Granular flow simulation moves most message passing onto coarse grids: HCG-GNN trains 6.47 times faster and rolls out 10,000 grains in 31 seconds

A granular-flow surrogate can now keep per-grain motion prediction while performing most of its relational computation on coarser spatial cells. In a conventional particle-level GNN, each message-passing round extends the information range by only one edge, so covering larger physical distances requires more passes over the full particle graph or larger neighborhoods, raising compute and memory cost. In inclined-plane granular flow benchmarks, HCG-GNN with 5 of its 7 message-passing steps on coarse graphs achieved multi-step accuracy comparable to a conventional GNN running all 10 steps on the particle graph, trained 6.47 times faster, and cut GPU memory from 40.271 GB to 21.659 GB.

The model first passes messages directly between neighboring grains, then aggregates particle features into occupied grid cells, exchanges information on two successively coarser graphs, and returns coarse-scale features to the particle graph. Coarsening uses mean pooling to aggregate nodes in the same cell and concatenates the logarithm of cell occupancy, distinguishing cells with similar mean features but different node counts; the node-to-cell assignments recorded during pooling are reused when features are transferred back. Training and comparison used the same NVIDIA H100 GPU, batch size 2, and 500 epochs; the training set held 9 DEM trajectories, the validation set 3 trajectories at an unseen slope angle, and the test set 6 trajectories.

The demonstrated scope is DEM benchmarks of granular flow released down an incline onto a horizontal bed, with polydisperse spheres of about 2 mm median diameter, periodic lateral boundaries, and 2 s recorded per trajectory over 100 frames; the model was trained on trajectories of up to 5000 grains and tested for extrapolation on 7500- and 10000-grain systems.

Instantaneous acceleration fluctuations near the flow front are not fully reproduced, and the predicted free surface sits about one median grain diameter above DEM at the front; the kinetic-energy peak is slightly higher and later, with these differences concentrated in the most dynamic stage. A third coarse level further improves multi-step prediction but requires 50% more training time than the two-level model.