Micro-scale mechanisms, such as inter-particle and particle-fluid interactions, govern the behaviour of granular systems. While particle-scale simulations provide detailed insights into these interactions, their computational cost is often prohibitive. At a recent Lorentz Center Workshop on “Machine Learning for Discrete Granular Media”, researchers explored how machine learning approaches can aid the development of constitutive laws and efficient data-driven surrogates for granular materials while also addressing uncertainty quantification. Attended by researchers from both the granular materials (GM) and machine learning (ML) communities, the workshop brought the ML community up to date with GM challenges. This position paper emerged from the workshop discussions. In this position paper, we define granular materials and identify seven key challenges that characterise their distinctive behaviour across various scales and regimes–ranging from gas-like to fluid-like and solid-like. Addressing these challenges is essential for developing robust and efficient models for the digital twinning of granular systems in various industrial applications. To showcase the potential of ML to the GM community, we present classical and emerging machine/deep learning techniques that have been, or could be, applied to granular materials. We reviewed sequence-based learning models for path-dependent constitutive behaviour, followed by encoder-decoder type models for representing high-dimensional data in reduced spaces. We then explore graph neural networks and recent advances in neural operator learning. The latter captures the emerging field evolution of interacting particles via efficient latent space representation. Lastly, we discuss model-order reduction and probabilistic learning techniques for high-dimensional parameterised systems, both of which are crucial for quantifying and incorporating uncertainties arising from physics-based and data-driven models. We present a typical workflow aimed at unifying data structures and modelling pipelines and guiding readers through the selection, training, and deployment of ML surrogates for granular material simulations. Finally, we illustrate the workflow’s practical use with two representative examples, focusing on granular materials in solid-like and fluid-like regimes.

In design optimization of bulk handling equipment (BHE) we generally focus on the mean performance of the equipment. However, granular materials behave stochastic due to irregularities in particle shape and size which leads to stochastic performance of the equipment. To include the stochastic performance we propose robust metamodel-based design optimization (MBDO). The used metamodels are trained with stochastic performance data from randomly repeated discrete element method (DEM) simulations and predict mean and variance of the equipment performance. This method is compared to the conventional deterministic optimization method by means of a case study of a discharging hopper including verification and validation. The robust MBDO shows more distinctive optimal designs compared to the deterministic approach. In addition, the DEM-based metamodel is a relatively accurate method to predict DEM-model simulation results. However, the validation indicates that differences between DEM-model and experimental results highly affect the reliability of the found optima.

In calibration of model parameters for discrete element method (DEM) based models the focus lies on matching the mean key performance indicator (KPI) values from laboratory experiments to those from simulation results. However, due to the stochastic nature of granular processes experimental results can show large variances. To include stochastic behaviour, interpolation-based and regression-based metamodels are trained with stochastic data. These metamodels are used in the standard mean calibration approach and newly introduced mean-variance calibration approach to predict the KPIs mean and variance. In addition, the effect of enriching data on the calibration is investigated up to 50 repetitions of experiments and simulations. Based on a hopper case study, use of regression-based metamodels trained with KPI data repeated at least 20 times is recommended. While differences between mean and mean-variance-based metamodels were minor in the considered case study, regression-based metamodeling clearly showed improved accuracy and stability over interpolation-based metamodels.

Developments in discrete element modelling (DEM) enable detailed modelling of granular flows in bulk handling equipment (BHE) but due to the computational expense of DEM, wide use in analysing equipment performance is not yet feasible. Metamodels are a viable option to effectively use DEM in analysing BHE performance. Metamodels are able to approximate the behaviour of BHE efficiently for a wide range of design parameter values. We present a methodology to construct and validate DEM-based metamodels as well as a discharging hopper case study illustrating the use and benefits of metamodels in combination with DEM. For three different metamodels trained on a DEM data set, the results show that the metamodel quality highly depends on the number of samples and finding proper hyper-parameter values. The constructed metamodels are found capable of adequately representing the relation between performance and design parameters. It is concluded that methodically constructed metamodels are a valuable addition in describing BHE behaviour.