## 3 Materials and Methods
### Random Forest Model
The graph shows the number of estimators, i.e., the number of trees in the forest, on the X-axis, and the mean test score on the Y-axis, which represents the accuracy of the test obtained during cross-validation for each combination of parameters. The maximum depth of the trees (max depth) and the minimum number of samples required to divide the nodes (min sample split) are also shown. From the examination of the graph, it can be observed that as the number of trees increases, the performance of the model improves, a greater depth leads to a more complex model, and a higher value of the min sample split can reduce the ability of the model to capture fine details in the data. With the parameters obtained, it can be verified that the average score of the test is the highest one, confirming that they are optimal for our model. At the bottom of the graph is a blue band that represents the confidence interval around the average of the test scores. A narrower confidence interval indicates less variability in test scores, attesting that the model is more stable and performs more consistently. Conversely, a wider range indicates greater variability, showing that model performance can vary more depending on the training and test data used. Out-of-bag (OOB) samples are data points not used during training, which allows for model evaluation without bias. The advantages of OOB samples include the following:  
* Extremely high performance of the model;
* Low probability of overfitting;
* Ability to handle large volumes of data;
* The feature bagging technique employed in random forest classifiers makes them practical for estimating missing values and maintaining accuracy, even when some data are absent. Figure 1: Grid search cross-validation results. When considering random forests, evaluating the model's performance is essential. Random forests require substantial processing power because they analyze large datasets for each decision tree. This leads to high computational requirements, and while a single decision tree is more straightforward to interpret, a forest consisting of multiple trees can be more complex and challenging to understand. Combining cellular automata and random forest techniques facilitates the simulation of complex phenomena [35]. Cellular automata's local rules are used alongside neural networks' learning capabilities. Together, these models play complementary and synergistic roles in calculating the landslide susceptibility index. Cellular automata are particularly valuable for modeling landslides' spatial and temporal dynamics. They simulate the propagation of landslides through the landscape over time, guided by transition rules that consider slope, rainfall, soil type, and vegetation. Each cell in the grid represents a portion of the terrain, which can change states--from stable to unstable or landslide--based on local conditions and the states of neighboring cells. This simulation enables cellular automata to identify areas most susceptible to instability or landslides, thus providing a preliminary risk map. The random forest model is a crucial component of our approach, utilized for predictive analysis and classification based on historical data and geospatial features. It incorporates the results from cellular automata simulations, which indicate the state of the cells after the simulation, as additional inputs, thus enhancing the predictive accuracy of the random forest model. Furthermore, the random forest analysis outcomes can be used to update the transition rules of the cellular automata, creating a feedback loop that continuously improves the model's precision. This integration allows for models that adapt to changes and perturbations within the system, ensuring efficiency and precision. Cellular automata reduce computational complexity, while neural networks maintain accuracy. These advantages make combining cellular automata and neural networks a powerful technique for predicting the susceptibility index in areas at risk, particularly in response to extreme weather events.