Metamaterials are emerging as a new paradigmatic material system to render unprecedented and tailorable properties for a wide variety of engineering applications. However, the inverse design of metamaterial and its multiscale system is challenging due to high-dimensional topological design space, multiple local optima, and high computational cost. To address these hurdles, we propose a novel data-driven metamaterial design framework based on deep generative modeling. A variational autoencoder (VAE) and a regressor for property prediction are simultaneously trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous, and organized latent space. We show in this study that the latent space of VAE provides a distance metric to measure shape similarity, enable interpolation between microstructures and encode meaningful patterns of variation in geometries and properties. Based on these insights, systematic data-driven methods are proposed for the design of microstructure, graded family, and multiscale system. For microstructure design, the tuning of mechanical properties and complex manipulations of microstructures are easily achieved by simple vector operations in the latent space. The vector operation is further extended to generate metamaterial families with a controlled gradation of mechanical properties by searching on a constructed graph model. For multiscale metamaterial systems design, a diverse set of microstructures can be rapidly generated using VAE for target properties at different locations and then assembled by an efficient graph-based optimization method to ensure compatibility between adjacent microstructures. We demonstrate our framework by designing both functionally graded and heterogeneous metamaterial systems that achieve desired distortion behaviors.

中文翻译：

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超材料系统基于机械学习和设计的深度生成建模

超材料正在成为一种新的范式材料系统，可为各种工程应用提供前所未有的可定制特性。然而，由于高维拓扑设计空间、多个局部最优和高计算成本，超材料及其多尺度系统的逆向设计具有挑战性。为了解决这些障碍，我们提出了一种基于深度生成建模的新型数据驱动超材料设计框架。在大型超材料数据库上同时训练变分自编码器 (VAE) 和属性预测回归器，以将复杂的微观结构映射到低维、连续和有组织的潜在空间中。我们在这项研究中表明，VAE 的潜在空间提供了一个距离度量来测量形状相似性，启用微结构之间的插值，并编码几何和属性中有意义的变化模式。基于这些见解，提出了系统的数据驱动方法来设计微观结构、分级族和多尺度系统。对于微结构设计，通过潜在空间中的简单矢量操作可以轻松实现机械性能的调整和微结构的复杂操作。通过在构建的图形模型上进行搜索，进一步扩展了矢量操作以生成具有受控机械性能等级的超材料族。对于多尺度超材料系统设计，使用 VAE 可以针对不同位置的目标属性快速生成一组多样化的微结构，然后通过基于图的有效优化方法进行组装，以确保相邻微结构之间的兼容性。我们通过设计实现所需失真行为的功能分级和异质超材料系统来展示我们的框架。