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1. t-METASET: Task-Aware Generation of Metamaterial Datasets by Diversity-Based Active Learning

   https://doi.org/10.1115/DETC2022-87653  

   Lee, Doksoo; Chan, Yu-Chin; Chen, Wei; Wang, Liwei; Chen, Wei (August 2022, American Society of Mechanical Engineers)

   Abstract Inspired by the recent achievements of machine learning in diverse domains, data-driven metamaterials design has emerged as a compelling paradigm that can unlock the potential of the multiscale architectures. The model-centric research trend, however, lacks principled frameworks dedicated to data acquisition, whose quality propagates into the downstream tasks. Built by naive space-filling design in shape descriptor space, metamaterial datasets suffer from property distributions that are either highly imbalanced or at odds with design tasks of interest. To this end, we present t-METASET: an active-learning-based data acquisition framework aiming to guide both balanced and task-aware data generation. Uniquely, we seek a solution to a commonplace yet frequently overlooked scenario at early stages of data-driven design: when a massive shape-only library has been prepared with no properties evaluated. The key idea is to harness a data-driven shape descriptor learned from generative models, fit a sparse regressor as a start-up agent, and leverage metrics related to diversity to drive data acquisition to areas that help designers fulfill design goals. We validate the proposed framework in three deployment cases, which encompass general use, task-specific use, and tailorable use. Two large-scale mechanical metamaterial datasets (∼ O(104)) are used to demonstrate the efficacy. Applicable to general design representations, t-METASET can boost future advancements in data-driven design. 

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2. 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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3. 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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4. Data‐Driven Design for Metamaterials and Multiscale Systems: A Review

   https://doi.org/10.1002/adma.202305254  

   Lee, Doksoo; Chen, Wei_Wayne; Wang, Liwei; Chan, Yu‐Chin; Chen, Wei (December 2023, Advanced Materials)

   Abstract Metamaterials are artificial materials designed to exhibit effective material parameters that go beyond those found in nature. Composed of unit cells with rich designability that are assembled into multiscale systems, they hold great promise for realizing next‐generation devices with exceptional, often exotic, functionalities. However, the vast design space and intricate structure–property relationships pose significant challenges in their design. A compelling paradigm that could bring the full potential of metamaterials to fruition is emerging: data‐driven design. This review provides a holistic overview of this rapidly evolving field, emphasizing the general methodology instead of specific domains and deployment contexts. Existing research is organized into data‐driven modules, encompassing data acquisition, machine learning‐based unit cell design, and data‐driven multiscale optimization. The approaches are further categorized within each module based on shared principles, analyze and compare strengths and applicability, explore connections between different modules, and identify open research questions and opportunities. 

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5. Probabilistic Representation and Inverse Design of Metamaterials Based on a Deep Generative Model with Semi‐Supervised Learning Strategy

   https://doi.org/10.1002/adma.201901111  

   Ma, Wei; Cheng, Feng; Xu, Yihao; Wen, Qinlong; Liu, Yongmin (July 2019, Advanced Materials)

   Abstract The research of metamaterials has achieved enormous success in the manipulation of light in a prescribed manner using delicately designed subwavelength structures, so‐called meta‐atoms. Even though modern numerical methods allow for the accurate calculation of the optical response of complex structures, the inverse design of metamaterials, which aims to retrieve the optimal structure according to given requirements, is still a challenging task owing to the nonintuitive and nonunique relationship between physical structures and optical responses. To better unveil this implicit relationship and thus facilitate metamaterial designs, it is proposed to represent metamaterials and model the inverse design problem in a probabilistically generative manner, enabling to elegantly investigate the complex structure–performance relationship in an interpretable way, and solve the one‐to‐many mapping issue that is intractable in a deterministic model. Moreover, to alleviate the burden of numerical calculations when collecting data, a semisupervised learning strategy is developed that allows the model to utilize unlabeled data in addition to labeled data in an end‐to‐end training. On a data‐driven basis, the proposed deep generative model can serve as a comprehensive and efficient tool that accelerates the design, characterization, and even new discovery in the research domain of metamaterials, and photonics in general. 

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