## 2 Materials and Methods
### Training Process and Measures  
The neural network models, as well as the GRU models, were trained using the Root Mean Squared Error (RMSE) as the loss function, which is well suited for regression tasks and has been used as the standard statistical measure to evaluate a model's performance when it comes to meteorological and air quality studies [67; 68]. RMSE emphasizes larger errors more heavily than smaller ones due to the squaring of differences. It also preserves the same units as the target variable, making it particularly effective for evaluating long-term forecasting accuracy. RMSE calculates the square root of square averages of the differences between predicted and actual values and is defined based on Equation (10):  
\[\text{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}}, \tag{10}\]  
where \(n\) is the total number of observations, \(y_{i}\) represents the actual value of the \(i\)-th observation, \(\hat{y}_{i}\) the predicted value for the \(i\)-th observation, and \((y_{i}-\hat{y}_{i})^{2}\) is the squared error for the \(i\)-th prediction. The performance of the models was evaluated using three key error measures: the Root Mean Squared Error (RMSE), Mean Squared Error (MSE), and Mean Absolute Error (MAE). The RMSE was defined above by Equation (10). The Mean Squared Error (MSE) computes the average of the squared differences between the predicted and actual values. It is mathematically expressed by Equation (11):  
\[\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}. \tag{11}\]  
MSE provides a smooth and sensitive measure of the prediction error. However, larger deviations have a disproportionately higher impact due to the squaring operation. RMSE is the square root of MSE, providing a measure that retains the same units and smooth increases in error magnitude as the target variable (in this case, AQI), thereby making the error magnitude easier to interpret in real-world terms. On the other hand, the MAE is less robust to outliers, providing fair forecasting when outlier values are primarily due to measurement noise. The MAE is expressed by Equation (12):  
\[\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}\lvert y_{i}-\hat{y}_{i}\rvert, \tag{12}\]  
where \(y_{i}\) is the actual value, \(y_{i}\) is the predicted value, and \(n\) is the total number of predictions. This measure is particularly useful when it is necessary to interpret prediction accuracy in terms of actual AQI units. This is because MAE, as a measure, treats all errors linearly. At the same time, as meteorological and particulate matter data typically spike due to the nature of the phenomena, specifically due to the irregularity and asymmetry of climate change events, they were excluded as scenario evaluation measures. The independent samples' \(t\)-test evaluation was used to compare whether the means of the two model groups were statistically different. For model comparisons, Equation (13) was used in this evaluation. \[t=\frac{\bar{X}_{1}-\bar{X}_{2}}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{ \sigma_{2}^{2}}{n_{2}}}}, \tag{13}\]  
where \(\bar{X}\) is the sample mean, \(\sigma\) the standard deviation, and \(n\) the sample size. Having as the Null hypothesis (\(H_{0}\)) the lack of difference between arbitrary model performances concerning the first model (\(64\to 2\)), a \(p\)-value of \(<0.05\) rejects \(H_{0}\) with 95% confidence. On the other hand, [PERSON]'s d was used to measure the standardized difference between the two group means, expressed in units of pooled standard deviation, as captured by Equation (14).