# VDMS: An Improved Vision Transformer-Based Model for PM\({}_{2.5}\) Concentration Prediction
## 5 Discussion  
### Analysis in Model Performance  
In this study, the model leverages several advanced deep learning techniques, including ViT, DLSTM, and a multi-head self-attention mechanism. These techniques enhance model performance, particularly in processing spatiotemporal features and complex patterns, and confer several advantages.  
LSTM networks are designed to process time series data, effectively capturing long-term dependencies within temporal sequences [39]. By utilizing gating mechanisms, LSTMs successfully capture these prolonged dependencies, enabling the model to handle temporal variations in PM\({}_{2.5}\) concentrations more accurately [35]. This results in improved prediction accuracy, especially in capturing dynamic changes in air pollution. However, single-layer LSTMs exhibit limitations in learning complex temporal dependencies, leading to only modest performance gains [40]. To enhance performance, a double-layered LSTM is introduced. By increasing network depth, the double-layered LSTM captures short-term dependencies at lower layers and long-term dependencies at higher layers, providing a more comprehensive modeling of complex temporal dynamics. Therefore, this model processes complex time-series data more effectively, achieving significantly improved predictive accuracy compared to a single-layer LSTM.  
The multi-head self-attention mechanism is a core component of the Transformer architecture, facilitating the capture of various relationships and dependencies within input data through the computation of multiple attention heads in parallel. Each attention head focuses on different subspaces, enabling the model to capture a broader range of features effectively. The incorporation of the multi-head self-attention mechanism in this study led to enhanced performance in processing the spatial features of PM\({}_{2.5}\) concentrations [41]. The self-attention mechanism selectively emphasizes different parts of the input data, weighting them according to their importance, thus allowing the model to identify key patterns and features [42]. Moreover, by leveraging parallel processing across multiple attention heads, the multi-head mechanism further enriches the diversity of feature representations. Therefore, with this module integrated, the model can better capture the spatial variations of PM\({}_{2.5}\) concentrations across different regions, particularly in areas with complex air pollution, thereby significantly enhancing its predictive capability and accuracy [41].  
SimCLR is a contrastive learning-based model that learns improved data representations by maximizing the similarity between similar samples while minimizing the distance between dissimilar ones [43]. The incorporation of the SimCLR module further optimizes the model's feature learning capabilities. By employing a self-supervised learning approach, SimCLR enables the model to acquire more discriminative features without the need for labeled data, which is particularly crucial for managing complex environmental datasets [43]. In the context of PM\({}_{2.5}\) concentration prediction, SimCLR assists the model in discerning similarities and differences within the input data, enhancing its sensitivity to temporal and spatial variations in PM\({}_{2.5}\) levels [43]. Ultimately, the integration of SimCLR allows the model to adaptively capture latent features of the data, improving the predictive accuracy, especially in high-pollution areas and under complex environmental patterns, where SimCLR demonstrates robust feature extraction capabilities [44].