# Short-Term Power Load Forecasting Using an Improved Model Integrating GCN and Transformer
## 4 Analysis of Experimental Results
### Comparative Experiment
#### 4.5.2 Ettm1 Dataset Experiment  
Table 4 comprehensively compares the RMSE, MAE, and R\({}^{2}\) performances of MSGNet-MLLA-Transformer and the benchmark model under different prediction step sizes (1, 3, 6, and 12 steps) for the ETTm1 dataset. In the visualization of the results, we present the models other than ARIMA, which have relatively small differences. Combined with the analysis in Figures 10-13, it can be seen that in the short- and medium-term predictions (steps 1, 3, and 6), all indicators of this model are superior to traditional models, such as GRU and TCN (with a maximum increase of 1.6% in R\({}^{2}\)), while in the 12-step long-term prediction, the accuracy is comparable to that of the MSGNet prototype model. This phenomenon indicates that for the ETTm1 dataset, capturing the multi-scale spatio-temporal coupling characteristics of power load (such as minute-level fluctuations and hour-level periods) contributes significantly more to the prediction accuracy than the long-term reliance on modeling capabilities. This explains why MSGNet and its improved MSGNet-MLLA-Transformer (with stronger multi-scale feature extraction capabilities) have become the optimal combination. Although the overall performance of the MrCAN model is not satisfactory, its spatial attention mechanism is still valuable in capturing regional correlations.  
Figure 9: Comparison chart fitting the 12-step prediction experimental model of the ETTh1 dataset, listed as (**a**) GRU; (**b**) TCN; (**c**) GRU-Attention; (**d**) TCN-Attention; (**e**) MrCAN; (**f**) MSGNet; and (**g**) Ours.  
_Appl. Sci._**2025**, _15_, 7003  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Metrics**} & \multirow{2}{*}{**Method**} & \multicolumn{5}{c}{**Predicted Length**} \\ \cline{3-6}  & & **1** & **3** & **6** & **12** \\ \hline \multirow{6}{*}{RMSE} & ARIMA & 1.432 & 2.857 & 3.586 & 4.338 \\  & GRU & 0.460 & 0.640 & 0.751 & 0.951 \\  & TCN & 0.385 & 0.690 & 0.879 & 0.999 \\  & GRU-Attention & 0.510 & 0.658 & 0.894 & 0.963 \\  & TCN-Attention & 0.678 & 0.857 & 0.943 & 0.956 \\  & MrCAN & 0.378 & 0.606 & 0.728 & 0.913 \\  & MSGNet & 0.365 & 0.514 & 0.735 & 0.855 \\  & Ours & 0.346 & 0.470 & 0.613 & 0.855 \\ \hline \multirow{6}{*}{MAE} & ARIMA & 1.217 & 2.625 & 3.398 & 4.164 \\  & GRU & 0.370 & 0.518 & 0.577 & 0.719 \\  & TCN & 0.292 & 0.551 & 0.642 & 0.731 \\  & GRU-Attention & 0.378 & 0.500 & 0.670 & 0.710 \\  & TCN-Attention & 0.580 & 0.640 & 0.799 & 0.704 \\  & MrCAN & 0.283 & 0.471 & 0.560 & 0.676 \\  & MSGNet & 0.273 & 0.352 & 0.531 & 0.611 \\  & Ours & 0.252 & 0.320 & 0.415 & 0.603 \\ \hline \multirow{6}{*}{R\({}^{2}\)} & ARIMA & 0.736 & 0.682 & 0.545 & 0.331 \\  & GRU & 0.966 & 0.955 & 0.942 & 0.913 \\  & TCN & 0.970 & 0.949 & 0.935 & 0.906 \\  & GRU-Attention & 0.958 & 0.953 & 0.932 & 0.908 \\  & TCN-Attention & 0.951 & 0.938 & 0.925 & 0.923 \\  & MrCAN & 0.971 & 0.959 & 0.945 & 0.920 \\  & MSGNet & 0.972 & 0.967 & 0.942 & 0.928 \\  & Ours & 0.979 & 0.971 & 0.958 & 0.928 \\ \hline \hline \end{tabular}
\end{table}
Table 4: RMSE, MAE, \(\mathbf{R^{2}}\) evaluation metrics of the ETTm1 dataset.  
Figure 10: _Cont._  
Figure 11: _Cont._  
Figure 10: Comparison chart fitting the 1-step prediction experimental model of the ETTm1 dataset, listed as (**a**) GRU; (**b**) TCN; (**c**) GRU-Attention; (**d**) TCN-Attention; (**e**) MrCAN; (**f**) MSGNet; and (**g**) Ours.  
Figure 11: Comparison chart fitting the 3-step prediction experimental model of the ETTm1 dataset, listed as (**a**) GRU; (**b**) TCN; (**c**) GRU-Attention; (**d**) TCN-Attention; (**e**) MrCAN; (**f**) MSGNet; and (**g**) Ours.  
Figure 12: _Cont._  
Figure 12: Comparison chart fitting the 6-step prediction experimental model of the ETTm1 dataset, listed as (**a**) GRU; (**b**) TCN; (**c**) GRU-Attention; (**d**) TCN-Attention; (**e**) MrCAN; (**f**) MSGNet; and (**g**) Ours.  
Figure 13: _Cont._