## 3 Results
### Experimental Comparison
#### 3.3.2 Model Evaluation  
The model evaluation experiment consists of three stages. In the first stage, we conducted ablation experiments on the pre-optimized model to demonstrate the superiority of the optimized model. In the second stage, we compared different types of neural network architectures commonly used for handling time series data using the same test data as in Section 3.3.1. In the third stage, we performed residual analysis to observe the presence of any outliers. Residual analysis was conducted on five randomly selected datasets out of 30. Firstly, ablation experiments were conducted on the pre-optimized model to demonstrate the superiority of the optimized model. Similarly, we selected data from the first 15 temperature measurement points for display, as shown in Table 2 (The complete experimental results are in Table A2 of the Appendix A). It can be observed from Table 2 that the \(R^{2}\) values of all models are around 0.9, indicating that these models all have certain predictive capabilities. The model proposed in this paper achieved the highest \(R^{2}\) score, while the predictive performance of the remaining models gradually decreased, indicating that optimization of the model was effective. Secondly, different types of neural network architectures commonly used for handling time series data were compared. Transformer, as an excellent model in natural language processing, also exhibits excellent performance in time series data processing [32]. Meanwhile, GRU, as a variant of LSTM, combines the forget gate and the input gate into a single \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Site**} & \multicolumn{2}{c}{**CNN-BiLSTM-Attention**} & \multicolumn{3}{c}{**CPO-CNN-BiLSTM-Attention**} \\ \cline{2-7}  & \(R^{2}\) & \(MAE\) & \(RMSE\) & \(R^{2}\) & \(MAE\) & \(RMSE\) \\ \hline
1 & 0.966 & 0.219 & 0.344 & 0.983 & 0.182 & 0.266 \\
2 & 0.957 & 0.223 & 0.304 & 0.983 & 0.194 & 0.284 \\
3 & 0.946 & 0.197 & 0.307 & 0.990 & 0.186 & 0.300 \\
4 & 0.955 & 0.231 & 0.354 & 0.987 & 0.192 & 0.274 \\
5 & 0.954 & 0.215 & 0.293 & 0.980 & 0.186 & 0.264 \\
6 & 0.958 & 0.190 & 0.345 & 0.979 & 0.187 & 0.284 \\
7 & 0.961 & 0.212 & 0.345 & 0.982 & 0.197 & 0.267 \\
8 & 0.958 & 0.226 & 0.288 & 0.974 & 0.192 & 0.299 \\
9 & 0.950 & 0.217 & 0.298 & 0.969 & 0.183 & 0.292 \\
10 & 0.953 & 0.229 & 0.366 & 0.979 & 0.197 & 0.284 \\
11 & 0.951 & 0.224 & 0.289 & 0.974 & 0.181 & 0.271 \\
12 & 0.965 & 0.202 & 0.338 & 0.979 & 0.186 & 0.288 \\
13 & 0.940 & 0.210 & 0.349 & 0.976 & 0.188 & 0.276 \\
14 & 0.945 & 0.193 & 0.304 & 0.978 & 0.187 & 0.299 \\
15 & 0.950 & 0.231 & 0.320 & 0.974 & 0.194 & 0.268 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The impact of optimization algorithms on the performance metrics of model prediction results. update gate and also plays a significant role in time series data processing. According to the data in Table 2, both the Transformer and GRU models achieved high levels of performance in temperature prediction. However, the proposed model in this paper achieved even better performance, with \(R^{2}\) scores all above 0.97. We also conducted experiments to compare MAE and RMSE values. For the RMSE and MAE values of each model in the temperature prediction experiments across 30 temperature measurement points, we still display data from the first 15 measurement points (The complete experimental results are in Tables A3 and A4 of the Appendix A). Observing Tables 3 and 4, it is evident that our model has the lowest mean absolute error (MAE) and root mean square error (RMSE) values on average.