## 3 Experimental Results and Analysis
### Ablation Study  
To assess the importance of different features and modules in our method, ablation studies were conducted on both the feature and module components. Figure 8: Calibration plots for seven models. Figure 9: Reference vs. calibrated values with error bars and coverage indicators. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MAE** & **RMSE** & **MSE** & **MAPE (\%)** \\ \hline RF [41] & 7.950 & 10.040 & 100.798 & 38.920 \\ SVR [42] & 7.319 & 9.312 & 86.710 & 30.584 \\ MLR [43] & 7.673 & 10.062 & 101.244 & 29.668 \\ XGBoost [44] & 7.713 & 9.730 & 94.663 & 38.401 \\ MLP [45] & 6.666 & 8.467 & 71.688 & 25.318 \\ LSTM [46] & 6.340 & 8.339 & 69.543 & 20.938 \\ MCRTF-CM & 5.450 & 7.206 & 51.926 & 19.216 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of evaluation metrics across models. (1) Feature-level Ablation Study: The input features include internal and external factors, with the latter divided into other air pollutants and weather-related factors. To evaluate the impact of these external factors on model performance, we conducted an ablation study by removing each type of external factor from the initial feature set. The performance of the MCRTF-CM model was then assessed with the remaining features. The model with other air pollutant features removed is denoted as MCRTF-CM(AF), and the model with weather-related features removed is denoted as MCRTF-CM(WF). Table 4 summarizes the experimental results. Removing other air pollutants (except PM\({}_{2.5}\)) resulted in MCRTF-CM(AF) showing increases in the MAE, RMSE, MSE, and MAPE by 12.44%, 11.14%, 23.52%, and 16.75%, respectively, compared to MCRTF-CM. This indicates that the features of other pollutants enhance model performance. The correlation between different pollutants suggests that PM\({}_{2.5}\) sensor readings may be indirectly influenced by these pollutants. Specifically, pollutants such as PM\({}_{10}\), CO, NO\({}_{2}\), SO\({}_{2}\), and O\({}_{3}\) are often found to be temporally and spatially correlated with PM\({}_{2.5}\) concentrations, as they share similar sources and atmospheric behaviors. For instance, high concentrations of NO\({}_{2}\) and O\({}_{3}\) may indicate urban emissions, which also contribute to the formation of fine particulate matter. Removing these pollutant features reduces the amount of information available to the model, resulting in decreased calibration accuracy for PM\({}_{2.5}\). On the other hand, removing weather-related features led to reductions in the MAE, RMSE, MSE, and MAPE by 27.06%, 25.66%, 44.74%, and 27.29% compared to MCRTF-CM(AF). This result demonstrates that weather conditions, particularly temperature, humidity, and wind speed, have a more significant impact on the calibration of PM\({}_{2.5}\) sensors. Weather variables influence the dispersion, dilution, and deposition of airborne particles, thereby affecting the observed concentration of PM\({}_{2.5}\). For instance, high humidity levels can increase particle size, making them easier to detect, while temperature and wind speed can influence the vertical mixing and horizontal transport of particulate matter. Therefore, it is crucial to consider both pollutant and weather-related features in air quality monitoring systems to enhance model accuracy and reliability. (2) Module-level Ablation Study: This section evaluates the importance of each module in the model through ablation experiments. Eight variants of the model, denoted as Models 1-8, were created based on different module removals. Model 1 omits the \(3\times 3\) convolutional kernels and residual connections; Model 2 omits the \(1\times 1\) convolutional kernels and residual connections; Model 3 omits the \(3\times 3\) convolutional kernels; Model 4 omits the \(1\times 1\) convolutional kernels; Model 5 omits the residual connections; Model 6 omits the FECAM; Model 7 omits both multi-scale convolution and residual connections; and Model 8 includes only the GRU.