## 3 Summary of the Artificial Neural Network (ANN) for the CO2 Emission Prediction Model
### Tcn-Lstm  
Among the hybrid architecture models proposed in this study, we introduce the TCN-LSTM deep learning model, which integrates TCNs and LSTM networks to effectively predict CO\({}_{2}\) emissions from vessel engine data, as illustrated in Figure 6. This model leverages TCNs to efficiently extract features from complex data structures, while LSTM networks enhance the model's ability to process time-series data and capture long-term dependencies. Additionally, to improve data quality and minimize noise, we applied the  
Figure 4: Inner structure of long short-term memory (LTSM). Figure 5: Structure of temporal convolutional networks (TCNs). Savitzky-Golay (SG) filter, as proposed by [PERSON] et al. (2021), to the hybrid model before training [48]. In the first step, the SG filter is applied to the normalized input data (\(X_{nm}\)) to reduce noise, producing \(\overline{X}\):  
\[\overline{X}=SG(X_{nm},w,t), \tag{8}\]  
where \(SG0\) represents the \(SG\) filter function, \(w\) is the window size, and \(t\) is the highest polynomial order used for smoothing. In the second step, the denoised data \(\overline{X}\) is passed through a TCN consisting of two residual blocks, which extract relevant temporal features. The empirical hyperparameters for each residual block are used. \[\text{L}=RB\big{(}\overline{X},\,k,\,d\big{)}, \tag{9}\]  
where \(RB()\) represents the residual block function of the TCN, \(k\) is the kernel size, and \(d\) is the dilation factor. In the third step, the extracted feature set \(L\) is input into the LSTM network, which captures long-term dependencies and outputs \(h_{t}\) at time \(t\) according to Equations (10)-(14). The hyperparameters for the LSTM layer were also empirical values. \[i_{t}=\sigma(W_{i}\cdot[h_{t-1,L_{t}}]+b_{i}), \tag{10}\]  
\[f_{t}=\sigma\Big{(}W_{f}\cdot[h_{t-1,L_{t}}]+b_{f}\Big{)}, \tag{11}\]  
where \(i_{t}\) and \(f_{t}\) are the computed values of the input and forget gates, respectively. \(W_{i}\) and \(W_{f}\) are weight matrices, \(h_{t-1}\) is the output of the previous cell, \(L_{t}\) is the input at time \(t\), and \(b_{i}\) and \(b_{f}\) are bias vectors. The next step is to update the cell state \(C_{t}\) via Equation (12). \[C_{t}=f_{t}\cdot C_{t-1}+i_{t}\cdot(tanh(W_{c}\cdot[h_{t-1},\,L_{t}]+b_{c})), \tag{12}\]  
where \(W_{c}\) is the weight matrix, \(b_{c}\) is the bias vector, and \(C_{t-1}\) is the previous cell. The output gate \(o_{t}\) and the final output \(h_{t}\) are represented as follows:  
\[o_{t}=\sigma(W_{o}\cdot[h_{t-1,L_{t}}]+b_{o}) \tag{13}\]  
\[h_{t}=o_{t}\cdot\text{tanh}\left(C_{t}\right), \tag{14}\]  
where \(W_{o}\) is the weight matrix, and \(b_{o}\) is the bias vector. Figure 4:0 Structure of the TCN–LSTM hybrid model with a Savitzky–Golay (SG) filter. The output \(h_{t}\) from the LSTM layer is then passed through a fully connected layer with a rectified linear unit (ReLU) activation function to generate the output \(z_{t}\). Figure 4:1  
where _relu_ is the ReLU activation function, \(v\) is the weight matrix, and _bias_ refers to the bias vector. The fully connected layer output \(z_{t}\) is input into the output layer to generate the prediction value \(y_{t}\). Figure 4:2  
where _linear_() is the linear function, \(u\) is the weight parameter of the fully connected layer, and \(q\) is the bias parameter. The TCN-LSTM network for CO\({}_{2}\) emission prediction using engine data was configured according to the specifications in Figure 4:3 The architecture includes four temporal convolutional layers and two bidirectional LSTM layers, along with an attention mechanism to focus on critical patterns within the training data. The optimal parameters--such as the number of filters, kernel size, and dilation rate of the TCN blocks--were determined through multiple experiments. Table 8 provides a detailed breakdown of the parameters across all layers. To maintain optimal performance and prevent overfitting, we implemented a learning rate schedule and early stopping during training.