## 3 Methodology
### Our Model, Spatio-Temporal Graph Convolution--Transformer Conv (STGC-TC)  
This section details the methodological approach used for predicting noise pollution in an urban setting. As previously noted, the proposed framework integrates three deep learning techniques: Convolutional Neural Networks (CNNs), Long Short-Term Memory networks (LSTMs), and Graph Convolutional Networks (GCNs).  
This combination addresses the need to model the spatiotemporal dynamics that characterize urban noise pollution. While each method offers specific advantages, none alone is sufficient to capture the complex spatial and temporal dependencies involved. CNNs are particularly effective at extracting local patterns and relevant features within fixed temporal windows, facilitating the identification of recurring structures in high-dimensional time series. However, their ability to model long-range dependencies is limited. This shortcoming is addressed by LSTM networks, which are well suited for capturing long-term temporal relationships and significant variations over extended periods--essential for modeling daily and weekly noise patterns. Nevertheless, both CNNs and LSTMs neglect the spatial dimension and the interactions between geographically distributed stations. GCNs overcome this limitation by explicitly modeling the spatial structure through graphsthat connect measurement stations based on geographic proximity. This integration enables the model to learn not only how noise evolves over time but also how it propagates spatially across locations.  
By combining CNN, LSTM, and GCN components, the proposed model overcomes the limitations of each individual technique, providing a robust and effective solution for urban noise prediction.  
To implement this integration, the model (shown in Figure 2) takes as input three-dimensional tensors of shape \([num\_nodes,num\_timesteps,num\_features]\), where each node represents a measurement station and each feature corresponds to an acoustic variable recorded over time.  
First, the input data are rearranged to apply two 1D convolutional layers along the temporal axis of each node, transforming the original input into a tensor of shape \([num\_nodes,num\_features,num\_timesteps]\). These convolutions allow local patterns in the data to be extracted, highlighting variations over short time periods. Subsequently, the data are rearranged again into shape \([num\_nodes,num\_timesteps,num\_features]\), and processed through an LSTM layer responsible for capturing more complex and long-term temporal dependencies. The output of this LSTM layer, shaped \([num\_nodes,hidden\_channels]\), is then passed to a TransformerConv layer [23], which uses attention mechanisms to evaluate and weigh the importance of spatial connections between nodes, enabling the model to emphasize those spatial relationships most relevant to prediction. Finally, a linear layer produces the final predictions for each node, integrating all temporal and spatial information extracted in the previous stages.  
Figure 2: Schematic of the CNN1D+LSTM+TransformerConv model proposed for urban noise prediction. The architecture processes spatio-temporal multivariate data and combines temporal and spatial relationships using 1D convolutions, LSTM and graphs with attention. The input tensor has nodes (H), time steps (W) and features (C). The output has the predicted time steps, where the model forecasts the next 14 time steps for each node. Red arrows show how each node receives information from its neighbors during the spatial graph convolution.