Visual information guided physics informed neural networks framework for predictive coagulant dose optimization

Real-time sensing and visual information provide significant opportunities to reveal the internal dynamics of flocculation–coagulation processes in water treatment systems. Industrial operations commonly rely on turbidity measurements, while research studies frequently employ the degree of flocculation (DF) as a process indicator. However, both parameters exhibit inherent physical delays because they represent macroscopic outcomes of particle aggregation and sedimentation that require time to become observable. As a result, conventional control strategies depend on reactive adjustments based on previous system states, reducing operational efficiency and limiting prediction accuracy. To overcome these limitations, this study proposes a Real-Time Sensing and Visual Information-Guided Physics-Informed Neural Networks (RTS-VG PINNs) framework. The proposed method integrates real-time sensing, deep visual perception, and governing physical laws into unified learning architecture. A ResNet-50-based feature extractor combined with YOLOv8 is employed to identify regions of interest and extract early-stage predictive features from image sequences. These features are mapped to the time-varying effective sedimentation velocity within the Kynch sedimentation partial differential equation and coupled with the Langmuir–Smoluchowski formulation to predict coagulant-dose optimization using real-time process measurements. Experimental evaluation using independent jar-test experiments demonstrates that the proposed framework achieves competitive predictive performance relative to conventional machine-learning models, with the highest $$\:{R}^{2}$$ and lowest RMSE and MAE among the evaluated approaches, while maintaining low physics-based residuals on the order of 10− 3. The framework successfully captures nonlinear relationships among coagulant dosage, turbidity, and zeta potential, reconstructs internal floc density distributions, and provides robust inverse predictions under limited and noisy data conditions.