Andreas Mayr, Sebastian Lehner, Arno Mayrhofer, Christoph Kloss, Sepp Hochreiter, and Johannes Brandstetter
The progress of deep learning in modeling physical systems, including fluid dynamics, aerodynamics, and structural mechanics, is driven mainly by graph neural networks (GNNs). Typical engineering problems involve complex geometric boundaries, which are modeled by surface triangulation. The accurate description of curved geometries involves a large number of triangles of different sizes and orientations. For modeling such systems, many particle-boundary interactions need to be considered, which is often computationally unfeasible.
Here, we introduce boundary graph neural networks (BGNNs) for modeling physical processes with complex boundary surfaces. BGNNs dynamically enhance graph structures to include boundaries: if a boundary triangle region is within a cut-off distance to any particle, a virtual node is dynamically added to the triangle. This dynamic boundary graph structure covers only the relevant part of the boundary surface, which significantly reduces computational costs. Based on the additional node features, the neural network is able to distinguish between real particles and virtual nodes and learn different dynamics for particle-particle and particle-boundary interactions.
BGNNs are implemented to simulate complex 3D granular material flow in hoppers and rotating drums, which are standard parts of industrial machinery. We consider two types of properties: non-cohesive, describing liquid-like, oily materials, and cohesive, describing dry, sand-like materials. BGNNs are trained on simulation data generated with the open-source software LIGGGHTS based on the discrete element method (DEM). DEM represents granular media by discrete objects, such as spheres or polyhedra, which interact by exchanging momentum. To evaluate the effectiveness of our model, BGNNs are compared to the LIGGGHTS simulations. The accuracy of BGNNs is measured by aggregate quantities, including average particle positions, flows, and mixing entropies. The results show that BGNNs are able to accurately model 3D granular material flow and are computationally more efficient than the LIGGGHTS simulations.