# High-Performance Computing and Parallel Algorithms for Urban Water Demand Forecasting
## 3 Results and Discussion
### Comparison with Related Studies  
Our findings in computational performance can be put in perspective with other studies in the field of water demand forecasting and, more broadly, in time-series forecasting. Many prior works have concentrated on improving forecasting accuracy, often by developing novel model architectures or incorporating additional data. For example, [PERSON] et al. (2023) [22] introduced the MACLA-LSTM architecture, which aimed to improve accuracy through a multi-component LSTM design. Their work demonstrated better predictive accuracy than baseline LSTMs, but the computational cost of their more complex architecture was not a focal point. In contrast, our study did not introduce a new model architecture but rather a data-centric approach that ensured that a strong existing model (standard LSTM) could be trained and executed efficiently at scale. The two approaches are complementary: one could potentially implement the MACLA-LSTM within our HPC framework to benefit from both improved accuracy and faster training. Similarly, [PERSON] et al. (2022) [23] and [PERSON] et al. (2023) [6] each proposed sophisticated hybrid models (CNN-LSTM and Attention-BiLSTM-XGBoost, respectively) to push forecast accuracy higher. These models involve more layers or components, which likely increases training time. While they report excellent accuracy, deploying such models in a real utility setting might face challenges if training or inference is slow. Our contribution to an HPC pipeline is highly relevant in such contexts: the parallel algorithms and GPU usage we demonstrated can be applied to those advanced models as well, reducing the barrier of computational feasibility. We respectfully note that those studies focused on algorithmic innovation, whereas we focus on engineering and scalability innovation; both are necessary for advancing the field. The present work essentially provides a template for how any advanced forecasting method can be operationalized in an efficient manner. There are also studies that indirectly touch on computation through the lens of big data. For instance, [PERSON] et al. 's (2022) [24] work in the agricultural water demand domain highlighted the use of big data and HPC for processing large datasets. Their emphasis was on leveraging remote sensing and multiple data sources, which inevitably requires robust computing infrastructure. Our work serves as a concrete case study of leveraging such infrastructure for the urban water sector. We go a step further in quantifying the performance gains, which is not commonly reported in typical forecasting papers. By presenting metrics like speedup and efficiency, we align with best practices in parallel computing research, bringing those into the water informatics arena. Compared to general time-series forecasting literature, relatively few papers report on the runtime or scalability of their approaches. An exception is research in energy demand forecasting or smart grids, where sometimes the deployment aspects are discussed (e.g., needing to forecast in real-time on devices with limited resources). In water demand forecasting, the timeline is a bit more forgiving (forecasts are often daily or hourly, not every second), but as data volume grows (smart metering could provide much more granular data), the computational load will increase. Our results preemptively address this, showing that a pipeline can efficiently handle 48 streams of data and complex models in parallel. In terms of limitations, we acknowledge that not all utilities have immediate access to high-end GPUs or HPC clusters. However, the landscape is changing--cloud computing services now offer on-demand HPC resources, and the cost of GPUs has been decreasing relative to the operational value they provide.