Physics-Informed Neural Network for Solving Forward and Inverse Problems of Granular Flow in the Homogeneous Cooling State

The advent of machine learning has prompted the emergence of innovative methodologies for predicting the hydrodynamics of granular flows. In this study, the physics-informed neural network (PINN) approach was employed to solve the forward and inverse problems of a simple granular flow with smooth particles in the homogeneous cooling state. The three techniques, which are the dimensionless granular temperature as the optimization of the loss functions, the normalized time information as the input layer, and adjusting local weights of sample points based on the physical characteristics, have been shown to significantly contribute to enhancing the precision of classical PINN in predicting the variation of granular temperature over time. The proposed method (developed PINN) has been validated for many different cases and the influence of numbers of sampled date in the solution process was also investigated.