Predicting suspended floc size in estuarine waters using self-adaptive parameterized physics-informed neural networks

The size dynamics of suspended flocs play fundamental roles in sediment transport processes and ecological functioning in estuarine waters. However, conventional flocculation dynamic models typically rely on fixed empirical parameters, limiting their adaptability under complex hydrodynamic conditions and reducing predictive accuracy. This study presents a new self-adaptive parameterized physics-informed neural networks (SAP-PINNs) model, dynamically optimizing aggregation coefficient, breakage coefficient and erosion parameters within the flocculation dynamic equation, enhancing the accuracy and physical consistency of floc size predictions by integrating data-driven methodologies with physical constraints. Laboratory experiments demonstrate that the model, calibrated under low shear stress conditions, accurately predicts mean floc size under high shear stress, confirming its robustness across variable hydrodynamic regimes. Field validations further indicate a significant improvement in predictive performance compared to traditional models, with an 88.31 % increase in accuracy, a coefficient of determination of 0.99, and a mean absolute error of 0.78. SHapley Additive exPlanations (SHAP) analysis reveals that shear stress and salinity are the dominant factors influencing flocculation, while suspended sediment concentration exhibits a facilitative effect within an optimal range. Temperature exerts a comparatively minor influence. This study demonstrates that the SAP-PINNs effectively combines physical laws with machine learning techniques, improving the modeling accuracy, interpretability, and generalizability of floc dynamics. It offers a new promising potential for application in complex hydrodynamic systems, supporting sediment transport predictions, ecological assessments, and water quality management in estuarine and coastal waters.