## 3 Results
### Comparison with Other Models  
In this paper, we constructed the RF-LSTM and RF-TPE-LSTM prediction models to investigate the evolution of CO\({}_{2}\) concentrations in classrooms under different model applications using time series prediction hotspot research methods. To explore the generalizability of the impact of influencing factor selection on the prediction accuracy, after selecting the hyperparameters for the RF-LSTM model, we employed multiple model algorithms for comparison. We used the recurrent neural network (RNN), back-propagation neural network (BPNN), and LSTM models, along with another hyperparameter optimization framework, Optuna, to construct the Optuna-LSTM model. We trained on all the environmental factors separately. Subsequently, we adopted the RF algorithm for these models to screen the influencing factors as model inputs, resulting in the RF-RNN, RF-BPNN, RF-ARIMAX, RF-LSTM, and RF-Optuna-LSTM models. The results are shown in Table 7. The training results of the RF-TPE-LSTM model have been added at the end of this table for comparison.  
As shown in Table 7, compared with the _MAE_, _RMSE_, _MAPE_, and \(R^{2}\) values achieved using the RNN model, after constructing the RF-RNN model to screen the influencing factors, the proposed model's error values were reduced by 17.23%, 6.97%, and 17.51%, respectively, and the goodness of fit, \(R^{2}\), improved by 1.95%. When comparing the MAE, _RMSE_, _MAPE_, and \(R^{2}\) values achieved using the BPNN with those achieved using the RF-BPNN model, the latter reduced the _MAE_ by 25.01%, the _RMSE_ by 13.63%, and the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & _MAE_ & _RMSE_ & _MAPE_ & \(R^{2}\) \\ \hline RNN [39] & 10.27 & 19.94 & 2.17\% & 87.38\% \\ BPNN [40] & 11.28 & 18.49 & 0.92\% & 93.53\% \\ LSTM [23] & 16.70 & 11.73 & 2.49\% & 91.17\% \\ Optuna–LSTM [41] & 5.71 & 9.81 & 1.19\% & 96.79\% \\ RF–RNN & 8.50 & 18.55 & 1.79\% & 89.08\% \\ RF-BPNN & 8.45 & 15.97 & 0.63\% & 95.11\% \\ RF-LSTM & 8.27 & 11.71 & 1.78\% & 95.66\% \\ RF–Optuna–LSTM & 4.27 & 8.20 & 0.89\% & 97.76\% \\ RF-TPE-LSTM & 2.96 & 5.54 & 0.60\% & 98.02\% \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of the prediction accuracies of different models.  
_MAPE_ by 31.52%, respectively, while improving the \(R^{2}\) by 1.69%. Similarly, in terms of the results of the LSTM model constructed by inputting nine feature values obtained from our previous experiments and the RF-LSTM model constructed by screening the influencing factors, the latter significantly reduced the _MAE_ by 50.48% and the _RMSE_ and _MAPE_ by 0.17% and 28.51%, respectively, while improving the \(R^{2}\) by 4.92%. Additionally, we used another hyperparameter optimization framework, Optuna, based on the LSTM algorithm, and we constructed the Optuna-LSTM and RF-Optuna-LSTM models. In terms of the training results of the two models, the latter reduced the _MAE_ by 25.22%, the _RMSE_ by 16.41%, and the _MAPE_ by 25.21% while improving the \(R^{2}\) by 1.00%.  
Furthermore, among the state-of-the-art methods (RNN [39], BPNN [40], LSTM [23], and Optuna-LSTM [41]) presented in Table 7, the Optuna-LSTM achieved the best results. However, compared with the Optuna-LSTM, the proposed RF-TPE-LSTM demonstrated significantly improved performance. Specifically, it reduced the _MAE_ by 48.16% and the _RMSE_ and _MAPE_ by 43.52% and 49.58%, respectively, while enhancing the \(R^{2}\) by 1.27%.  
In conclusion, the above results show that the influencing factor screening method proposed in this paper is suitable for multiple prediction models and improves the prediction accuracy of these models. These results also further validate the need to screen influencing factors. Finally, we present the RF-TPE-LSTM model proposed in this paper. The results indicate that the proposed model has the best predictive ability and the highest degree of fit, thus verifying that the RF-TPE-LSTM model we constructed has a certain degree of optimality.