# VDMS: An Improved Vision Transformer-Based Model for PM\({}_{2.5}\) Concentration Prediction
## 4 Results
### Model Estimation
This study forecasts PM\({}_{2.5}\) concentrations across China for the period from 2017 to 2022 based on an established model, with related predictions depicted in Figure 5. Analysis of this figure indicates significantly higher PM\({}_{2.5}\) concentrations in the western regions of China, particularly near Xinjiang, where it appears as a prominent red area. This suggests that air pollution in this region is more severe, likely influenced by both natural factors (such as sandstorms) and anthropogenic factors (such as industrial emissions). In contrast, PM\({}_{2.5}\) concentrations in most other regions are lower, primarily represented in green or yellow, indicating better air quality. Notably, the southeastern coastal regions of China exhibit lower PM\({}_{2.5}\) concentrations, likely associated with improved air circulation and more stringent pollution control measures in these areas. The visualization results of \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Sam-CV**} & \multicolumn{3}{c}{**Sta-CV**} \\ \cline{2-7}  & **R\({}^{2}\)** & **RMSE** & **MAE** & **R\({}^{2}\)** & **RMSE** & **MAE** \\ \hline CNN & 0.75 & 7.77 & 6.42 & 0.70 & 9.29 & 7.40 \\ ViT & 0.53 & 8.05 & 6.51 & 0.48 & 9.57 & 7.49 \\ SimCLR & 0.86 & 7.43 & 5.78 & 0.81 & 8.95 & 6.76 \\ VDMS & 0.93 & 4.05 & 3.23 & 0.88 & 5.57 & 4.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the Sam-CV and Sta-CV results for various models. Figure 4: Density scatter plots illustrating the performance of VDMS. Plots (**a,b**) show the Sam-CV and Sta-CV results, respectively, with integrated meteorological data. Plots (**c,d**) show the Sam-CV and Sta-CV results, respectively, without integrated meteorological data. this study facilitate the identification of spatial distribution patterns of PM\({}_{2.5}\) pollution across China, providing valuable insights for pollution source identification and regional air quality assessment. These findings not only serve as a foundation for subsequent environmental monitoring but also offer scientific support for focusing on high-pollution areas and the formulation of pollution control strategies. Table 3 presents the statistical results of annual and seasonal PM\({}_{2.5}\) concentrations in Beijing. Data from Table 3 indicate a year-on-year decline from 2017 to 2022. The annual average PM\({}_{2.5}\) concentration decreased from 58.14 \(\mu\)g/m\({}^{3}\) in 2017 to 30.47 \(\mu\)g/m\({}^{3}\) in 2022, signifying an improvement in air quality during this period. Seasonal variations reveal that PM\({}_{2.5}\) pollution in Beijing is more severe in spring and winter, with the highest concentrations recorded in winter. Conversely, summer exhibits the lowest PM\({}_{2.5}\) concentrations, indicating clear seasonal variation. The overall trend of annual PM\({}_{2.5}\) concentrations follows a U-shaped curve, reflecting substantial seasonal fluctuations, while the three-year average PM\({}_{2.5}\) concentration demonstrates a declining trend, indicative of a long-term improvement in air quality. Figure 5: Spatial distributions of the estimated PM\({}_{2.5}\) concentrations in (**a–f**) 2017–2022 across China. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Season\_Year** & **2017** & **2018** & **2019** & **2020** & **2021** & **2022** \\ \hline Spring & 59.87 & 69.79 & 46.50 & 34.07 & 49.09 & 32.96 \\ Summer & 44.31 & 43.12 & 31.76 & 33.06 & 17.71 & 20.52 \\ Autumn & 51.98 & 45.23 & 39.97 & 33.54 & 29.74 & 29.17 \\ Winter & 76.40 & 43.29 & 48.30 & 49.44 & 43.18 & 39.21 \\ Annual & 58.14 & 50.36 & 41.63 & 37.53 & 34.93 & 30.47 \\ \hline \end{tabular}
\end{table} 
Table 3: Seasonal variation of PM\({}_{2.5}\) concentration (\(\mu\)g/m\({}^{3}\)) from 2017 to 2022.