# VDMS: An Improved Vision Transformer-Based Model for PM\({}_{2.5}\) Concentration Prediction
## 1 Introduction  
Smog constitutes a serious environmental hazard, leading to degraded air quality, increased economic losses, and higher incidences of lung cancer and mortality [1, 2, 3]. In recent years, the frequency of smog events in China has risen, making the mitigation of fine particulate matter (PM\({}_{2.5}\)) a formidable challenge that demands considerable effort [4, 5]. PM\({}_{2.5}\)--particles with diameters of 2.5 \(\mathrm{\SIUnitSymbolMicro m}\) or less--is recognized as a major contributor to smog [6]. Research indicates that PM\({}_{2.5}\) not only exerts adverse effects on physical health, potentially causing asthma, bronchitis, and other cardiovascular diseases [7, 8, 9], but alsonegatively influences mental health [10]. Given China's vast population, the monitoring and control of PM\({}_{2.5}\) are critically important. High concentrations of PM\({}_{2.5}\) further threaten the environment and agriculture by obstructing sunlight absorption by plants and weakening photosynthetic processes [11]. Effective monitoring of the concentration and spatiotemporal distribution of PM\({}_{2.5}\) is essential to protect human health and improve living conditions. Although the government initially intended to improve PM\({}_{2.5}\) surveillance through an extensive monitoring network [12], the rapid pace of urbanization and industrialization has outstripped the expansion of monitoring stations. The limited and uneven distribution of these stations fails to capture adequately the spatial and temporal heterogeneity of PM\({}_{2.5}\) in China [13], thus challenging the effective monitoring and evaluation of its health effects. Therefore, acquiring high-resolution distribution maps of PM\({}_{2.5}\) is essential to plan and implement effective pollution control measures. To address these challenges, advanced predictive models have been developed that integrate the capabilities of Vision Transformer (ViT) with double-layered LSTM (DLSTM) networks and multi-head self-attention mechanisms. This hybrid approach improves the modeling of temporal dynamics and global dependencies, thereby improving prediction accuracy even in regions with sparse monitoring data. Previous studies have demonstrated that the integration of remote sensing data with statistical models is an effective approach to estimate PM\({}_{2.5}\) concentrations [14]. Aerosol Optical Depth (AOD) derived from remote sensing products is often considered highly correlated with PM\({}_{2.5}\) levels and has been widely utilized for PM\({}_{2.5}\) simulation [15,16]. AOD-based products, using satellite remote sensing technology, have become a common tool for estimating PM\({}_{2.5}\) concentrations [17; 18; 19]. In recent years, the moderate resolution imaging spectroradiometer (MODIS) AOD product has received significant attention due to its improved retrieval accuracy and finer spatial resolution [20]. Some studies have combined AOD data with linear mixed-effects models to enhance the spatial resolution of PM\({}_{2.5}\) predictions [21; 22]. However, these methods face several challenges in practical applications. AOD retrieval algorithms are highly susceptible to factors such as cloudy weather, snow coverage, and high surface reflectivity, which can lead to non-random missing data [23], resulting in high data loss rates that complicate PM\({}_{2.5}\) estimation [24; 25]. This data incompleteness inevitably introduces sampling biases, negatively impacting the accuracy of PM\({}_{2.5}\) predictions [26]. Although traditional PM\({}_{2.5}\) prediction methods based on ground monitoring data perform well in feature extraction, they often rely heavily on ground station data, making it difficult to model effectively the influence of geographic and meteorological factors on PM\({}_{2.5}\) distribution.