Triply periodic minimal surface (TPMS) metamaterials characterized by mathematically-controlled topologies exhibit better mechanical properties compared to uniform structures. The unit cell topology of such metamaterials can be further optimized to improve a desired mechanical property for a specific application. However, such inverse design involves multiple costly 3D finite element analyses in topology optimization and hence has not been attempted. Data-driven models have recently gained popularity as surrogate models in the geometrical design of metamaterials. Gyroid-like unit cells are designed using a novel voxel algorithm, a homogenization-based topology optimization, and a Heaviside filter to attain optimized densities of 0-1 configuration. Few optimization data are used as input-output for supervised learning of the topology optimization process from a 3D CNN model. These models could then be used to instantaneously predict the optimized unit cell geometry for any topology parameters, thus alleviating the need to run any topology optimization for future design. The high accuracy of the model was demonstrated by a low mean square error metric and a high dice coefficient metric. This accelerated design of 3D metamaterials opens the possibility of designing any computationally costly problems involving complex geometry of metamaterials with multi-objective properties or multi-scale applications.

翻译：由数学控制拓扑的三周期极小曲面（TPMS）超材料相较于均匀结构展现出更优异的力学性能。为进一步提升特定应用所需的力学特性，可对这类超材料的单胞拓扑进行优化。然而，这种逆向设计需要在拓扑优化过程中进行多次高成本的三维有限元分析，因此至今尚未实现。数据驱动模型作为超材料几何设计中的代理模型近来广受关注。本文采用新型体素算法、基于均匀化的拓扑优化方法及Heaviside滤波函数，设计出具有0-1优化密度的类螺旋体单胞。利用少量优化数据作为输入输出，通过三维卷积神经网络模型对拓扑优化过程进行监督学习。该模型可即时预测任意拓扑参数下的优化单胞几何结构，从而免去未来设计中的拓扑优化计算。低均方误差和高Dice系数指标证明了模型的高精度。这种加速设计三维超材料的方法，为涉及复杂几何结构的多目标或多尺度超材料计算问题提供了可行方案。