
MOR than DEM: Model Order Reduction for Discrete Element Simulations
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Granular materials play a crucial role in various industries, sparking growing interest in the development of digital twins to replicate industrial scenarios. However, these materials show complex behaviours that challenge traditional simulation methods. While the discrete element method (DEM) offers a promising solution that accurately captures key physics, it is computationally too expensive for large-scale applications. To address this limitation, we propose a model order reduction (MOR) framework that accelerates DEM simulations while preserving physical fidelity. The approach combines two open-source frameworks: pyMOR to apply MOR techniques that will enable to enhance the efficiency of high-fidelity DEM simulations from MercuryDPM. As a starting point, we focus on projection-based MOR using proper orthogonal decomposition (POD), where high-dimensional particle data is projected onto a low-dimensional subspace constructed from snapshot data. Additionally, we explore a neural network trained to predict system states on the reduced subspace in a non-intrusive manner. This hybrid strategy reduces the simulation runtime from days to seconds, enabling applications such as virtual prototyping and digital twins. A key challenge in applying MOR to particle methods lies in the inherently complex, random, and high dimensional dynamics of individual particles, which disrupts traditional low-rank structures in state-space solution manifolds. To overcome this obstacle, we introduce MercuryCG – a homogenisation tool developed by our team – to extract continuum fields from discrete particle data while conserving local mass and momentum. Through homogenisation, we mitigate the stochastic nature of particle simulations and establish a surrogate model that approximates the rheology of its underlying particle model. Our approach represents a significant advancement in the simulation of granular materials, bridging the gap between computational efficiency and physical accuracy. Through the synergy of expertise and software resources from multiple institutions, we showcase a novel approach with the potential to transform the simulation of granular materials, offering unprecedented speed and reliability for process optimisation and design.