392 2.2.5 Artificial Neural Network Landslide susceptibility was modelled using a binary artificial neural network (ANN) implemented in RStudio with the neuralnet package, employing resilient backpropagation with weight backtracking (rprop+) (Riedmiller, 1994). The final dataset comprised 24,317 landslide and 80,864 non-landslide samples (105,181 total), merged with DEM-derived predictors (slope, aspect, curvature, TWI, SPI, and land cover) and randomly split into training (70%; 76,017 samples) and testing (30%; 29,164 samples) subsets using spatial random selection (QGIS). A single hidden-layer architecture was adopted following the universal approximation theorem (Hornik et al., 1989; Rosales-Huamani et al., 2020). With 21 input variables, hidden neuron configurations ranging from 5 to 11 were evaluated (upper bound defined as 2n+1, while hyperparameters were kept fixed to minimize overfitting and maintain model stability under rprop-based optimization. The network used a logistic activation function, cross-entropy error, a convergence threshold of 0.01, a maximum of 1x10^8 iterations, random weight initialization, and a single training repetition. 3. RESULTS 3.1. Model Evaluation and Selection Model performance was evaluated using Receiver Operating Characteristic (ROC) curves and the Area Under the Curve (AUC), computed for both training and testing datasets using the ROCR package. To identify the optimal ANN configuration, multiple models with a single hidden layer and varying numbers of neurons were tested. Performance was assessed based on convergence behaviour, processing time, and AUC values for training and testing datasets. The comparative results are summarized in Table 1. Table 1 - Performance Comparison of Hidden Layers and Neurons Hidden Layers Neurons Iterations Processing Time (h) Min Threshold AUC % (Training) AUC % (Testing) 1 5 578,303 6.65 0.010067087 97.37 95.55 (Best Model) 1 6 1,609,000 16.35 0.177181674 Nonconvergence Nonconvergence 1 7 2,175,000 25.52 0.114354682 Nonconvergence Nonconvergence 1 8 775,027 10.76 0.010162271 97.85 92.87 1 9 673,800 9.67 0.010022379 97.85 94.89 1 10 1,800,123 48.00 0.01014001 97.82 91.04 1 11 1,284,000 28.00 0.052727695 Nonconvergence Nonconvergence Note: Time more than 2 hours, the value for the threshold is not going down after another iteration. Among the evaluated configurations, the ANN with one hidden layer and five neurons achieved the best balance between predictive performance and computational efficiency. This model reached an AUC of 97.37 % for training and 95.55 % for testing, which corresponds to excellent predictive quality. Convergence was achieved in approximately 6.7 hours with a minimum threshold of 0.0101, while models with a higher number of neurons frequently failed to converge or required substantially longer processing times. The selected model also demonstrated strong classification capability, with high sensitivity, specificity, and balanced precision, indicating robust discrimination between landslide and non-landslide conditions. This configuration was therefore adopted for subsequent landslide susceptibility mapping across the 229 hydrographic units of the Peruvian territory.
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