Physics-Informed Neural Networks with Mass Conservation Constraints for Predicting Particle Sedimentation in...

To address the challenge of sparse monitoring data for particle sedimentation in non-Newtonian suspensions in stirred tanks and the risk of non-physical solid-phase inventory drift in purely data-driven models during long-term extrapolation, this study proposes a parametrized physics-informed neural network (P-PINN). The method embedded a two-dimensional depth-averaged sedimentation equation and a macroscopic mass conservation constraint into the neural-network framework. Specifically, to reduce the gradient competition between local data fitting and global physical constraints, a ramp strategy was designed to gradually adjust the weight of the conservation term. Furthermore, a log-time mapping was also introduced to improve the resolution of early-stage high-gradient sedimentation dynamics. The model was validated by using nine-point ultrasonic thickness measurements from bench-scale experiments under multiple operating conditions. The results showed that P-PINN successfully reconstructed the continuous spatiotemporal evolution of the sediment bed with a global root-mean-square error (RMSE) of 3.71 mm. It also exhibited stable generalization in leave-one-out tests. Compared with purely data-driven baselines, the ramp strategy substantially reduced solid-phase inventory drift during long-term extrapolation and helped maintain macroscopic mass conservation. This study offers a physically constrained surrogate modeling approach for sediment-bed prediction under sparse observations with potential for online monitoring of complex multiphase flow systems.