通过插入虚拟数据缓解极端点误差，实现低复杂度实时水需求预测

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.