## 2 Materials and Methods
### Data Collection and Preprocessing
#### 2.3.1 Data Preprocessing  
The air pollutant indicators used in this study were particulate matter (PM) concentrations, and they were divided into four distinct types based on their size: PM\({}_{1}\), PM\({}_{2.5}\), PM\({}_{4}\), and PM\({}_{10}\). These pollutants are significant contributors to air quality degradation, originating from various natural and anthropogenic sources, such as industrial emissions, vehicle exhausts, and biomass burning [58; 59]. The dataset consists of time-series measurements of these particulate concentrations, recorded in micrograms per cubic meter (\(\upmu\)g/m\({}^{3}\)). Particulate matter features were subjected solely to standardization using z-score normalization. This method transforms each input variable such that it has a mean of zero and a standard deviation of one, effectively centering and scaling the data:  
\[X_{std}=\frac{X-\mu}{\sigma}. \tag{4}\]Here, \(\mu\) is the mean and \(\sigma\) is the standard deviation of each PM variable computed using the training data. This transformation is significant for neural networks as it ensures that features with larger numeric ranges do not dominate the training process. It also improves the conditioning of the optimization problem and speeds up the convergence during training [60,61]. Meteorological variables are crucial for AQI forecasting as they influence pollutant dispersion, deposition, and transformation. This study incorporated temperature (\({}^{\circ}\)C), relative humidity (%), wind speed (m/s), and wind direction (\({}^{\circ}\)) [62]. For the meteorological variables, a two-stage preprocessing pipeline was implemented. The raw values of the meteorological variables were first standardized using the same z-score formula as Equation (4). Standardization was followed by min-max normalization to scale the standardized values into a bounded range between 0 and 1, as shown in Equation (5):  
\[X_{norm}=\frac{X_{std}-X_{min}}{X_{max}-X_{min}}. \tag{5}\]  
This combined approach was chosen to accommodate both the need for zero-centered inputs and the benefits of scaled features within a uniform range [63]. Notably, min-max normalization was applied after standardization using the minimum and maximum values of the standardized training data to ensure consistency and to prevent information leakage. The output dataset, consisting of future Air Quality Index (AQI) values, underwent a preprocessing strategy designed to accommodate the structure of the prediction models and improve training stability. Specifically, the number of future AQI values used as prediction targets varied depending on the model configuration. Four distinct input sizes, corresponding to 64, 128, 256, and 512 hourly data points, were selected. For each of these, the output consisted of the subsequent 2, 4, 8, and 16 hourly AQI values, respectively. To construct the output dataset, specific rows were selected from the complete AQI time series. More specifically, for each input size, the following \(2^{k}\) hourly AQI data, where \(k=1,2,3\), and 4, were chosen as prediction targets for every \(2^{i}\) consecutive row, where \(i=3,4,5\), and 6. This slicing strategy ensured temporal separation between training samples and helped prevent excessive overlap in prediction windows, thereby reducing potential data leakage and autocorrelation bias during training and evaluation [64]. For further clarity regarding the input and output configurations, Table 3 presents a summary of the respective settings used in the prediction process. After the slicing process, the final output dataset that was used was created, and all the AQI target values were standardized using z-score normalization in accordance with Equation (6):  
\[Y_{std}=\frac{Y-\mu_{Y}}{\sigma_{Y}}, \tag{6}\]