## 3 Materials and Methods
### Methodology  
The process begins with defining a cell grid representing the territory to be analyzed. This grid includes all relevant data and variables necessary for risk analysis, such as land  
Figure 3: SNN network architecture. Figure 2: SELU activation function. use, digital elevation models (DEMs) for land slope, and other characteristics influencing the susceptibility index. The \"create_cell_grids\" function generates the grid by establishing cell coordinates based on the dataset's size. Transition rules are associated with various cell characteristics, including land use, slope, precipitation, geology, and lithology. These rules determine a cell's next state based on its current state and the states of neighboring cells. The rules for the transition of the cell state take into account the combination of the factors already mentioned such as ground slope, precipitation, geological and lithological factors, and the states of the neighboring cells. The transition formula in this context is expressed as follows:  
S_[t+1](i,j) = f(S_t(i,j), N_t(i,j), P(i,j), U(i,j), R(i,j), G(i,j), L(i,j)) dove:  
(S[t+1](i,j): cell state((i,j)) at time (t+1)  
(S_t(i,j)): cell state ((i,j)) at time (t ). (N_t(i,j)): states of neighboring cells. (P(i,j)): slope of the ground in the cell ((i,j)). (U(i,j)): land use in cell ((i,j)). (R(i,j)): precipitation in the cell ((i,j)). (G(i,j)): geological factors in the cell ((i,j)). (L(i,j)): lithological factors in the cell ((i,j)). Each factor contributes to the final decision on the state of the cells. Transition thresholds represent critical values that determine when a cell changes state, which, in our case, is unstable when it takes on a value of 1 (probability of landslide) and stable when it is 0. For the evaluation of the transition from stable to unstable state, the following conditions were evaluated:  
Condition 1:  
The cell ((i,j)) becomes unstable ((S [t+1](i,j) = 1)) if the slope (P(i,j)) is greater than a critical threshold > 30\({}^{\circ}\) and the precipitation ( R(i,j)) is greater than a critical threshold > 40 mm. Condition 2:  
The cell ((i,j)) becomes unstable ((S_[t+1](i,j) = 1)) if land use (U(i,j)) indicates a high risk. This could mean, for example, that the area has been deforested or urbanized, increasing the risk of landslides. Condition 3:  
The cell ((i,j)) becomes unstable ((S_[t+1](i,j) = 1)) if geological factors (G(i,j)) or lithological factors (L(i,j)) indicate instability. For example, clay soils, fractured rocks, or inconsistent materials may be more susceptible to landslides. Condition 4:  
The cell ((i,j)) becomes unstable ((S_[t+1](i,j) = 1)) if the sum of the states of the neighboring cells (\(\backslash\)sum_[(k,l)\(\backslash\)in N(i,j)] S_t(k,l)) exceeds a certain threshold. If three neighboring cells are unstable, the probability that the cell ((i,j)) will also become unstable increases. Condition 5:  
If none of the above conditions are met, the cell ((i,j)) remains stable ((S_[t+1](i,j) = 0)). At the beginning of the code, a column titled \"susceptibility index\", initially set to zero for all cells, is added to the data frame. The first transition rule is implemented in the \"calculate_susceptibility\" function, which uses a random forest model to predict the cells' susceptibility index. Clipping is applied to ensure the susceptibility index remains within a valid range (non-negative). Following this, the random forest model is initialized and trained, allowing it to predict the susceptibility index. The iteration between the cellular automaton and the random forest takes place in the function iterate_ca_rf. In each iteration, the random forest model is trained and used to predict the susceptibility index (no. iterations = 10). Through iterations, the model can adapt and progressively improve its predictions. Each iteration provides feedback that is incorporated into the model, allowing for refinement of the predictions of the susceptibility index. A more robust model is obtained that accounts for variations in the data.