Maximising the computational efficiency of the neural physics discrete element method

Traditional Discrete Element Method (DEM) simulations face significant computational challenges, primarily due to high memory demands and long execution times when modelling systems with large numbers of particles. These limitations restrict the scalability of DEM and hinder its application to complex or industrial-scale problems. To overcome these challenges, this study improves the performance of the NN4DEM solver (Neural Networks for the Discrete Element Method), part of the novel Neural Physics framework. In Neural Physics, DEM kernels are written as discrete convolutions and programmed as convolutional layers whose weights are prescribed analytically by the chosen contact laws and discretisation. Requiring no training, the Neural Physics approach preserves the underlying DEM contact physics. This contrasts with machine-learning approaches, which train neural networks to approximate contact detection or force prediction. Our contribution is twofold. First, we develop an octree data structure based on linear octree compression which transforms cell-based motion state grids into particle-based representations. This reduces memory consumption and accelerates computation for large problems. Second, we introduce Morton-order partitioning, which optimises memory utilisation and enables substantially larger particle counts. We present two dynamic benchmarks: a rotary drum test case, to investigate the influence of the Froude number on particle motion, and a granular landslide benchmark that develops large void regions and strong spatial heterogeneity. GPU profiling is carried out for particle-packing cases to evaluate the fine-grain single-GPU parallel performance of the implementation. The results demonstrate that the proposed Neural Physics framework achieves computational efficiency comparable with state-of-the-art DEM codes. • Octree compression converts grid-aligned tensors to compact particle-based buffers. • Leaf-wise neighbour search reduces memory traffic in contact detection and updates. • NN4DEM–Octree delivers ≈ 1.74× speed-up and ≈ 1.4× higher single-GPU capacity. • Domain decomposition increases maximum particle counts in large packing simulations. • Rotary-drum benchmark: ≈ 2.14× faster and 13 M → 32 M particles on A100–40 GB.