Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

翻译：晶格是性能强烈依赖于几何设计的人工超材料。晶格与图结构的相似性使得图神经网络（GNN）能够作为比有限元建模等传统方法更快速的替代模型。本文生成了基于支柱的晶格结构-性能关系大数据集，该数据集面向学界开放，可推动基于物理原理的四阶张量拟合方法发展。此外，我们提出了在该数据集上训练的高阶GNN模型，其关键特征包括：（i）SE(3)等变性；（ii）与热力学能量守恒定律的一致性。通过多项误差指标对比非等变模型，我们验证了该模型在预测性能提升和训练需求降低方面的优势。最后，我们展示了该模型在人工材料设计任务中的应用实例。本方法可推广至弹性之外的其它四阶张量（如压电光学张量等）。