## 1 Introduction  
The PM\({}_{2.5}\), as known as fine particulate matter, denotes particulate matter with an aerodynamic diameter less than 2.5 \(\upmu\)m. PM\({}_{2.5}\) has raised significant public concerns over the past decades because of its adverse effects on human health [1]. Studies have shown that people who exposed to PM\({}_{2.5}\) for long periods of time are more likely to suffer from respiratory and cardiovascular diseases and even die prematurely [2, 3]. Therefore, long-term continuous regional PM\({}_{2.5}\) concentration monitoring is important for the assessment of various haze impacts. To monitor air pollutants, China started to develop a ground-based monitoring network at the end of 2012, which has covered major cities by now. The ground-based monitoring network can grasp the real-time information of PM\({}_{2.5}\) concentration overtime at the observation sites with high accuracy, but it is difficult to support the assessment of regional haze impact due to the inability to accurately represent non-site regional concentrations. Meanwhile, the cost of site maintenance is high and the distribution is uneven with most located in urban centers. To overcome these limitations, the use of satellite remote sensing technology to derive the spatial and temporal distribution characteristics of PM\({}_{2.5}\) was proposed [4], due to its advantages such as wide spatial coverage and long time series [5; 6]. The AOD retrieved by satellite is a measure of the integration of the extinction coefficient of the medium between satellite remote sensing and the ground in the vertical direction [7], which cannot directly represent the ground-level PM\({}_{2.5}\). Therefore, various methods have been proposed to represent the relationship between AOD and PM\({}_{2.5}\), and obtain the near-ground PM\({}_{2.5}\) concentration. Up to now, the main methods for estimating PM\({}_{2.5}\) concentration using AOD are scale factor methods, semi-empirical formula methods, statistical model methods, and machine learning methods. The scale factor method simulates the scale coefficient between PM\({}_{2.5}\) and AOD by atmospheric radiative transfer model and then multiplies the coefficient by the AOD obtained from satellite retrieval, which does not involve ground-based monitoring data and is conducive to estimating PM\({}_{2.5}\) concentration during the period when there is no ground-based monitoring station, but the estimation accuracy is low [8; 9; 10]. The semi-empirical formula method is based on the physical properties between AOD and PM\({}_{2.5}\) such as humidity and vertical profile features of AOD [11; 12; 13; 14; 15]. However, it is difficult to fully express the relationship between PM\({}_{2.5}\) and AOD by a simple function due to its complex physical mechanism, while some parameters in the semi-empirical formula are not easily accessible, which limits the extension of this method. The statistical model method evolved from the initial linear model (e.g., linear mixed-effect regression, LME) [16; 17] to the nonlinear regression model (e.g., generalized additive model, GAM; geographically and temporally weighted regression, GTWR) [18; 19; 20]. Some researches improve the accuracy of the model by introducing meteorology, topography, land use and other relevant parameters [21; 22], but the nonlinear relationship between the factors still cannot be fully expressed. Machine learning algorithms have significant advantages over statistical models for classification and prediction [23], and a variety of models are widely used for PM\({}_{2.5}\) estimation, e.g., random forest (RF) [24; 25], Deep Neural Networks (DNN) [26; 27], Capsule Networks (CapsNet) [28], space-time extremely randomized trees (STEM) [29]. Machine learning methods have the advantage of expressing nonlinear relationships between large data and achieve excellent results in estimation accuracy compared with other methods but ignore the physical characteristics between AOD and PM\({}_{2.5}\).