## 4 Results and Discussion  
The validation loss change rates for the CNN, LSTM, TCN, and TCN-LSTM models are shown in Figure 7. These rates were analyzed to assess the stability of the models. With the exception of the TCN model, all models exhibited a sharp decrease in loss during the initial training phase, indicating rapid optimization in the early learning stages. The TCN model, however, showed the largest initial change rate in loss at the beginning of training, followed by stable learning, with its change rate converging to zero between epochs 13-17. For the LSTM model, the first 0-5 epochs demonstrated gradual optimization due to its recurrent structure. Most models exhibited stabilization, with the change rate approaching zero after 10 epochs. Among all models, the TCN-LSTM architecture displayed the fastest decline in change rate, indicating stable learning. These findings suggest that the hybrid model offers better generalization ability and a lower risk of overfitting compared to individual architectures. To prevent overfitting, we applied early stopping before 10 epochs for the hybrid model and after 10 epochs for the single models. The validation change rate analysis demonstrated that the TCN-LSTM model proposed in this study exhibited a consistently decreasing change rate, confirming their stability and applicability in predicting CO2 emissions from engine data. However, for models that displayed fluctuations in the change rate during training, we anticipate that the introduction of advanced optimization techniques and further hyperparameter tuning will be necessary to enhance their performance and stability. The prediction results of the CNN, LSTM, and TCN single architectures and the TCN-LSTM hybrid model are shown in Figure 8. Figure 8a shows the overall time-series comparison, while Figure 8b-e provides zoomed-in views of representative segments with notable prediction performance differences. In Figure 8b, all models exhibit noticeable prediction inaccuracies in this segment, with significant deviations from the measured values. This discrepancy may stem from the model's limited capacity to respond effectively to abrupt transitions or irregular input patterns. These results indicate that the architectures  
Figure 7: Validation loss change rate of all the prediction models. including the proposed model may struggle to fully capture nonlinear behaviors or unmodeled dynamics in such regions. To address this limitation, future work should consider incorporating additional representative training data and performing cross-model analysis to enhance robustness and generalization under transient conditions. While all models generally performed well, some exhibited underprediction or overprediction tendencies. Compared to the hybrid model, the LSTM and TCN single architectures (excluding CNN) showed greater deviations, particularly in sections where engine RPM gradually increased (see Figure 8d) or decreased (see Figure 8c). This discrepancy likely stems from differences in training methods influenced by each model's structural characteristics and the nature of the data. LSTM model excels at capturing long-term dependencies by retaining past information. However, in sections with rapid changes, their predictive accuracy decreases, as they rely heavily on historical data, leading to noticeable deviations. TCN model is effective at learning localized patterns, but their predictions may be unstable due to sensitivity to noise or outliers in the input data [49]. Further parameter optimization could mitigate this issue. CNN models, although traditionally used for image processing, have proven highly effective for time-series prediction [50]. Their convolutional layers excel at detecting localized features, allowing them to capture pattern changes in short segments of extensive time-series data. Additionally, CNNs naturally filter noise, leading to superior predictive performance compared to LSTM and TCN models, even in rapidly changing data [51].