Landslide susceptibility modeling by interpretable neural network

The study addresses the challenge of accurately and interpretably assessing landslide susceptibility, a major natural hazard influenced by numerous topographic, geologic, climatic, hydrologic, and seismic factors. Conventional approaches include physically based models that balance driving and resisting forces but are limited by simplified assumptions, few variables, and costly subsurface data needs. Data-driven statistical models (e.g., logistic regression, likelihood ratios) and machine learning methods (e.g., random forests, SVMs, deep neural networks) can exploit many controls but often lack interpretability and disentanglement of feature contributions. Deep neural networks typically outperform statistical methods but function as black boxes, hindering trust and decision-making in high-stakes hazard mitigation. Motivated by explainable AI initiatives and arguments for inherently interpretable models, the authors propose a fully interpretable, accurate, and generalizable additive neural approach to quantify individual and interacting feature contributions to landslide susceptibility across diverse Himalayan regions.

The paper reviews three main classes of landslide susceptibility models: (1) physically based models (e.g., SHALSTAB, TRIGRS) that use slope stability and hydrologic formulations but are restricted by simplified geometries, environmental assumptions, and limited subsurface characterization; (2) statistical models such as logistic regression and likelihood/frequency ratios, which can handle multiple controls but depend on expert preprocessing and do not decouple feature contributions or interdependencies; and (3) machine learning methods, particularly deep neural networks, which capture nonlinearities and complex interactions and generally achieve superior predictive performance but suffer from a lack of interpretability. The authors discuss the rise of explainable AI, noting trade-offs between interpretability and accuracy in post-hoc explanations (e.g., SHAP) and highlighting arguments for inherently interpretable models that can avoid this trade-off. They situate their work within generalized additive models and recent neural additive model developments, aiming to preserve high accuracy while providing global and local interpretability, including explicit modeling of multivariate feature interactions.

The authors present a Superposable Neural Network (SNN) framework: an additive ANN where each input (single or composite feature) is connected to its own simple network with radial basis (Gaussian) activations and no interconnections among inputs, enabling full interpretability. Interdependencies between original features are represented explicitly via composite features, formed as products of original features up to a specified level (Level-2 in this work). The training pipeline consists of: (1) multivariate polynomial expansion to generate composite features; (2) tournament ranking (automated feature selection using repeated grouping, backward elimination, and AUROC scoring with second-order Levenberg–Marquardt training) to identify relevant features; (3) training a high-performance deep teacher model using multistage training (MST) to provide soft targets and regularization; (4) fractional knowledge distillation to iteratively isolate and quantify each feature’s contribution; (5) parallel knowledge distillation to train a single-layer network per feature; and (6) network superposition to sum the single-layer outputs into the final SNN susceptibility score. Data and study area: Three regions in the easternmost Himalaya (Dibang—N-S, range front—NW-SE, Lohit—E-W) were analyzed. A semi-automatic landslide inventory was built by combining manual delineation (Landsat 8, Google Earth, PlanetScope) with a CNN segmentation approach and subsequent expert corrections, producing 2,289 mapped landslides across 4.19×10^9 m^2. Fifteen input features were used: aspect, mean/planform/profile/total curvature, discharge, distance to channel, distances to faults and to the Main Frontal Thrust and suture zone, drainage area, elevation, local relief, mean annual precipitation (MAP), number of extreme rainfall events (NEE), and slope. Topographic variables were derived from 90 m SRTM; climate variables (MAP, NEE) from TRMM/APHRODITE resampled to 30 m; geologic distances from regional maps. Model implementation: Level-1, -2, and -3 SNNs were tested; Level-2 was selected as optimal due to high accuracy and simplicity. Spatially representative data partitioning used Pythagorean tiling to create a 70/30 training/testing split. Class imbalance was handled by weighting positive (landslide) samples higher in loss functions. Comparators included: single-feature classifiers; a modified physically based SHALSTAB failure index; logistic regression; likelihood ratios; and a teacher DNN (MST). Performance metrics included AUROC, accuracy, sensitivity (POD), specificity (POFD), POD–POFD, with 10-fold cross-validated AUROC confidence intervals for neural and statistical models. The SNN also enabled extraction of individual feature contribution functions Sj and local/global importance analyses, including windowed (2.25 km^2) primary control identification and decomposition of slope vs climate contributions.

- Performance: Level-2 SNN achieved average AUROC 0.890 across the three regions (Level-1: 0.856), capturing over 98% of the teacher DNN (MST) performance and over 99% for Level-3. - Improvements over baselines: SNN improved average AUROC by ~21% over the best single original features (MAP or slope; AUROC 0.737), ~22% over SHALSTAB (AUROC 0.727), and 5–8% over logistic regression (AUROC 0.848) and likelihood ratios (AUROC 0.823). The SNN’s 95% AUROC confidence intervals were statistically higher than those of statistical models. Other metrics (accuracy, POD, POFD, POD–POFD) also generally favored SNN. - Primary controls: Composite features MAP*Slope and NEE*Slope, as well as Aspect (Asp) and Asp*Relief, consistently emerged as important contributors across regions. Functions SMAP*Slope and SNEE*Slope showed steep increases then asymptotic behavior with increasing feature values. Aspect contributions peaked for south-facing slopes (~145–180°), suggesting microclimatic effects. - Local vs global importance: Windowed analyses (2.25 km^2) identified MAP*Slope and NEE*Slope as frequent local primary controls, even when not the largest absolute contributors to total susceptibility. - Climate vs slope contributions: Climate features (Asp, NEE, MAP and their composites with slope) contributed more to susceptibility than slope in approximately 74% (N-S), 54% (NW-SE), and 54% (E-W) of localities, indicating dominant climatic control over much of the study area.

The SNN framework resolves the interpretability–accuracy tension by delivering state-of-the-art predictive performance while providing fully decoupled, quantitative contributions from each feature and explicitly modeled interdependencies. The identified dominant composite controls (MAP*Slope, NEE*Slope) and aspect-related effects suggest strong slope–climate coupling and microclimatic influences on landslide occurrence in the easternmost Himalaya. The nonlinear asymptotic forms of SMAP*Slope and SNEE*Slope align with physical expectations for rainfall-induced landslides: increased pore-water pressures and subsurface saturation lower stability, with an upper bound on saturation effects analogous to the failure index formulation from SHALSTAB. The relative lack of drainage area or discharge as primary contributors suggests that local infiltration (precipitation rate and intensity) may be a first-order control on saturation in this region, though topographic convergence could be underrepresented due to input resolution. By offering both global and local decompositions, the SNN informs which controls dominate in specific locales, improving the utility of susceptibility maps for decision-makers. The results underscore that climatic variability across the steep orographic gradient strongly modulates susceptibility and that incorporating interaction features directly yields measurable gains over traditional statistical and physically based models.

The study introduces an interpretable, additive neural framework (SNN) for landslide susceptibility mapping that matches deep neural network accuracy while providing transparent, decoupled contributions of individual and interacting features. Applied to three regions in the easternmost Himalaya, the SNN outperformed physically based and statistical models and highlighted key, underappreciated controls—particularly MAP*Slope, NEE*Slope, and Asp/Asp*Relief—consistent with precipitation-driven landslides and microclimatic effects. The approach generalizes across varied environmental conditions, uses open-source datasets, and can be extended to other hazards and regions. Future work should incorporate higher-resolution topographic, climatic, and geologic data; time-series landslide inventories to link triggers and timing; and supplementary sensors (e.g., InSAR) to capture slow-moving landslides. The framework can also exploit alternative teacher models (e.g., random forests) and adapt as improved data and computation become available.

- Temporal and spatial averaging: Input features are averaged and do not link specific triggering events (e.g., rainstorms, earthquakes) to individual landslides; the inventory timing is constrained by 2017 optical imagery and post-failure signatures. - Event/type ambiguity: Lack of precise timing and landslide type differentiation (soil vs bedrock, slow vs fast) limits event-scale interpretation. - Data resolution: Coarse to moderate resolutions (Landsat 30 m, SRTM 90 m, TRMM ~5 km^2) may bias features sensitive to resolution (e.g., topographic metrics, rainfall intensity, drainage convergence). - Regional specificity: Dominant controls identified are specific to the easternmost Himalaya and may differ elsewhere. - Potential underrepresentation of convergence effects: Absence of drainage area/discharge as primary contributors may reflect data resolution limits rather than negligible physical influence.