DMGTNet: A graph-temporal deep learning model for membrane fouling prediction in dual-membrane wastewater treatment systems

Membrane fouling-induced permeate flux decline remains a major limitation to the widespread deployment of membrane separation technologies. To better capture the structural dependencies and time-varying patterns among membrane modules in dual-membrane systems, we propose the Dual Membrane Graph-Temporal Network (DMGTNet). This model utilizes the Graph Attention Network (GAT) to dynamically learn nonlinear spatial dependencies among membrane components, while the gated structure of the Long Short-Term Memory Networks (LSTM) module is employed to capture the long-term evolution of membrane fouling behaviors. Additionally, a dual-stage progressive training strategy is devised to improve both the accuracy and the balance of multivariate prediction performance. The proposed model is validated on data from four full-scale dual-membrane water treatment facilities collected over 50 months, involving 240 sensor nodes and 6.8 billion high-frequency sensor readings. DMGTNet achieves average R² values of 0.925, 0.897, and 0.846 for 5-step, 10-step, and 15-step predictions of transmembrane pressure difference (TMP) and permeate flux (PF), respectively, with corresponding MAPE values of 6.981 %, 10.443 %, and 17.082 %. This performance surpasses existing baseline models, yielding average R² improvements of 0.032, 0.035, and 0.040, and MAPE reductions of 5.600 %, 8.321 %, and 9.635 %. The model demonstrates excellent interpretability, as its attention mechanism autonomously identifies key regulatory parameters for inter-process coupling, thereby offering a theoretical foundation for the intelligent optimization of complex membrane treatment processes.