Machine learning methods for strut-based architected solids are attractive for reducing computational costs in optimisation calculations. However, the space of all realizable strut-based periodic architected solids is vast: not only can the number of nodes, their positions and the radii of the struts be changed but the topological variables such as the connectivity of the nodes brings significant complexity. In this work, we first examine the structure-property relationships of a large dataset of strut-based architected solids (lattices). We enrich the dataset by perturbing nodal positions and observe four classes of mechanical behaviour. A graph neural network (GNN) method is then proposed that directly describes the topology of the strut-based architected solid as a graph. The differentiating feature of our work is that key physical principles are embedded into the GNN architecture. In particular, the GNN model predicts fourth-order tensor with the required major and minor symmetries. The predictions are equivariant to rigid body and self-similar transformations, invariant to the choice of unit cell and constrained to provide a positive semi-definite stiffness tensor. We further demonstrate that augmenting the training dataset with nodal perturbations enables the model to better generalize to unseen lattice topologies.

中文翻译：

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基于支柱的架构实体的图神经网络


基于支柱的架构实体的机器学习方法对于降低优化计算中的计算成本很有吸引力。然而，所有可实现的基于支柱的周期性结构实体的空间都很大：不仅节点的数量、位置和支柱的半径可以改变，而且拓扑变量（如节点的连通性）也带来了极大的复杂性。在这项工作中，我们首先检查了基于支柱的架构实体（晶格）的大型数据集的结构-属性关系。我们通过扰动节点位置来丰富数据集，并观察四类机械行为。然后提出了一种图神经网络 （GNN） 方法，该方法将基于 Strut 的架构实体的拓扑直接描述为图。我们工作的不同之处在于关键物理原理被嵌入到 GNN 架构中。特别是，GNN 模型预测具有所需主要和次要对称性的四阶张量。预测对刚体和自相似变换是等变的，对晶胞的选择不变，并受约束以提供正的半定刚度张量。我们进一步证明，用节点扰动来增强训练数据集使模型能够更好地泛化到看不见的晶格拓扑。