Physics-informed latent conditional flow matching for generative modeling of granular flows on inclined planes

Abstract

The internal kinematic and mechanical states of granular flows are difficult to observe or measure, limiting the interpretation of internal particle interactions and their role in flow evolution. In this study, we propose a physics-informed latent conditional flow matching (PI-LCFM) framework for reconstructing complete multivariable flow sequences from partial boundary observations. A variational autoencoder and temporal flow-matching model learn a reusable latent prior over velocity, granular temperature, stress, and solid volume fraction. During inference, boundary-velocity or basal-stress observations and mass- and momentum-conservation constraints guide the latent trajectory through the decoded physical fields, without retraining either model. The results demonstrate that the model accurately reconstructs full spatiotemporal fields from observations containing only 0.3\% of the complete field information, extrapolates beyond the training ranges of inclination and particle number, and recovers key trends in runout scaling, energy evolution, and stress profiles. Compared with a frame-by-frame conditional flow-matching baseline, PI-LCFM reduces the mean velocity-component root-mean-square error by 45.2\%, while observation-guided reconstruction of 500-frame sequences achieves an approximately 44-fold speedup. Physics guidance further improves conservation consistency, supporting the broader potential of this framework for inferring hidden states in particulate systems, with potential applications envisioned in geophysical hazard assessment and industrial process monitoring.