Tapped Granular Systems: Simulations and Machine Learning Approaches

We report on simulations of microstructure development in assemblies of monodisperse spheres in a tapped container.  The average solids fraction of an assembly was computed at a tap completion when its kinetic energy was essentially zero.  An ensemble of 25 realizations was evolved over the span of M =15,000 taps from which evolution curves of the solids fractions were obtained. Drastically different progressions of the individual realizations were observed that featured sporadic jumps in solids fraction over the duration of a small number of taps. This behavior is consistent with a collective reorganization process that has been previously reported in the literature. Visualizations further revealed the formation of crystalline regions separated by dislocations facilitating bulk sliding motion in the system through periodic boundaries. Simulations conducted at a higher tap acceleration promoted a larger frequency of jumps in density over the M taps, resulting in more of the realizations attaining an apparent final saturation density.

 

A recurrent neural network model developed with a 60% training set was used to forecast the ensemble-averaged density in the limit of a large number of taps. The model appeared to be able to capture jumps exhibited in the simulations beyond the training set.  Our findings suggest that it may be possible to analyze the evolution of granular microstructure by applying deep learning methods. The inclusion of physics-informed quantities into the learning feature space may provide an enhanced ability to understand the process towards the development of predictive surrogate models.