## 2 Materials and Methods
### Artificial Neural Networks  
In this study, models to predict the next-day PM\({}_{2.5}\) daily average for NW and AD were developed using an ANN. To develop prediction models using ANN, R version 4.1.0 was used with the \"neuralnet\" library. The variables in Table 1 were used to develop the models; y was used as a dependent variable, while the rest were used as independent variables. PM\({}_{2.5}\) prediction model was developed separately for NW and AD. All independent variables are connected to the neurons in the hidden layer, which is composed of two columns, as shown in Figure 1. These neurons pass through the activation function and produce an output. In this study, a Logistic Function, Equation (1), was used as the activation function. Therefore, an optimal function is obtained when the neuron inputs are between 0 and 1, and the numerical independent variables of air pollutants and meteorological factors are converted into data between 0 and 1 through the min-max normalization of Equation (2) [40]. \[f(x)=\frac{1}{1+e^{-g(x)}} \tag{1}\]  
\[Normalized\ data=\frac{Original\ data-X_{min}}{X_{max}-X_{min}} \tag{2}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Factors** & **Categories** & **Variables** \\ \hline Air Pollutant Factors (Daily Average) & PM\({}_{10}\), NO\({}_{2}\), SO\({}_{2}\), O\({}_{3}\), CO, PM\({}_{2.5}\) & x1, x2, x3, x4, x5, x6 \\ Air Pollutant Factors (Daily Variance) & PM\({}_{10}\), NO\({}_{2}\), SO\({}_{2}\), O\({}_{3}\), CO, PM\({}_{2.5}\) & xv1, xv2, x3, xv4, xv5, x6 \\ Meteorological Factors (Daily Average) & Temperature, Humidity, Wind Speed, Atmospheric & z1, 22, z3, z4, z5, z6 \\ Meteorological Factors (Daily Variance) & Temperature, Humidity, Wind Speed, Atmospheric & zv1, zv2, xv3, zv4, zv5, zv6 \\ Next-day PM\({}_{2.5}\) (Daily Average) & PM\({}_{2.5}\) & y \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Variables for prediction model development. The value that has passed through the neurons of the hidden layer is gathered in the output layer and calculated, and a response variable is subsequently derived. The error between the predicted and actual values is reduced, and the model is repeatedly learned. A model is learned to allow the partial derivative of the sum of squared error (SSE), which is the error function for the difference between the predicted and actual values derived from the model, to become smaller than the threshold [41]. This method is known as the \"Rprop+\" algorithm. Model learning is terminated when the absolute partial differential value of the SSE becomes smaller than the specified threshold or when the set number of training reaches \(10^{6}\)[42]. ANN showed high prediction performance for time-series prediction in previous studies, but the ANN model could not entirely explain the relationship between the dependent and independent variables [43]. Therefore, the developed model should be verified using data not employed for model development. Two-thirds of the total data were used for model development (called \"in-sample\") and the remaining data (called \"out-of-sample\") were used for model validation. Two-thirds of each comprehensive air quality index category (good, normal, bad, and very bad) were randomly extracted and used as an in-sample (Tables S1 and S2). The decision to use a monthly factor to account for seasonal patterns affected the accuracy of the model. In addition, in Figure 1, the number of nodes and the number of hidden layers are shown, and this combination is called the hidden layer layout. The hidden layer layout should be optimized for best performance [44]. In addition, an appropriate threshold must be determined to prevent model overfitting. Table 2 shows the level of the factors used to determine the optimal ANN model. The presence or absence of the month factor, hidden layer layout, and threshold were tested and analyzed using a factorial design. In the pre-experiment, at least three layers showed no significant performance improvement, and the use of one layer was not appropriate for the ANN [45].