A discrete element solution method embedded within a Neural Network

Abstract

This paper introduces a novel methodology, the Neural Network framework for the Discrete Element Method (NN4DEM), as part of a broader initiative to harness specialised AI hardware and software environments, marking a transition from traditional computational physics programming approaches. NN4DEM enables GPU-parallelised computations by mapping particle data (coordinates and velocities) onto uniform grids as solution fields and computing contact forces by applying mathematical operations that can be found in convolutional neural networks (CNN). Essentially, this framework transforms a DEM problem into a series of layered “images” composed of pixels, using stencil operations to compute the DEM physics, which is inherently local. The method revolves around custom kernels, with operations prescribed by the laws of physics for contact detection and interaction. Therefore, unlike conventional AI methods, it eliminates the need for training data to determine network weights. NN4DEM utilises libraries such as PyTorch for relatively easier programmability and platform interoperability. This paper presents the theoretical foundations, implementation and validation of NN4DEM through hopper test benchmarks. An analysis of the results from random packing cases highlights the ability of NN4DEM to scale to 3D models with millions of particles. The paper concludes with potential research directions, including further integration with other physics-based models and applications across various multidisciplinary fields.