## 4 Experimental Results and Analyses
### Analysis of BP Neural Network Prediction Results  
An empirical formula was used to determine the number of neurons in the hidden layer of the neural network for this experiment. This formula offers an interval range for the number of neurons in the hidden layer of the neural network. The empirical formula is shown below:  
\[H=\sqrt{m+n}+a \tag{15}\]  
where \(m\) and \(n\) are the number of input and output neurons, respectively, and \(a\) is a constant between 1 and 10. The experiments in this paper have 3 input neurons and 1 output neuron, so the number of hidden layer neurons should be between 3 and 12. The dimensionality-reduced data is imported into the procedure written using Matlab R2021b for solving the best-hidden layer of the neural network. The optimum number of hidden layer neurons for this experiment was solved to be 10. Subsequently, the neural network prediction module in Matlab R2021b was used for prediction, the training method was the commonly used Levenberg-Marquardt algorithm, and the hidden layer activation function was the Tanh function. 75% of the dataset is set as the training set and 25% as the test set. The results of the network training are shown in Figure 5. \begin{table}
\begin{tabular}{c c c c} \hline
**Year** & **Factor\_1** & **Factor\_2** & **Factor\_3** \\ \hline
2010 & 0.00314 & 0.07949 & \(-1.53201\) \\
2011 & 0.81866 & \(-0.97357\) & \(-0.19903\) \\
2012 & 1.10003 & \(-0.87051\) & \(-0.33696\) \\
2013 & 1.13923 & \(-1.05458\) & \(0.44497\) \\
2014 & 1.72081 & \(-0.87636\) & \(-0.38454\) \\
2015 & 1.37638 & \(-0.63810\) & \(0.27886\) \\
2016 & 0.78650 & 0.13559 & \(0.41601\) \\
2017 & 0.72043 & 0.44500 & \(0.60881\) \\
2018 & \(-0.17869\) & 0.32164 & \(3.09303\) \\
2019 & 0.14649 & 1.68686 & \(0.27305\) \\
2020 & 0.60653 & 2.38330 & \(-1.50996\) \\
2021 & \(-0.00263\) & 2.21911 & \(0.79533\) \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._  
Figure 5: Error decline plot for LM training algorithm. During the training process using BR as the training algorithm and LeCun Tanh function as the activation function of the neural network, due to the increase in the complexity of the training algorithm and activation function, it results in the number of training iterations often exceeding the maximum number of iterations set, and the prediction accuracy of its network exists unstable from time to time. In order to improve the above situation, this paper uses genetic algorithm to optimize the initial transfer weights and thresholds of the neural network. This makes the network prediction accuracy increase while reducing the number of training iterations and improving the stability of the network. A comparison of the experimental results of the optimized neural network with the BP neural network (both using BR as the training algorithm and LeCun Tanh as the hidden layer activation function) is shown in Figure 9 and Table 8.  
The various evaluation parameters of the prediction model are shown in Table 9. \begin{table}
\begin{tabular}{c c c} \hline
**Evaluation Indicators** & **Tanh Activation** & **LeCun Tanh Activation** \\ \hline SSE & 0.04450 & 0.02034 \\ MAE & 0.05828 & 0.05616 \\ MSE & 0.00890 & 0.00407 \\ RMSE & 0.09434 & 0.06378 \\ MAPE & 6.85\% & 5.53\% \\ Accuracy Rate & 93.15\% & 94.47\% \\ \hline \end{tabular}
\end{table} 
Table 7: Evaluation of Tanh function and LeCun Tanh function prediction results. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Year** & **Actual Value** & \multicolumn{2}{c}{**BPNN**} & \multicolumn{2}{c}{**GA-BPNN**} \\ \hline  & & **Fitted** & **Errors** & **Fitted** & **Errors** \\ \hline
2017 & 0.4656 & 0.5177 & 0.0521 & 0.476 & 0.0103 \\
2018 & 0.9272 & 0.8919 & \(-\)0.0353 & 0.8932 & \(-\)0.0340 \\
2019 & 1.2675 & 1.3753 & 0.1078 & 1.4013 & 0.1339 \\
2020 & 1.9027 & 1.8365 & \(-\)0.0661 & 1.8507 & \(-\)0.0520 \\
2021 & 2.7883 & 2.7689 & \(-\)0.0195 & 2.7539 & \(-\)0.0344 \\ \hline \end{tabular}
\end{table} 
Table 8: Comparison of BPNN and GA-BPNN prediction results. Figure 9: Comparison of BPNN and GA-BPNN prediction results.