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

   https://doi.org/10.1115/1.4048629  

   Chan, Yu-Chin; Ahmed, Faez; Wang, Liwei; Chen, Wei (March 2021, Journal of Mechanical Design)

   null (Ed.)

   Abstract 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. 

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2. A Dataset Generation Framework for Symmetry-Induced Mechanical Metamaterials

   https://doi.org/10.1115/1.4066169  

   Abu-Mualla, Mohammad; Huang, Jida (April 2025, Journal of Mechanical Design)

   Abstract The surge in machine learning research and recent advancements in 3D printing technologies have significantly enriched materials science and engineering, particularly in the domain of mechanical metamaterials, which commonly consist of periodic truss materials. Despite the extensive exploration of their tailorable properties, truss-based metamaterial design has predominantly adhered to cubic and orthotropic unit cells, a limitation arising from the conventional design method, where the type of symmetry related to the designed truss-based material is determined after the design process is done. To overcome this issue, this work introduces a groundbreaking 3D truss material designing framework that departs from this constraint by employing six distinctive material symmetries (cubic, hexagonal, tetragonal, orthotropic, trigonal, and monoclinic) within the design process. This innovative approach represents a versatile paradigm shift compared to previous design approaches. Furthermore, we are able to integrate anisotropy into the design framework, thus enhancing the property space exploration capability of the proposed design framework. Probing the property space of unit cells using our design framework demonstrates its capacity to achieve a diverse range of mechanical properties. The analysis of the generated samples shows that they can surpass the most extensive datasets available in the literature in regions where directional elastic properties are not linked by structural symmetry. The proposed method facilitates the generation of a truss dataset, which can be represented in a trainable format suitable for machine learning and data-driven approaches. This advancement paves the way for the development of robust inverse design tools for truss materials, marking a significant contribution to the mechanical metamaterial community. 

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3. Symmetry-Induced Mechanical Metamaterials Design Framework and Dataset Generation

   https://doi.org/10.1115/DETC2024-141866  

   Abu-Mualla, Mohammad; Huang, Jida (August 2024, American Society of Mechanical Engineers)

   Abstract The surge in machine learning research and recent advancements in 3D printing technologies have significantly enriched materials science and engineering, particularly in the domain of mechanical metamaterials, which commonly consist of periodic truss materials. Despite the extensive exploration of their tailorable properties, truss-based metamaterial design has predominantly adhered to cubic and orthotropic unit-cells, a limitation arising from the conventional design method, where the type of symmetry related to the designed truss-based material is determined after the design process is done. To overcome this issue, this work introduces a groundbreaking 3D truss material designing framework that departs from this constraint by employing six distinctive material symmetries (cubic, hexagonal, tetragonal, orthotropic, trigonal, and monoclinic) within the design process. This innovative approach represents a versatile paradigm shift compared to previous design approaches. Furthermore, we are able to integrate anisotropy into the design framework, thus enhancing the property space exploration capability of the proposed design framework. Probing materials property space using our design framework demonstrates its capacity to achieve a diverse range of mechanical properties, surpassing even the most extensive datasets available in the literature. The proposed method facilitates the generation of a comprehensive truss dataset, which can be represented in a trainable continuous format suitable for machine learning and data-driven approaches. This advancement paves the way for the development of robust inverse design tools for truss materials, marking a significant contribution to the mechanical metamaterial community. 

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4. GLOBALLY APPROXIMATE GAUSSIAN PROCESSES FOR BIG DATA WITH AN APPLICATION TO DATA-DRIVEN METAMATERIALS DESIGN

   Bostanabad, Ramin (January 2019, International Design Engineering Technical Conference)

   We introduce a novel method to enable Gaussian process (GP) modeling of massive datasets, called globally approximate Gaussian process (GAGP). Unlike most largescale supervised learners such as neural networks and trees, GAGP is easy to fit and can interpret the model behavior, making it particularly useful in engineering design with big data. The key idea of GAGP is to build an ensemble of independent GPs that distribute the entire training dataset among themselves and use the same hyperparameters. This is based on the observation that the GP hyperparameter estimates negligibly change as the size of the training data exceeds a certain level that can be estimated in a systematic way. For inference, the predictions from all GPs in the ensemble are pooled which allows to efficiently exploit the entire training dataset for prediction. Through analytical examples, we demonstrate that GAGP achieves very high predictive power that matches (and in some cases exceeds) that of state-of-the-art machine learning methods. We illustrate the application of GAGP in engineering design with a problem on data-driven metamaterials design where it is used to link reduced-dimension geometrical descriptors of unit cells and their properties. Searching for new unit cell designs with desired properties is then achieved by employing GAGP in inverse optimization. 

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5. Globally Approximate Gaussian Processes for Big Data With Application to Data-Driven Metamaterials Design

   https://doi.org/10.1115/1.4044257  

   Bostanabad, Ramin; Chan, Yu-Chin; Wang, Liwei; Zhu, Ping; Chen, Wei (November 2019, Journal of Mechanical Design)

   Abstract We introduce a novel method for Gaussian process (GP) modeling of massive datasets called globally approximate Gaussian process (GAGP). Unlike most large-scale supervised learners such as neural networks and trees, GAGP is easy to fit and can interpret the model behavior, making it particularly useful in engineering design with big data. The key idea of GAGP is to build a collection of independent GPs that use the same hyperparameters but randomly distribute the entire training dataset among themselves. This is based on our observation that the GP hyperparameter approximations change negligibly as the size of the training data exceeds a certain level, which can be estimated systematically. For inference, the predictions from all GPs in the collection are pooled, allowing the entire training dataset to be efficiently exploited for prediction. Through analytical examples, we demonstrate that GAGP achieves very high predictive power matching (and in some cases exceeding) that of state-of-the-art supervised learning methods. We illustrate the application of GAGP in engineering design with a problem on data-driven metamaterials, using it to link reduced-dimension geometrical descriptors of unit cells and their properties. Searching for new unit cell designs with desired properties is then achieved by employing GAGP in inverse optimization. 

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