Multimodal Deep Survival Analysis for Sinkhole Susceptibility

Existing multi-hazard susceptibility mapping (MHSM) studies often rely on spatially uniform models, treat hazards independently, and provide limited representation of cross-hazard dependence and uncertainty. To address these limitations, this study proposes a deep learning (DL) workflow for joint flood-landslide multi-hazard susceptibility mapping (FL-MHSM) that combines two-level spatial partitioning, probabilistic Early Fusion (EF), a tree-based Late Fusion (LF) baseline, and a soft-gating Mixture of Experts (MoE) model, with MoE serving as final predictive model. The proposed design preserves spatial heterogeneity through zonal partitions and enables data-parallel large-area prediction using overlapping lattice grids. In Kerala, EF remained competitive with LF, improving flood recall from 0.816 to 0.840 and reducing Brier score from 0.092 to 0.086, while MoE provided strongest performance for flood susceptibility, achieving an AUC-ROC of 0.905, recall of 0.930, and F1-score of 0.722. In Nepal, EF similarly improved flood recall from 0.820 to 0.858 and reduced Brier score from 0.057 to 0.049 relative to LF, while MoE outperformed both EF and LF for landslide susceptibility, achieving an AUC-ROC of 0.914, recall of 0.901, and F1-score of 0.559. GeoDetector analysis of MoE outputs further showed that dominant factors varied more across zones in Kerala, where susceptibility was shaped by different combinations of topographic, land-cover, and drainage-related controls, while Nepal showed a more consistent influence of topographic and glacier-related factors across zones. These findings show that EF and LF provide complementary predictive behavior, and that their spatially adaptive integration through MoE yields robust overall predictive performance for FL-MHSM while supporting interpretable characterization of multi-hazard susceptibility in spatially heterogeneous landscapes.

Floods and landslides often co-occur, but their relationships with environmental controls vary spatially. This study develops a spatial heterogeneity-aware framework for flood-landslide susceptibility and relative-risk mapping in Kerala, India, and Nepal. It combines 15 km x 15 km grid cells with region-specific contextual zones and compares proximity-gated cross-zone training (S1) and ecology-gated zone-constrained training (S2). S1 permits geographically nearby models to be assigned across contextual boundaries, whereas S2 restricts model development and assignment to the same zone. Random Forest models for each hazard use strategy-specific predictor sets and are evaluated on spatially held-out test samples. Susceptibility surfaces are integrated with CRITIC-weighted exposure and vulnerability indices to produce hazard-specific and nine-class bivariate relative-risk maps. S1 achieved higher mean accuracy, precision, recall, F1-score, AUC-ROC, and PR-AUC for both hazards and regions. The largest difference occurred for Nepal flood susceptibility, where AUC-ROC increased from 0.728 under S2 to 0.886 under S1 and PR-AUC from 0.512 to 0.823. S2 produced lower Brier scores for both Nepal hazards and retained zone-specific differences in predictor selection, SHAP rankings, and response patterns, particularly in Kerala. Both strategies reproduced flood-prone lowland and landslide-prone upland patterns but differed in susceptibility and risk classes. Bivariate risk-map agreement was 0.521 in Kerala and 0.711 in Nepal, with allocation disagreement exceeding quantity disagreement in all S1-S2 comparisons. Susceptibility-to-risk correspondence remained below 0.350, showing that exposure and vulnerability changed priority locations. Overall, cross-zone learning strengthens regional discrimination, while zone-constrained learning preserves environmental differences, supporting their integration.

Recent multimodal survival prediction models have demonstrated strong predictive performance by leveraging complementary information across modalities. However, such models generally assume data completeness and exhibit limited robustness toward missing modalities, which are frequently encountered in real-world clinical settings. We propose the Evidential Missing Modality Survival Fusion (EMMS) model for multimodal survival prediction under missing modalities. EMMS offers a straightforward, computationally effective approach to survival analysis without requiring a generative phase for missing data. By employing Dempster-Shafer theory and Gaussian Random Fuzzy Numbers for multimodal decision fusion, it considers both aleatoric and epistemic uncertainty alongside modality reliability for fusion. Moreover, the model treats missing modalities as vacuous evidence, preventing interference with available inputs and naturally reflecting increased uncertainty and calibrated predictions. Extensive experiments on four cancer datasets demonstrate state-of-the-art performance while providing calibrated and interpretable uncertainty estimates under incomplete multimodal observations, without introducing additional computational overhead.