Physics-informed neural networks for rapid flow field reconstruction in fluidized bed drying

To address the challenges of real-time observation of gas-solid two-phase flow and the high computational cost/lack of real-time capability of traditional Computational Fluid Dynamics (CFD) simulations in fluidized bed drying processes, this paper proposes a rapid flow field reconstruction method based on Physics-Informed Neural Networks (PINNs). This method integrates sparse observation data with governing flow equations to achieve simultaneous prediction of key physical quantities including gas-phase velocity, solid-phase velocity, pressure, and solid volume fraction. A systematic evaluation was conducted under various conditions: spatial sparsity (20%, 5%, 1%), temporal sparsity (50%, 20%, 10%), noise interference (1%–20%), and cross-temporal extrapolation. Results show that with a spatial sampling rate as low as 5%, PINNs can still accurately reconstruct typical fluidization features such as bubble motion, solid-phase stratification, and pressure gradients. Even under an extreme sparsity of 1%, the overall flow pattern remains correct. Under dual spatio-temporal sparsity, the model demonstrates good information compensation capability, generating continuous and plausible transient evolution. With noise levels up to 20%, reconstruction errors exhibit only minor fluctuations, indicating strong noise resistance. Cross-temporal extrapolation experiments reveal that error growth over unseen time periods is steady and controllable, without non-physical oscillations. This study validates the stability, physical consistency, and robustness of PINNs under complex industrial scenarios involving sparsity, noise, and extrapolation, providing a viable technical pathway for real-time flow field reconstruction and intelligent monitoring in fluidized bed drying processes.