Physical-anchored graph learning for process key indicator prediction

Data-driven soft sensors in the process industry, whilst intensively investigated, struggle to handle unforeseen disruptions and operating changes not covered in the training data. Incorporating physical knowledge, such as mass/energy balances and reaction mechanisms, into a data-driven model is a potential remedy. In this study, a physical-anchored graph learning (PAGL) soft sensor is proposed, integrating process variable causality and mass balances. Knowledge-derived causality is further supplemented by mining dependencies from data. PAGL uses causality and mass balance as physical anchors to predict key indicators and evaluate whether the prediction logic aligns with physical principles, ensuring physical consistency in inference. The case study on wastewater treatment demonstrates PAGL's interpretability and reliability, maintaining physical consistency instead of acting as a black box.