## 4 Results and Discussion
A hybrid architecture model can compensate for the weaknesses of a single model by leveraging their complementary strengths. The TCN-LSTM model effectively captures complex time-series patterns by simultaneously considering short-term fluctuations and long-term dependencies, thereby enhancing prediction accuracy. As shown in Figure 8, the hybrid model demonstrates high predictive accuracy, particularly in variation sections where single models struggle. This confirms their robustness in handling dynamic changes in engine data (see Figure 8c,e). To enable a quantitative evaluation of each model, Table 9 presents the R\({}^{2}\), mean absolute error (MAE), root mean squared error (RMSE), MAPE, and Pearson's correlation coefficient (R) for the test results. Additionally, Figure 9 provides a bar graph for a visual comparison of the results. All four models exhibited high accuracy, with R\({}^{2}\)\(\geq\) 0.9, and the TCN-LSTM model outperformed the others across all metrics. Among the single-architecture models, the CNN model achieved the highest accuracy (R\({}^{2}\) = 0.9697) and the smallest errors, as indicated by its MAE (49.6663), RMSE (60.0875), and MAPE (4.2337%)--highlighting its minimal deviation from actual measurements. Overall, the hybrid architecture model demonstrated strong performance, with the TCN-LSTM model achieving the highest accuracy (R\({}^{2}\) = 0.9726), slightly outperforming the CNN-based model. Additionally, the TCN-LSTM model exhibited the lowest prediction deviation and variance, as indicated by its MAE (47.3447) and RMSE (58.5737). These results suggest that the TCN-LSTM hybrid model provides the most accurate CO\({}_{2}\) emission predictions, particularly in response to variations in engine operation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Contents** & **CNN** & **LSTM** & **TCN** & **TCN–LSTM** \\ \hline R\({}^{2}\) & 0.9697 & 0.9386 & 0.9391 & 0.9726 \\ MAE & 49.6663 & 60.0086 & 63.0889 & 47.3447 \\ RMSE & 60.0875 & 73.1944 & 73.0336 & 58.5737 \\ MAPE & 4.2337 & 7.7985 & 8.2610 & 4.2335 \\ R & 0.9874 & 0.9737 & 0.9711 & 0.9889 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Evaluation of the models. Figure 8: Comparison of the prediction results of the models. (**a**) Over all-time series prediction results of the models. (**b**) Prediction results in the segment with significant variance. (**c**) Prediction results during a load decrease. (**d**) Prediction results during a load increase. (**e**) Prediction results under steady load conditions. The TCN-LSTM hybrid model outperformed all other models across all evaluation metrics, as it effectively leverages the strengths of both TCN and LSTM to capture complex time-series patterns in the input data. Compared to the TCN single model, the TCN-LSTM model achieved improvements of 3.6% in R\({}^{2}\), 24.9% in MAE, 19.8% in RMSE, and 48.8% in MAPE. Additionally, compared to the LSTM single model, it showed enhancements of approximately 3.6% in R\({}^{2}\), 21.1% in MAE, 19% in RMSE, and 45.7% in MAPE. These results highlight the effectiveness of the hybrid approach in improving CO\({}_{2}\) emission prediction accuracy. The TCN-LSTM hybrid model also has the best evaluation metrics, with higher prediction accuracy than the single-architecture models. In contrast, the TCN and LSTM model exhibited relatively higher errors and lower R\({}^{2}\) values, indicating their individual limitations in accurately predicting CO\({}_{2}\) emissions. Figure 9(a) visually compares the errors between the actual and predicted values across the four models. The LSTM and TCN models exhibit larger residual variances, with noticeable outliers in sections where rapid changes in engine-operating conditions occur. This suggests that these models struggle to adapt to sudden variations in the data, highlighting the need for additional data supplementation and model correlation analysis in future research.