Geometrical Neural Surrogate for Granular Systems

Density relaxation is a phenomenon where bulk granular materials subjected to external time-dependent forces experience an increase in solids fraction. We report on a graphical neural surrogate of the process using training sets generated by discrete element simulations of uniform, inelastic, frictional soft spheres. Ensembles of assemblies of N particles are generated via gravity deposition into a periodic box with a rigid floor, that is subjected to a half-sinusoidal motion of amplitude a and frequency ω to mimic tapping. The complexity of the phenomenon is consequent upon a large parameter space, and the long time scale associated with microstructural rearrangements. Training sets are comprised two ensembles (Γ=aω²/g= 2.75, 3.25) consisting of the sphere positions at relaxed states for each of the 15,000 applied taps. We use geometric deep learning to forecast the evolution of the assembly microstructure by constructing 15,000 adjacency matrices (N x N) endowed with particle coordinates as added features from the contact networks for 25 realizations of each ensemble. With a 70% training set, a variational autoencoder is used to estimate a probability distribution over possible configurations in the latent space, while a decoder generates new configurations based on the previous tap and the latent space. Particle positions beyond the training set are then used to compute solids fractions and distributions of coordination number and free volume that are found to be in good agreement with the simulations.