Multi-step time-series prediction is an essential supportive step for decision-makers in several industrial areas. Artificial intelligence techniques, which use a neural network component in various forms, have recently frequently been used to accomplish this step. However, the complexity of the neural network structure still stands up as a critical problem against prediction accuracy. In this paper, a method inspired by the proportional-integral-derivative (PID) control approach is investigated to enhance the performance of neural network models used for multi-step ahead prediction of periodic time-series information while maintaining a negligible impact on the complexity of the system. The PID-based method is applied to the predicted value at each time step to bring that value closer to the real value. The water demand forecasting problem is considered as a case study, where two deep neural network models from the literature are used to prove the effectiveness of the proposed boosting method. Furthermore, to prove the applicability of this PID-based booster to other types of periodic time-series prediction problems, it is applied to enhance the accuracy of a neural network model used for multi-step forecasting of hourly energy consumption. The comparison between the results of the original prediction models and the results after using the proposed technique demonstrates the superiority of the proposed method in terms of prediction accuracy and system complexity.

Short-term water demand forecasting (StWDF) is the foundation stone in the derivation of an optimal plan for controlling water supply systems. Deep learning (DL) approaches provide the most accurate solutions for this purpose. However, they suffer from complexity problem due to the massive number of parameters, in addition to the high forecasting error at the extreme points. In this work, an effective method to alleviate the error at these points is proposed. It is based on extending the data by inserting virtual data within the actual data to relieve the nonlinearity around them. To our knowledge, this is the first work that considers the problem related to the extreme points. Moreover, the water demand forecasting model proposed in this work is a novel DL model with relatively low complexity. The basic model uses the gated recurrent unit (GRU) to handle the sequential relationship in the historical demand data, while an unsupervised classification method, k -means, is introduced for the creation of new features to enhance the prediction accuracy with less number of parameters. Real data obtained from two different water plants in China are used to train and verify the model proposed. The prediction results and the comparison with the state-of-the-art illustrate that the method proposed reduces the complexity of the model six times of what achieved in the literature while conserving the same accuracy. Furthermore, it is found that extending the data set significantly reduces the error by about 30%. However, it increases the training time. Introduction Water scarcity has become a threat to humankind in recent decades. Many efforts in all possible directions are being made to compensate for this growing problem (Northey et al., 2016; González-Zeas et al., 2019). The major reliable strategies for that include water treatment (Zinatloo-Ajabshir et al., 2020a), water desalination, and optimization of water management systems. Nanotechnology is the most powerful technology employed for water treatment, where researchers have done impressive work (Zinatloo-Ajabshir et al., 2020b, 2017; Moshtaghi et al., 2016). On the other hand, StWDF is the foundation stone of the optimization of water management systems.

Advancements in smart metering technologies have significantly improved the ability to monitor and manage water utilities. In the context of increasing uncertainty due to climate change, securing water resources and supply has emerged as an urgent global issue with extensive socioeconomic ramifications. Hourly consumption data from end-users have yielded substantial insights for projecting demand across regions characterized by diverse consumption patterns. Nevertheless, the prediction of water demand remains challenging due to influencing non-deterministic factors, such as meteorological conditions. This work introduces a novel method for short-term water demand forecasting for District Metered Areas (DMAs) which encompass commercial, agricultural, and residential consumers. Unsupervised contrastive learning is applied to categorize end-users according to distinct consumption behaviors present within a DMA. Subsequently, the distinct consumption behaviors are utilized as features in the ensuing demand forecasting task using wavelet-transformed convolutional networks that incorporate a cross-attention mechanism combining both historical data and the derived representations. The proposed approach is evaluated on real-world DMAs over a six-month period, demonstrating improved forecasting performance in terms of MAPE across different DMAs, with a maximum improvement of 4.9%. Additionally, it identifies consumers whose behavior is shaped by socioeconomic factors, enhancing prior knowledge about the deterministic patterns that influence demand.

Accurate water consumption forecasting is a crucial tool for water utilities and policymakers, as it helps ensure a reliable supply, optimize operations, and support infrastructure planning. Urban Water Distribution Networks (WDNs) are divided into District Metered Areas (DMAs), where water flow is monitored to efficiently manage resources. This work focuses on short-term forecasting of DMA consumption using deep learning and aims to address two key challenging issues. First, forecasting based solely on a DMA's historical data may lack broader context and provide limited insights. Second, DMAs may experience sensor malfunctions providing incorrect data, or some DMAs may not be monitored at all due to computational costs, complicating accurate forecasting. We propose a novel method that first identifies DMAs with correlated consumption patterns and then uses these patterns, along with the DMA's local data, as input to a deep learning model for forecasting. In a real-world study with data from five DMAs, we show that: i) the deep learning model outperforms a classical statistical model; ii) accurate forecasting can be carried out using only correlated DMAs' consumption patterns; and iii) even when a DMA's local data is available, including correlated DMAs' data improves accuracy.

Machine and statistical learning algorithms can be reliably automated and applied at scale. Therefore, they can constitute a considerable asset for designing practical forecasting systems, such as those related to urban water demand. Quantile regression algorithms are statistical and machine learning algorithms that can provide probabilistic forecasts in a straightforward way, and have not been applied so far for urban water demand forecasting. In this work, we aim to fill this gap by automating and extensively comparing several quantile-regression-based practical systems for probabilistic one-day ahead urban water demand forecasting. For designing the practical systems, we use five individual algorithms (i.e., the quantile regression, linear boosting, generalized random forest, gradient boosting machine and quantile regression neural network algorithms), their mean combiner and their median combiner.

Machine and statistical learning algorithms can be reliably automated and applied at scale. Therefore, they can constitute a considerable asset for designing practical forecasting systems, such as those related to urban water demand. Quantile regression algorithms are statistical and machine learning algorithms that can provide probabilistic forecasts in a straightforward way, and have not been applied so far for urban water demand forecasting. In this work, we aim to fill this gap by automating and extensively comparing several quantile-regression-based practical systems for probabilistic one-day ahead urban water demand forecasting. For designing the practical systems, we use five individual algorithms (i.e., the quantile regression, linear boosting, generalized random forest, gradient boosting machine and quantile regression neural network algorithms), their mean combiner and their median combiner. The comparison is conducted by exploiting a large urban water flow dataset, as well as several types of hydrometeorological time series (which are considered as exogenous predictor variables in the forecasting setting). The results mostly favour the practical systems designed using the linear boosting algorithm, probably due to the presence of trends in the urban water flow time series. The forecasts of the mean and median combiners are also found to be skilful in general terms.

Water demand is a highly important variable for operational control and decision making. Hence, the development of accurate forecasts is a valuable field of research to further improve the efficiency of water utilities. Focusing on probabilistic multi-step-ahead forecasting, a time series model is introduced, to capture typical autoregressive, calendar and seasonal effects, to account for time-varying variance, and to quantify the uncertainty and path-dependency of the water demand process. To deal with the high complexity of the water demand process a high-dimensional feature space is applied, which is efficiently tuned by an automatic shrinkage and selection operator (lasso). It allows to obtain an accurate, simple interpretable and fast computable forecasting model, which is well suited for real-time applications. The complete probabilistic forecasting framework allows not only for simulating the mean and the marginal properties, but also the correlation structure between hours within the forecasting horizon. For practitioners, complete probabilistic multi-step-ahead forecasts are of considerable relevance as they provide additional information about the expected aggregated or cumulative water demand, so that a statement can be made about the probability with which a water storage capacity can guarantee the supply over a certain period of time. This information allows to better control storage capacities and to better ensure the smooth operation of pumps. To appropriately evaluate the forecasting performance of the considered models, the energy score (ES) as a strictly proper multidimensional evaluation criterion, is introduced. The methodology is applied to the hourly water demand data of a German water supplier.