated nested Laplace approximation (INLA). The framework produces calibrated and uncertainty-aware landslide susceptibility maps by integrating empirical relationships captured by RF, slope stability dynamics simulated by TRIGRS, and a spatially-structured residual variability represented through a latent Gaussian field. The RF model captures nonlinear associations between landslide occurrences and their conditioning factors, whereas TRIGRS encodes the physics of slope stability during rainfall infiltration. INLA couples these complementary signals and yields nonlinear posterior adjustments that suppress weak RF probabilities and strengthen mid-to-high values, while elevating low-to-mid ranges of the Fs distribution and tempering the upper tail. The resulting susceptibility surfaces are spatially smoother, better calibrated, and more interpretable than either input model. At the slope unit (SU) scale, the INLA model attained an area under the receiver operating characteristic curve (AUROC) of 0.96, outperforming RF (0.91) and TRIGRS (0.83). Spatial cross-validation confirmed consistently high discrimination across sub-basins. The posterior credible intervals provide spatially explicit uncertainty patterns, narrower in high-susceptibility hotspots (0.8-1) and wider at moderate probabilities (0.3-0.7), offering guidance for setting decision thresholds, prioritising field validation, and optimising monitoring network design. By combining machine learning (ML), physics-based modelling, and Bayesian spatial inference in a unified workflow, this scalable and transferable framework delivers interpretable, decision-relevant susceptibility estimates suitable for operational landslide risk management.