Exformer: A Transformer-Based Forecasting Framework with Temporal Knowledge Assistance for Multistep Multivariate Influent Prediction in Wastewater Treatment Plants

Abstract Accurate forecasting of influent flow rates and water quality is of great importance to facilitate wastewater treatment plants (WWTPs) towards early fault warning and optimal operations. However, due to the seasonality, complex multivariate nexus and inherent disturbances, the predictive performance of WWTP influent is often unsatisfactory, particularly for multistep forecasting. This limitation usually frustrates the practical utility of such models for operational guidance and decision-making. To address these challenges, this study proposes a Transformer-based forecasting framework called Exformer. The framework employs a Channel-Independent (CI) representation strategy to preserve variable-specific temporal characteristics and reduce cross-variable interference. In addition, a Temporal Knowledge Guided Attention (TKGA) mechanism incorporates temporal prior knowledge into the attention process to enhance long-range dependency modeling. The proposed framework is evaluated on both the Benchmark Simulation Model No.2 (BSM2) dataset and a real-world WWTP dataset collected from Dongguan, China, under forecasting horizons of 6, 12, 24, and 48 steps. The experimental results show that Exformer delivers competitive performance across different forecasting horizons, with increasingly pronounced advantages at longer horizons, particularly at 24 and 48 steps. Additional robustness, interpretability, reliability and ablation analyses further demonstrate the effectiveness of Exformer for practical wastewater influent forecasting applications.