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：准确模拟颗粒流动力学对于评估各类岩土工程风险（包括滑坡和泥石流）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流态响应的复杂过渡。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，但这些模型本质上经验性强，仅依赖有限参数集。由于传统机器学习模型依赖于置换的学习方式，它们需要海量训练数据才能实现泛化。为解决这些问题，我们采用图神经网络这一前沿机器学习架构来学习局部相互作用。图表示动态变化的颗粒流状态及相互作用规律（如颗粒间的能量和动量交换）。我们开发了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，基于欧拉显式积分法，以当前颗粒流状态预测下一时刻状态。我们在不同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。GNS能精确预测训练中未出现的不同长宽比柱状坍塌的流动动力学，其计算速度比高保真数值模拟器快数百倍。该模型还能泛化至远超训练数据尺度的领域，处理粒子数达到训练数据两倍以上的系统。