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Accurate demand forecasting is crucial for the efficient management of smart cities. However, the non-stationary and nonlinear characteristics of daily water demand series present significant challenges, leading to the lag forecasting problem and unreliable predictions. To address these challenges, this paper introduces a novel bi-correction model based on knowledge extraction, named the knowledge-based bi-correction model (KbBcM). The KbBcM leverages prior and posterior knowledge to achieve effective lag-free forecasting. The prior knowledge, in the form of sequence and feature information, is extracted using an autoregressive long short-term memory (AR-LSTM) network and a newly proposed lag penalty attention (LPA) module. Furthermore, a hybrid stacked LSTM network is employed to obtain primary forecasting results, which are then corrected with a masked weighted Markov chain (MWMC) based on posterior knowledge. Addressing the limitations of current metrics focused on absolute error, we also introduce the novel mean prediction trend effectiveness (MPTE) to comprehensively evaluate the effectiveness of lag-free forecasting performance. Comparation experiments performed on the urban water demand dataset of a megacity demonstrate the superiority of the KbBcM over baseline models. Additionally, ablation studies are performed to examine the effectiveness of the proposed sub-modules, further validating the robustness and reliability of the KbBcM in addressing the complexities of urban water demand forecasting. • A bi-correction model is proposed for daily urban water demand forecasting. • Priori and posteriori knowledge are utilized to attenuate lag forecasting problem. • We propose the novel lag penalty attention to extract effective priori knowledge. • We modify the weighted Markov chain to make it suitable for application here. • The proposed model performs superior on lag-free forecasting with baseline methods. [ABSTRACT FROM AUTHOR]