Accurate simulation of granular flow dynamics is crucial for assessing various geotechnical risks, including landslides and debris flows. Granular flows involve a dynamic rearrangement of particles exhibiting complex transitions from solid-like to fluid-like responses. Traditional continuum and discrete numerical methods are limited by their computational cost in simulating large-scale systems. Statistical or machine learning-based models offer an alternative. Still, they are largely empirical, based on a limited set of parameters. Due to their permutation-dependent learning, traditional machine learning-based models require huge training data to generalize. To resolve these problems, we use a graph neural network, a state-of-the-art machine learning architecture that learns local interactions. Graphs represent the state of dynamically changing granular flows and the interaction laws, such as energy and momentum exchange between grains. We develop a graph neural network-based simulator (GNS) that takes the current state of granular flow and predicts the next state using Euler explicit integration by learning the local interaction laws. We train GNS on different granular trajectories. We then assess the performance of GNS by predicting granular column collapse. GNS accurately predicts flow dynamics for column collapses with different aspect ratios unseen during training. GNS is hundreds of times faster than high-fidelity numerical simulators. The model also generalizes to domains much larger than the training data, handling more than twice the number of particles than it was trained on.

翻译：精确模拟颗粒流动力学对于评估包括滑坡和泥石流在内的多种岩土工程风险至关重要。颗粒流涉及颗粒的动态重排，表现出从类固态到类液态响应的复杂转变。传统的连续介质和离散数值方法在模拟大规模系统时受限于其计算成本。基于统计或机器学习的模型提供了一种替代方案，但它们大多依赖于有限参数集的经验方法。由于传统机器学习模型依赖于排列顺序的学习方式，需要大量训练数据才能实现泛化。为解决这些问题，我们采用了图神经网络——一种学习局部相互作用的最新机器学习架构。图结构表示动态变化的颗粒流状态及其相互作用规律（例如颗粒间的能量与动量交换）。我们开发了一种基于图神经网络的模拟器（GNS），该模拟器通过学习局部相互作用规律，以欧拉显式积分方法接收颗粒流当前状态并预测下一状态。我们在不同的颗粒运动轨迹上训练GNS，并通过预测颗粒柱坍塌来评估其性能。结果表明，GNS能够准确预测训练中未见的、不同长宽比的颗粒柱坍塌的流动力学行为。其计算速度比高保真数值模拟器快数百倍。该模型还能泛化到远超训练数据规模的域，处理颗粒数量可达训练样本的两倍以上。