## 4 Validation and Comparison
### Predicted Results  
Table 14 shows the performance of different path loss prediction methods on the test set. According to the data, the neural network integration model optimized by WOA output weights, proposed in this paper, performs exceptionally well in predicting the path loss of HSR seats. Compared to CI, CNN, RNN, GNN, Transformer, AutoML, and the ensemble \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Optimal Value** \\ \hline Number of Particles & 50 \\ Inertia Weight & 0.7 \\ Cognitive Coefficient & 1.4 \\ Social Coefficient & 1.4 \\ Maximum Number of Iterations & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Parameters for PSO optimization. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Regression Method** & **Parameter** & **Setting** \\ \hline \multirow{8}{*}{Stochastic Gradient Descent} & Regularization Type & L1 + L2 \\  & L1 Regularization Ratio & 75\% \\  & L2 Regularization Ratio & 25\% \\ \cline{2-3}  & Regularization Penalty & None \\ \cline{2-3}  & Initial Learning Rate & 0.1 \\ \cline{2-3}  & Learning Rate Strategy & Gradual decay \\ \cline{2-3}  & Learning Rate Decay & Controlled factor \\ \cline{2-3}  & Intercept Calculation & Enabled \\ \cline{2-3}  & Loss Function Sensitivity & Low error sensitivity \\ \hline \multirow{4}{*}{Random Forest} & Number of Trees & 100 \\ \cline{2-3}  & Feature Ratio & 5\% features \\ \cline{1-1} \cline{2-3}  & Minimum Samples per Leaf & 7 \\ \cline{1-1} \cline{2-3}  & Minimum Samples for Split & 17 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Key parameter settings of the regression methods used in AutoML tool. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Optimal Value** \\ \hline Population Size & 50 \\ Crossover Probability & 0.8 \\ Mutation Probability & 0.01 \\ Number of Generations & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Parameters for GA optimization. models with GA-Optimized and PSO-Optimized output weights, the proposed model significantly outperforms the others in four key metrics: RMSE, MAE, MAPE, and R\({}^{2}\). To further assess the robustness of the proposed model, we select representative data points from location E, with the receiving antenna positioned at height III. The prediction results are compared and analyzed against those of the CI model, CNN, Transformer, AutoML, and the ensemble model optimized using the PSO. As illustrated in Figure 12, the legend provides detailed annotations, where Ensemble (PSO Opt.) represents the ensemble model optimized using the PSO, and Ensemble (WOA Opt.) denotes the ensemble model optimized using the WOA. Additionally, the performance metrics for each method, calculated based on their predictions relative to the RT values, are displayed in the legend for clarity. As shown in the figure, the WOA-optimized ensemble model stands out, with key performance metrics of R\({}^{2}\) = 0.46, RMSE = 5.79 dB, and MAPE = 3.96%, all of which outperform the other models. Furthermore, the model exhibits minimal fluctuation in prediction curves across different carriages, demonstrating excellent robustness. Unlike other models, which show significant deviation from the actual values or poor stability, this model maintains consistent performance despite changes in carriage position, highlighting its superior ability to withstand environmental interference and maintain stability across different spatial locations. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Method** & **RMSE (dB)** & **MAE (dB)** & **MAPE (\%)** & **R\({}^{2}\)** \\ \hline CI & 8.39 & 6.82 & 6.04 & 0.24 \\ CNN & 7.39 & 5.53 & 4.74 & 0.41 \\ RNN & 7.85 & 6.31 & 5.55 & 0.34 \\ GNN & 8.30 & 6.61 & 5.78 & 0.26 \\ Transformer & 7.34 & 5.97 & 5.25 & 0.42 \\ AutoML & 7.01 & 5.53 & 4.82 & 0.47 \\ Ensemble Model with GA-Optimized & 7.25 & 5.78 & 5.02 & 0.43 \\ Ensemble Model with PSO-Optimized & 7.10 & 5.61 & 4.85 & 0.45 \\ Ensemble Model with WOA-Optimized & 6.92 & 5.37 & 4.67 & 0.48 \\ \hline \hline \end{tabular}
\end{table}