## 3 Results
### Experimental Comparison
#### 3.3.2 Model Evaluation
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Site** & **Bi-LSTM** & **Bi-LSTM-Attention*** & **Transformer*** & **GRU*** & **Our Model** \\ \hline
**1** & 0.87433 & 0.88881 & 0.96347 & 0.96512 & 0.98343 \\
**2** & 0.86245 & 0.89209 & 0.94456 & 0.95924 & 0.98281 \\
**3** & 0.86665 & 0.88945 & 0.95437 & 0.95887 & 0.99022 \\
**4** & 0.86554 & 0.89755 & 0.94864 & 0.96476 & 0.98677 \\
**5** & 0.87221 & 0.88235 & 0.95432 & 0.95643 & 0.98043 \\
**6** & 0.86449 & 0.89112 & 0.96543 & 0.96323 & 0.97864 \\
**7** & 0.87423 & 0.87897 & 0.94552 & 0.94888 & 0.98221 \\
**8** & 0.86999 & 0.88511 & 0.94897 & 0.95732 & 0.97431 \\
**9** & 0.85422 & 0.87553 & 0.94533 & 0.95345 & 0.96943 \\
**10** & 0.86131 & 0.88555 & 0.95342 & 0.94876 & 0.97853 \\
**11** & 0.83511 & 0.82132 & 0.94886 & 0.95443 & 0.97432 \\
**12** & 0.85889 & 0.89181 & 0.96345 & 0.93887 & 0.97866 \\
**13** & 0.86432 & 0.87883 & 0.93995 & 0.96342 & 0.97562 \\
**14** & 0.85764 & 0.86994 & 0.94337 & 0.94543 & 0.97786 \\
**15** & 0.86312 & 0.87443 & 0.95432 & 0.95116 & 0.97434 \\ \hline \end{tabular}  
* References [33; 34; 35] for the experimental model method.  
\end{table} 
Table 2: Comparison of \(R^{2}\) between different models. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Site** & **Bi-LSTM** & **Bi-LSTM-Attention** & **Transformer** & **GRU** & **Our Model** \\ \hline
**1** & 2.51426 & 2.07663 & 0.61428 & 0.44754 & 0.26617 \\
**2** & 2.38502 & 1.87753 & 0.51778 & 0.37282 & 0.28363 \\
**3** & 2.50762 & 1.88290 & 0.63639 & 0.39435 & 0.30016 \\
**4** & 2.62975 &  
To visualize the MAE and RMSE values, we plotted the MAE and RMSE values to show the trend of changes. The Figures 11 and 12 present the trend of MAE and RMSE for six models after conducting experiments on data from 30 temperature measurement points. The models, labeled as Model 1 to Model 6, are BiLSTM, BiLSTM-Attention, Transformer, GRU, CNN-BiLSTM-Attention, and Our model, respectively. From Figures 11 and 12, it can be observed that Models 1, 2, and 3 exhibited significant fluctuations, while Models 3, 4, 5, and 6 showed much smaller fluctuations. Smaller fluctuation amplitudes indicate that the models are less sensitive to different data, have strong robustness against interference, and are better able to adapt to various data sets. Our model, in particular, has the lowest values for both MAE and RMSE, with virtually no fluctuations. A more intuitive comparison of the various parameters of the models is presented in Table 5, which summarizes the average values for 30 temperature measurement points. Overall, our model performed at a higher level across all indicators, resulting in better predictive performance. Thirdly, we randomly selected five sets of results for residual analysis. The residual distribution plots for the six models are shown in Figure 13, and the residual histograms are shown in Figure 14. It can be observed that there are no outliers, with all models' residuals being within \(\pm 0.5\). Our model and the CNN-BiLSTM-Attention model narrowed the residual range to between \(\pm 0.25\). The histograms indicate that the residuals of all models are nearly normally distributed. Therefore, we conducted the Anderson-Darling test for normality. The results are presented in Table 6.  
Based on the principle of the Anderson-Darling normality test, the models whose residuals are closest to a normal distribution are those with statistics less than the critical values at all significance levels. This indicates that their residuals conform to a normal distribution across all levels. According to the Table 6, the GRU model's residuals do not conform to a normal distribution at the 15.0%, 10.0%, and 5.0% levels, only conforming at the 2.5% and 1.0% levels. The remaining five models have statistics below the critical values at all significance levels, indicating that their residuals conform to a normal distribution at all significance levels. Figure 14: Histogram of residual distribution for six models. Figure 13: Residual distribution of six models.