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

TL;DR

The paper tackles the accuracy-complexity tradeoff in neural network-based multi-step forecasting for periodic time-series by introducing a PID-inspired booster. The method applies a three-gain correction to NN predictions in an iterative prediction framework, requiring only Kp, Ki, and Kd to tune, and it is integrated without altering NN training. It is validated on water-demand forecasting with GRUN and DCGRU architectures and on hourly electricity consumption with CNN-LSTM, showing substantial accuracy gains and favorable complexity metrics (AIC) compared with existing correction strategies. The results demonstrate that the PID booster reduces prediction error with only modest increases in computation, suggesting broad applicability to periodic time-series prediction tasks beyond the reported domains. The work also discusses initialization, applicability conditions, and potential future extensions to non-periodic data and federated settings.

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.

Figures (18)

• Figure 1: Prediction process.
• Figure 2: Seven days of observations of water demand: (a) for DMA1; (b) for DMA2.
• Figure 3: The structure of the GRUN model.
• Figure 4: The structure of the SPNN model.
• Figure 5: The structure of the DCGRU model.