## 3 Experiments
### Visualization Experiments  
In order to conduct a thorough performance comparison between the proposed method and the baselines, this part visualizes the forecasting results alongside the actual results of the test set from the dataset [29]. This experiment focused explicitly on different sensors and time spans of 24 h and 48 h, extracting and analyzing the forecasting results for comparison. Please refer to Figure 6 for further details.  
The results shown in Figure 6 indicate that both the baseline models and EG-DGATN performed similarly in the 15-min forecasting task. A detailed analysis shows that the EG-DGATN exhibits a stronger correlation with the Ground Truth. As the granularity of the forecasting task increased, all models demonstrated a decrease in their ability to predict the Ground Truth accurately. The baseline models, in particular, displayed significant deviations from the local peaks, indicating a limited learning capacity for long-term dependencies. In contrast, the EG-DGATN consistently and effectively fits the Ground Truth curve at different forecasting granularities. This demonstrates its superior performance compared to the baseline models.  
To further validate the EG-DGATN model and elucidate the significance of \(R^{2}\) for evaluating the model, this study carried out a visual analysis experiment on the \(R^{2}\). The outcomes of this experiment are illustrated in Figure 7.  
Figure 7a-c presents the predictive accuracy of three models, EG-DGATN, ASTGCN, and STGCN, using data at 15-min intervals. Notably, the EG-DGATN outperformed the others with an \(R^{2}\) score of 0.97, signifying its capability to explain 97% of the variance in the prediction outcomes. This superiority is depicted in Figure 7a, where the discrete data points cluster more closely together, as opposed to outliers that are significantly distanced from the regression line. As we progress from Figure 7b,c, it is observable that the scatter of data points broadens with the increase in the \(R^{2}\). Concurrently, outliers appear more distant from the precise regression line, highlighting variations in model performance and prediction accuracy. Figure 7d shows the results of dynamic graph generation for the  
five graph generation layers in the three prediction spans. Compared to GraphWave, which also utilizes a self-learning adjacency matrix, the sparsified dynamics graph employed by the EG-DGATN is better equipped to extract pertinent nodes efficiently. This can be seen from the heatmap of neighbor matrices learned by the model before binarization, with fewer highlighted color blocks. The model avoids redundant data by selectively extracting information from a limited number of neighboring nodes.  
Figure 6: _Cont_.  
Figure 6: **(a)** Sensor #0 partial test set predictions for 15 min (3 time steps). **(b)** Sensor #1 partial Test set predictions for 45 min (9 time steps). **(c)** Sensor #3 partial test set predictions for 90 min (18 time steps). **(d)** Sensor #4 partial test set predictions for 45 min (9 time steps) in 48 h. The gray histogram exclusively illustrates the trend in water demand, enabling an easier comparison of the accuracy with which different models align with this trend.  
Figure 7: _Cont._