# A Hybrid Deep Learning-Based Load Forecasting Model for Logical Range
## 3 Results
### Performance Analysis  
To evaluate the performance of the proposed GCSG model in the Logical Range scenario, we conducted comparative experiments with several widely used deep learning models, including CNN, LSTM, GRU, LSTM-ED [25], BiLSTM [26], LSTM-GRU [27], and ConvLSTM [28] models. For a fair comparison, each baseline model was individually fine-tuned to achieve its best performance through grid search. All models were trained and evaluated using the same dataset splits and experimental conditions. The specific hyperparameter settings for each model, including hidden size, learning rate, number of training epochs, batch size, dropout rate, number of layers, and optimizer, are summarized in Table 2.  
(1)Input window size analysis. Figure 5 displays the performance metrics of different models under varying input window sizes \(w\) using the prediction step \(d=1\) in the Logical Range. As shown in Figure 5a, the GCSG model achieved the highest \(R^{2}\) values, consistently above 0.85 for \(w\) values between 16 and 40. The BiLSTM, ConvLSTM, LSTM-ED, and LSTM-GRU models (all LSTM variants) followed, with \(R^{2}\) scores of 0.83-0.85. The GRU and LSTM models demonstrated comparable performance (\(R^{2}\approx\) 0.80) due to their single-model architectures. The CNN showed the lowest \(R^{2}\) values (0.75-0.77), potentially due to its parameters and structural configuration. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Model** & **Hidden Size** & **LR** & **Epochs** & **Batch Size** & **Dropout** & **Layers** & **Optimizer** \\ \hline CNN & 100 & 0.001 & 100 & 50 & 0.3 & 1 & [PERSON] \\ LSTM & 10 & 0.1 & 50 & 50 & 0.3 & 1 & [PERSON] \\ GRU & 64 & 0.001 & 50 & 50 & 0.3 & 1 & [PERSON] \\ LSTM-ED & 64 & 0.0001 & 50 & 50 & 0.2 & 1 & [PERSON] \\ BiLSTM & 10 & 0.01 & 50 & 50 & 0.01 & 1 & [PERSON] \\ LSTM-GRU & 64 & 0.0001 & 50 & 50 & 0.4 & 1 & [PERSON] \\ ConvLSTM & 64 & 0.001 & 50 & 50 & 0.01 & 1 & [PERSON] \\ GCSG & 32 & 0.0001 & 100 & 100 & 0.01 & 2 & [PERSON] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model parameter configurations. In particular, Figure 4(a) demonstrates the fluctuation degree of \(R^{2}\) scores across different \(w\) values for each model in the Logical Range, with the GCSG model exhibiting the most stable performance. This indicates the GCSG model's superior robustness when adapting to varying \(w\) values. Figure 4(b),c present the MAE and MSE metrics of each model, respectively. The error trends consistently align with the \(R^{2}\) results in Figure 4(a). The GCSG model achieves the lowest errors, followed by the BiLSTM, ConvLSTM, LSTM-ED, and LSTM-GRU models, with marginally higher error rates. The GRU and LSTM models showed intermediate error levels, while the CNN yielded the highest number of errors. In summary, Figure 5 confirms that the GCSG model delivers optimal load forecasting accuracy across different input window sizes \(w\) in the Logical Range, outperforming both combined models (BiLSTM, ConvLSTM, LSTM-ED, LSTM-GRU) and traditional single models (LSTM, GRU, CNN). (2) Prediction step analysis. According to the results presented in Figure 5, an input window size \(w\) of 36 was chosen based on the average \(R^{2}\), MAE, and MSE values, and the prediction step \(d\) was varied from 1 to 29 in order to compare the prediction accuracy of the various models, as shown in Figure 6.  
Figure 6 demonstrates that the GCSG model consistently achieved superior load forecasting accuracy across different prediction steps \(d\) in the Logical Range compared to  
Figure 5: Comparison of models under different input window sizes. Figure 6: Comparison of models under different prediction steps. the other models. As shown in Figure 5(a), the combined models (ConvLSTM, LSTM-ED, and LSTM-GRU) exhibited higher \(R^{2}\) values than single models (LSTM, GRU, and CNN). Among all combined models, the GCSG model maintained the highest \(R^{2}\) values.