Physics-informed neural network enhanced particle image velocimetry for granular flows with pressure-dependent rheology

Accurate characterization of granular flows depends on the reliable identification of internal stress states and boundary slip behaviors, which remains challenging due to the limited observability of stress fields and near-wall dynamics in Particle Image Velocimetry (PIV) measurements. To address these limitations, this study proposes a physics-informed computational framework to extend the capabilities of traditional PIV. By employing the μ(I) rheology to constitutively couple kinematic states with internal stresses and by embedding macroscopic momentum conservation equations as rigorous constraints within a Residual Neural Network, this approach enables the simultaneous enhancement of PIV velocity fields and the inversion of latent pressure fields directly from the kinematic data. The method is first validated against analytical solutions for unsteady granular chute flows corrupted with a controlled noise. The results demonstrate exceptional noise robustness; even when the input data is corrupted by up to 20% noise, the method accurately reconstructs both velocity and pressure fields. The framework is subsequently applied to complex granular flows using synthetic PIV data generated from discrete element method simulations. The results show that the proposed method achieves physics-consistent super-resolution reconstruction of PIV measurements, successfully inverts the internal pressure distributions, and overcomes near-wall optical blind spots through physics-informed extrapolation, enabling accurate prediction of wall slip velocities. Overall, the proposed framework significantly enhances the information extraction capability of PIV and provides a new pathway for investigating granular rheology and boundary mechanisms.