## 5 Discussion
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Model** & **RMSE** & **MAE** & **R\({}^{2}\)** & **Correlation** & **Accuracy** \\ \hline GraphSage+LSTM & 0.0297 & 0.0274 & 0.6985 & 0.8982 & 0.8013 \\ CNN3D+LSTM & 0.0340 & 0.0340 & 0.6827 & 0.8803 & 0.6763 \\ GAT & 0.0361 & 0.0365 & 0.6382 & 0.8586 & 0.6485 \\ LSTM & 0.0305 & 0.0290 & 0.7188 & 0.8939 & 0.7725 \\ GraphSage & 0.0294 & 0.0268 & 0.7234 & 0.8997 & 0.8188 \\ Transformer & 0.0178 & **0.0171** & 0.6684 & 0.8807 & 0.9090 \\ TransformerConv & 0.0238 & 0.0205 & 0.6333 & 0.9330 & 0.7157 \\ CNN1D+LSTM+TransformerConv & **0.0169** & 0.0174 & **0.8927** & **0.9601** & **0.9158** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model results for LAeq. events. Interestingly, the RMSE and MAE for L1 remain relatively similar, suggesting that the model's errors relate more to its ability to capture extreme fluctuations than to general prediction errors. These results highlight the need to explore additional methods that help the model better anticipate anomalous peaks, such as using external data or models specialized in anomaly detection. Nonetheless, as shown in the Figure 8, the results fit the real values quite well. As an example of a spatio-temporal prediction, we present the Figure 9 (real noise) and Figure 10 (predicted noise) that illustrates a forecast for a specific time step. As observed, predictions are quite accurate. If we inspect a specific node at a specific moment (see Figure 11), we can observe variations between day and night, as well as the fact that the model slightly underestimates real values, possibly because the training data are mostly from the pre-COVID-19 period, while the test set is post-pandemic, where noise pol  
Figure 8: True vs. predicted test values for CNN1D+LSTM+TransformerConv. Values are normalized. LAeq: Min(0) = 32.1, Max(1) = 101.5. The correlation between both values demonstrate that results fit real values correctly (data is around the diagonal, in red). Figure 9: Example of real noise level (LAeq) data recorded by Madrid stations at a specific time instant. This study presents a hybrid methodology integrating Convolutional Neural Networks (CNN), Long Short-Term Memory Networks (LSTM), and Graph Convolutional Networks (GCN) for urban noise pollution prediction. The experimental results show improvements compared to simpler baseline models. However, several aspects require detailed analysis to better understand the scope of the proposed model. First, the complexity of the hybrid architecture must be considered. While the model yields better predictive performance, the combined use of CNN, LSTM, and TransformerConv must be clearly justified. Experimental results show that simpler methods like LSTM or GraphSAGE alone do not effectively capture the complex spatio-temporal dynamics of urban noise. Thus, the proposed combination provides an advantage by simultaneously modeling local temporal patterns, long-term dependencies, and spatial relationships between stations, justifying the approach's greater complexity. Additionally, it is necessary to conduct more extensive comparisons with current state-of-the-art models, especially recent architectures using attention mechanisms or purely Transformer-based time series models. While the comparisons made in this study are satisfactory, future work could include further comparisons with emerging techniques, reinforcing the validity and relevance of the proposed approach. Figure 11: Prediction example for a specific node using CNN1D+LSTM+TransformerConv. Each time step represents 12 h intervals, differentiating between daytime and nighttime. The vertical axis indicates noise levels. Figure 10: Prediction generated by the CNN1D+LSTM+TransformerConv model for the same time instant as Figure 9. The prediction adequately reproduces the spatial patterns present in the real data. In practical terms, the presented model has potential real-world applications, contributing to improved urban noise pollution management.