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 present a higher-order GNN model trained to predict the fourth-order stiffness tensor of periodic strut-based lattices. 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 the benefits of the encoded equivariance and energy conservation in terms of predictive performance and reduced training requirements.

翻译：晶格是一类性能高度依赖于几何设计的架构化超材料。晶格与图结构之间的类比性使得图神经网络（GNN）能够作为比传统方法（如有限元建模）更快速的替代模型。本文提出了一种高阶图神经网络模型，旨在预测周期性支柱基晶格的四阶刚度张量。该模型的关键特性包括：（i）SE(3)等变性，以及（ii）与热力学能量守恒定律的一致性。我们基于多种误差指标将所提模型与非等变模型进行对比，验证了编码等变性与能量守恒特性在提升预测性能与降低训练需求方面的优势。