Proportional integral derivative booster for neural networks-based time-series prediction: Case of water demand prediction

1 Proportional integral derivative booster for neural networks-based time-series prediction: Case of water demand prediction Tony Sallooma,b, Okyay Kaynaka,b,c, Xinbo Yub, Wei Hea,b,∗ aSchool of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China bInstitute of Artificial Intelligence, University of Science and Technology Beijing, Beijing 100083, China cBogazici University, Istanbul Turkey Abstract 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. Keywords: PID control, neural networks, time-series forecasting, water demand prediction ∗Corresponding author Email address: Weihe@ieee.org (Wei He) arXiv:2512.06357v2 [cs.LG] 10 Dec 2025 1. Introduction In recent years, the use of artificial intelligence techniques in the form of machine learn- ing (ML) and deep learning (DL) has swept through the vast majority of the research fields that may come to mind. Their superiority over traditional approaches has been confirmed in several comparative research in literature as in [1, 2, 3]. The basic component in such approaches is a neural network (NN). In numerous studies, the abilities of NNs are exploited in a number of ways. To mention a few, in the field of robotics, researchers use the approx- imation ability of NNs to compensate for the uncertain information in the dynamics of the robot as in [4, 5, 6]. In computer vision, NNs are used for objects detection such as drug bills [7], fabric defection [8], etc. The ability of feature extraction is used for classification and prediction, where Barchi et al. [9] prove the efficiency of deep convolution NN in source code classification, in [10], Song et al. use the extreme learning machine for fault detection and classification, and in [11], Capizzi et al. build a spiking neural network for long-term prediction of biogas production. The deep belief network is used for PM2.5 concentration prediction in Beijing [12]. Time series prediction is one of the most illustrious applications of neural networks (NNs), especially after the rise of the memory power provided by long-short term memory (LSTM) and gated recurrent unit (GRU). This research is concerned with NN models that are meant to forecast periodic time-series information. Periodicity is a natural phenomenon that characterizes many real-life events. Hourly water and power consumption, daily stream- flow, hourly average temperature, hourly pollution rate in the city, and rain rate are but a few examples of periodic time-series information. Prediction of time-series information enables planning in several fields of economic and industrial activities [13]. Particularly, multi-step prediction is commonly met in real-life scenarios, where planners need to predict future observations based on a given sequence of historical information [14]. Several papers that propose different NN-based methods for forecasting periodic time series data consider- ing both single-step and multi-step scenarios can be found in the literature. For example, Liu et al. [15] propose a novel NN model for time series forecasting based on dual-stage two-phase model and temporal attention recurrent NN and prove its applicability in the fields of energy, finance, environment and medicine. While Wang et al. [16] and Safari et al. [17] predict one step of short-term wind power interval based on GRU and decomposition approaches. In [18], Khodayar et al. provide a wind speed prediction method based on a rough deep NN. In [19], GRU and K-means classification methods are employed for fore- 2 casting quarterly w

This content is AI-processed based on open access ArXiv data.