# High-Performance Computing and Parallel Algorithms for Urban Water Demand Forecasting
## 3 Results and Discussion
### Model Performance and Accuracy  
While the HPC enhancements significantly improve computational efficiency, the forecasting models must also achieve sufficient accuracy for the solution to be practical. To evaluate model performance, the forecasting LSTM (f-LSTM) and Random Forest Regression (RFR) models were tested on a held-out test dataset comprising the final months of data from each reservoir. Additionally, the imputation Bi-LSTM was evaluated on its ability to reconstruct missing data, with its accuracy compared against results from our prior study, as presented in Table 3.  
The f-LSTM model achieved an average RMSE of 0.36 (in normalized units) and an MAE of 0.26 on the test set. The Random Forest achieved an average RMSE of 0.30 and MAE of 0.22. This means that, somewhat unexpectedly, the Random Forest slightly outperformed the LSTM in terms of accuracy on this particular test period--roughly a 17-20% lower RMSE. In real terms (denormalizing), these errors correspond to only a few centimeters of  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Study** & **Mean MSE** & **Mean MAE** & **Mean RMSE** \\ \hline Bi-LSTM & [PERSON] et al. (2024) [16] & 0.010 & 0.050 & 0.070 \\  & This Study (48 tanks) & 0.222 & 0.266 & 0.380 \\ F-LSTM & [PERSON] et al. (2024) [16] & 0.015 & 0.045 & 0.084 \\  & This Study (48 tanks) & 0.20 & 0.26 & 0.36 \\ RFR & [PERSON] et al. (2024) [16] & 0.020 & 0.060 & 0.090 \\  & This Study (48 tanks) & 0.13 & 0.22 & 0.30 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mean Accuracy Metrics Across Reservoirs.  
Figure 7: Execution Time Comparison with and without GPU Acceleration.  
water level error given typical tank level ranges, which is quite acceptable for operational use. Both models thus provide a high level of accuracy, capturing the general demand patterns with only small deviations.  
To investigate this result, we recall that our LSTM models did not undergo extensive hyperparameter tuning due to hardware limitations--only five trial configurations were attempted (Section 2.4.2). It is likely that the f-LSTM was not fully optimized and could be slightly under-fitting or over-fitting. The Random Forest, on the other hand, has fewer hyperparameters (number of trees, tree depth), which we tuned moderately, and it might inherently be more robust with the chosen features. In fact, in our previous study on a smaller dataset, an LSTM model did outperform Random Forest in most cases when properly tuned.  
The Bi-LSTM imputation model was assessed by removing known data points and testing its ability to reconstruct them. The model achieved an RMSE of 0.38 (38% error), which is higher than the 7% error observed in prior studies. This deviation could be attributed to the larger dataset and increased variability in reservoir dynamics. However, despite the increased RMSE, the Bi-LSTM imputer ensured that the forecasting models received clean, gap-free input, minimizing disruptions from missing values.  
Although the Random Forest model exhibited lower forecasting error, its adaptability in real-time settings is more limited compared to LSTM models. Once trained, a Random Forest model remains static, meaning that to integrate new data, full retraining is required. This could introduce latency and limit responsiveness to sudden changes in water demand patterns.  
In contrast, LSTM models can be continuously updated with new data, making them more suitable for environments where real-time adaptation is critical. The HPC infrastructure developed in this study enables frequent retraining of LSTM models in just minutes, allowing them to adjust dynamically to new consumption trends without requiring full retraining cycles. This makes LSTM models a compelling choice for long-term deployment in urban water forecasting systems.