From designing architected materials to connecting mechanical behavior across scales, computational modeling is a critical tool in solid mechanics. Recently, there has been a growing interest in using machine learning to reduce the computational cost of physics-based simulations. Notably, while machine learning approaches that rely on Graph Neural Networks (GNNs) have shown success in learning mechanics, the performance of GNNs has yet to be investigated on a myriad of solid mechanics problems. In this work, we examine the ability of GNNs to predict a fundamental aspect of mechanically driven emergent behavior: the connection between a column's geometric structure and the direction that it buckles. To accomplish this, we introduce the Asymmetric Buckling Columns (ABC) dataset, a dataset comprised of three sub-datasets of asymmetric and heterogeneous column geometries where the goal is to classify the direction of symmetry breaking (left or right) under compression after the onset of instability. Because of complex local geometry, the "image-like" data representations required for implementing standard convolutional neural network based metamodels are not ideal, thus motivating the use of GNNs. In addition to investigating GNN model architecture, we study the effect of different input data representation approaches, data augmentation, and combining multiple models as an ensemble. While we were able to obtain good results, we also showed that predicting solid mechanics based emergent behavior is non-trivial. Because both our model implementation and dataset are distributed under open-source licenses, we hope that future researchers can build on our work to create enhanced mechanics-specific machine learning pipelines for capturing the behavior of complex geometric structures.

翻译：从设计建筑材料到跨尺度的机械行为,计算模型是实实在在机械学中的一个关键工具。最近,人们越来越有兴趣使用机器学习来降低物理模拟的计算成本。值得注意的是,尽管依赖图形神经网络(GNNS)的机器学习方法在学习机械学方面表现出成功,但GNNs的性能还没有在无数的固体机械问题上进行调查。在这项工作中,我们研究了GNNs预测机械驱动的突发行为的基本方面的能力:一列的几何结构与它连接的方向之间的联系。为了完成这一任务,我们引入了Asymloging列(ABC)的数据集,这是一个由三个不对称和混杂列的子数据集组成的数据集,目的是在不稳定开始后将对断裂方向(左或右)进行分类。由于复杂的本地测算模型,“模拟式”数据表显示实施标准进化的神经网络基元模型下的元模型是不理想的。因此,我们引入了“Asymlogical 列列列列列列列(ABC) 数据集,从而将GNNNUR 的模型的模型的模型整合结果作为我们的数据模型的模型的模型的模型的模型的模型的模型, 显示了我们获取结果。