METASET: Exploring Shape and Property Spaces for Data-Driven Metamaterials Design
METASET: Exploring Shape and Property Spaces for Data-Driven Metamaterials Design
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DOI：
10.1115/1.4048629
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发表时间：
2020-06
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通讯作者：
Yu-Chin Chan;Faez Ahmed;Liwei Wang;Wei Chen
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作者：
Yu-Chin Chan;Faez Ahmed;Liwei Wang;Wei Chen
机械超材料的数据驱动设计是应对昂贵的物理模拟和巨大的、往往难以处理的几何设计空间的一种日益流行的方法。使用预计算的单元格数据集，可以通过组合搜索算法快速填充多尺度结构，并可以训练机器学习模型来加速这一过程。然而，对数据的依赖引发了一个独特的挑战：包含更多特定形状或物理属性的不平衡数据集可能不利于数据驱动方法的有效性。作为回答，我们假设较小但不同的单元单元集导致可扩展的搜索和无偏见的学习。为了选择这样的子集，我们提出了一种方法METASET，该方法(1)使用相似度量和半正定核来联合度量形状空间和属性空间中的单位单元的贴近度，(2)结合Definantal Point过程来有效地选择子集。此外，METASET允许在形状和属性多样性之间进行权衡，以便可以针对各种应用调整子集。通过具有目标位移分布的二维超材料的设计，我们证明了更小、更多样化的子集确实可以改善搜索过程和结构性能。通过消除使用对称规则创建的3D单元数据集中的固有重叠，我们还说明了我们的灵活方法可以提取唯一的子集，而不考虑所使用的度量。我们的各种子集都是公开提供的，供任何设计师使用。
Data-driven design of mechanical metamaterials is an increasingly popular method to combat costly physical simulations and immense, often intractable, geometrical design spaces. Using a precomputed dataset of unit cells, a multiscale structure can be quickly filled via combinatorial search algorithms, and machine learning models can be trained to accelerate the process. However, the dependence on data induces a unique challenge: an imbalanced dataset containing more of certain shapes or physical properties can be detrimental to the efficacy of data-driven approaches. In answer, we posit that a smaller yet diverse set of unit cells leads to scalable search and unbiased learning. To select such subsets, we propose METASET, a methodology that (1) uses similarity metrics and positive semi-definite kernels to jointly measure the closeness of unit cells in both shape and property spaces and (2) incorporates Determinantal Point Processes for efficient subset selection. Moreover, METASET allows the trade-off between shape and property diversity so that subsets can be tuned for various applications. Through the design of 2D metamaterials with target displacement profiles, we demonstrate that smaller, diverse subsets can indeed improve the search process as well as structural performance. By eliminating inherent overlaps in a dataset of 3D unit cells created with symmetry rules, we also illustrate that our flexible method can distill unique subsets regardless of the metric employed. Our diverse subsets are provided publicly for use by any designer.