# METASET: Exploring Shape and Property Spaces for Data-Driven Metamaterials Design

arXiv: https://arxiv.org/abs/2006.02142 · HTML: https://mlsanity.com/paper/2006.02142/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2020.

## Built on by (most cited first, 15 of 15)

- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains](https://mlsanity.com/paper/2104.10873/) (2021)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [Ship-D: Ship Hull Dataset for Design Optimization using Machine Learning](https://mlsanity.com/paper/2305.08279/) (2023)
- [t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning](https://mlsanity.com/paper/2202.10565/) (2022)
- [Guided Diffusion for Fast Inverse Design of Density-based Mechanical Metamaterials](https://mlsanity.com/paper/2401.13570/) (2024)
- [Challenges and opportunities for machine learning in multiscale computational modeling](https://mlsanity.com/paper/2303.12261/) (2023)
- [DATED: Guidelines for Creating Synthetic Datasets for Engineering Design Applications](https://mlsanity.com/paper/2305.09018/) (2023)
- [Remixing Functionally Graded Structures: Data-Driven Topology Optimization with Multiclass Shape Blending](https://mlsanity.com/paper/2112.00648/) (2021)
- [Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning](https://mlsanity.com/paper/2401.00003/) (2023)
- [MetaGen: A DSL, Database, and Benchmark for VLM-Assisted Metamaterial Generation](https://mlsanity.com/paper/2508.17568/) (2025)
- [An Uncertainty-aware Deep Learning Framework-based Robust Design Optimization of Metamaterial Units](https://mlsanity.com/paper/2407.20251/) (2024)
- [MetamatBench: Integrating Heterogeneous Data, Computational Tools, and Visual Interface for Metamaterial Discovery](https://mlsanity.com/paper/2505.20299/) (2025)
- [Smoothing the Rough Edges: Evaluating Automatically Generated Multi-Lattice Transitions](https://mlsanity.com/paper/2306.10055/) (2023)
- [Machine-Learning-Assisted Photonic Device Development: A Multiscale Approach from Theory to Characterization](https://mlsanity.com/paper/2506.20056/) (2025)

## Abstract (arXiv)

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.