Non-local physics-informed neural networks for forward and inverse solutions of granular flows

Abstract

Dense granular flows exhibit nonlocal effects due to stress transmission in microplastic events, especially in quasi-static or slowly sheared regions. Hence, traditional local rheological models fail to capture spatial cooperativity effects that are prominent in many granular systems. The nonlocal granular fluidity (NGF) model addresses this limitation by introducing a diffusive-like partial differential equation for a fluidity field, governed by a key material-dependent parameter: the nonlocal amplitude A. However, determining A from experiments or simulations is known to be difficult and typically requires extensive calibration across multiple geometries. In this work, we present a data-driven platform based on Physics-Informed Neural Networks (PINNs) embedded with the NGF model, capable of solving granular flows in a forward or inverse manner. We show that once trained on transient flow fields, these non-local PINNs can readily infer the material parameters, as well as the pressure and stress fields. These data-driven frameworks allow for accurate recovery of small variations in the nonlocal amplitude, A, which lead to sharp bifurcation-like transitions in the flow field. This approach demonstrates the feasibility of data-driven parameter inference in complex nonlocal models and opens up new possibilities for characterizing granular materials from sparse experimental observations.