  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.
