## 4 Experiments
### Experimental Results

Table 6: Data ranges for selected high-volatility regions. Figure 9: Selection process for five high-volatility regions. gradients but adjusts through a feedback-driven process, making the model more robust to these issues. * Enhanced Interpretability: The supervision mechanism offers higher interpretability. Its dynamic structural adjustments can reveal the relationship between data features and model behavior, providing a more transparent and efficient learning process. Figure 10 illustrates the forecasting performance of each model in Region 1. In the forecast plots for Region 1, the LSTM-RVFL model exhibits a significant deficiency in forecasting performance compared to other models. The data in this region are highly volatile, which results in most models being unable to accurately predict the changing trend of the power load at the turning points. However, the LSTM-SCN model effectively captures the changes in power load, with its predicted curve closely matching the actual curve. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Region Name** & **Model** & **RMSE** & **MAE** & **MAPE** \\ \hline \multirow{6}{*}{Region 1} & LSTM & 69.503 & 56.357 & 0.723\% \\  & BiLSTM & 43.366 & 34.632 & 0.453\% \\  & GRU & 49.503 & 40.009 & 0.511\% \\  & SCN & 82.894 & 69.422 & 0.894\% \\  & CNN-LSTM & 48.532 & 36.188 & 0.454\% \\  & LSTM-RVFL & 120.833 & 111.067 & 1.391\% \\  & LSTM-SCN (our) & 5.465 & 4.851 & 0.062\% \\ \hline \multirow{6}{*}{Region 2} & LSTM & 77.431 & 55.698 & 0.666\% \\  & BiLSTM & 63.474 & 46.654 & 0.566\% \\  & GRU & 47.208 & 36.597 & 0.451\% \\  & SCN & 58.148 & 47.428 & 0.591\% \\  & CNN-LSTM & 52.001 & 41.473 & 0.517\% \\  & LSTM-RVFL & 158.725 & 149.760 & 1.853\% \\  & LSTM-SCN (our) & 7.285 & 5.095 & 0.062\% \\ \hline \multirow{6}{*}{Region 3} & LSTM & 66.255 & 48.467 & 0.632\% \\  & BiLSTM & 48.305 & 36.094 & 0.477\% \\  & GRU & 53.502 & 43.131 & 0.573\% \\  & SCN & 86.465 & 81.428 & 0.794\% \\  & CNN-LSTM & 53.183 & 41.249 & 0.542\% \\  & LSTM-RVFL & 154.871 & 146.592 & 1.947\% \\  & LSTM-SCN (our) & 6.104 & 6.104 & 0.057\% \\ \hline \multirow{6}{*}{Region 4} & LSTM & 109.402 & 93.140 & 1.262\% \\  & BiLSTM & 56.048 & 37.506 & 0.506\% \\  & GRU & 71.450 & 54.467 & 0.733\% \\  & SCN & 93.136 & 82.856 & 1.492\% \\  & CNN-LSTM & 42.403 & 30.666 & 0.412\% \\  & LSTM-RVFL & 156.803 & 148.207 & 2.012\% \\  & LSTM-SCN (our) & 7.452 & 5.932 & 0.080\% \\ \hline \multirow{6}{*}{Region 5} & LSTM & 95.331 & 84.480 & 1.166\% \\  & BiLSTM & 41.727 & 30.050 & 0.406\% \\ \cline{1-1}  & GRU & 60.292 & 46.030 & 0.625\% \\ \cline{1-1}  & SCN & 79.458 & 69.475 & 0.916\% \\ \cline{1-1}  & CNN-LSTM & 58.118 & 45.542 & 0.617\% \\ \cline{1-1}  & LSTM-RVFL & 112.343 & 104.097 & 1.418\% \\ \cline{1-1}  & LSTM-SCN (our) & 7.175 & 5.976 & 0.081\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparative performance indicators of models across different regions. Figure 11 depicts the forecasting performance of each model in Region 2. Although the data volatility in Region 2 is lower than in Region 1, the forecast curves of all models except the LSTM-SCN deviate at the data turning points, indicating a deficiency in capturing the data trend. The forecasting curve of the LSTM-SCN model is essentially consistent with the actual curve, demonstrating its superior predictive capability. Figures 12-14 illustrate the forecasting performance of each model in regions 3, 4, and 5, each of which represents distinct high-volatility characteristics. In these regions, the LSTM-SCN model consistently demonstrates superior predictive performance, with its predicted curve closely aligned with the actual curve and effectively capturing the underlying data trends. This result corroborates findings from the first two regions, providing further evidence of the LSTM-SCN model's robustness and dependability in accurately forecasting the power load in high-volatility regions.