In the emerging field of mechanical metamaterials, using periodic lattice structures as a primary ingredient is relatively frequent. However, the choice of aperiodic lattices in these structures presents unique advantages regarding failure, e.g., buckling or fracture, because avoiding repeated patterns prevents global failures, with local failures occurring in turn that can beneficially delay structural collapse. Therefore, it is expedient to develop models for computing efficiently the effective mechanical properties in lattices from different general features while addressing the challenge of presenting topologies (or graphs) of different sizes. In this paper, we develop a deep learning model to predict energetically-equivalent mechanical properties of linear elastic lattices effectively. Considering the lattice as a graph and defining material and geometrical features on such, we show that Graph Neural Networks provide more accurate predictions than a dense, fully connected strategy, thanks to the geometrically induced bias through graph representation, closer to the underlying equilibrium laws from mechanics solved in the direct problem. Leveraging the efficient forward-evaluation of a vast number of lattices using this surrogate enables the inverse problem, i.e., to obtain a structure having prescribed specific behavior, which is ultimately suitable for multiscale structural optimization problems.

翻译：在力学超材料这一新兴领域中，采用周期性点阵结构作为基本组成已较为常见。然而，在这些结构中选用非周期性点阵在破坏（如屈曲或断裂）方面具有独特优势：由于避免了重复模式引发的全局失效，转而发生局部失效，这反而有利于延缓结构坍塌。因此，有必要开发能够高效计算不同普适特征点阵有效力学特性的模型，同时应对具有不同尺寸拓扑（或图结构）的挑战。本文提出一种深度学习模型，可有效预测线弹性点阵的能量等效力学特性。通过将点阵视为图结构并定义其材料和几何特征，我们证明图神经网络能提供比全连接稠密策略更精准的预测，这得益于图表示引入的几何先验偏置——它更接近正问题求解所依据的力学平衡定律。利用该代理模型对大量点阵进行高效正向评估，可进一步解决逆问题（即获得具有指定特定性能的结构），最终适用于多尺度结构优化问题。