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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)

   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. Deep Neural Operator Enabled Concurrent Multitask Design for Multifunctional Metamaterials Under Heterogeneous Fields

   https://doi.org/10.1002/adom.202303087  

   Lee, Doksoo ; Zhang, Lu ; Yu, Yue ; Chen, Wei ( March 2024 , Advanced Optical Materials)

   Multifunctional metamaterials (MMM) bear promise as next‐generation material platforms supporting miniaturization and customization. Despite many proof‐of‐concept demonstrations and the proliferation of deep learning assisted design, grand challenges of inverse design for MMM, especially those involving heterogeneous fields possibly subject to either mutual meta‐atom coupling or long‐range interactions, remain largely under‐explored. To this end, a data‐driven design framework is presented, which streamlines the inverse design of MMMs involving heterogeneous fields. A core enabler is implicit Fourier neural operator (IFNO), which predicts heterogeneous fields distributed across a metamaterial array, thus in general at odds with homogenization assumptions. Additionally, a standard formulation of inverse problem covering a broad class of MMMs is presented, together with gradient‐based multitask concurrent optimization identifying a set of Pareto‐optimal architecture‐stimulus (A‐S) pairs. Fourier multiclass blending is proposed to synthesize inter‐class meta‐atoms anchored on a set of geometric motifs, while enjoying training‐free dimension reduction and built‐it reconstruction. Interlocking the three pillars, the framework is validated for light‐by‐light programmable nanoantenna, whose design involves vast space jointly spanned by quasi‐freeform supercells, maneuverable incident phase distributions, and conflicting figure‐of‐merits (FoM) involving on‐demand localization patterns. Accommodating all the challenges, the framework can propel future advancements of MMM.

    

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3. Machine learning assisted design of shape-programmable 3D kirigami metamaterials

   https://doi.org/10.1038/s41524-022-00873-w  

   Alderete, Nicolas A. ; Pathak, Nibir ; Espinosa, Horacio D. ( September 2022 , npj Computational Materials)

   Kirigami-engineering has become an avenue for realizing multifunctional metamaterials that tap into the instability landscape of planar surfaces embedded with cuts. Recently, it has been shown that two-dimensional Kirigami motifs can unfurl a rich space of out-of-plane deformations, which are programmable and controllable across spatial scales. Notwithstanding Kirigami’s versatility, arriving at a cut layout that yields the desired functionality remains a challenge. Here, we introduce a comprehensive machine learning framework to shed light on the Kirigami design space and to rationally guide the design and control of Kirigami-based materials from the meta-atom to the metamaterial level. We employ a combination of clustering, tandem neural networks, and symbolic regression analyses to obtain Kirigami that fulfills specific design constraints and inform on their control and deployment. Our systematic approach is experimentally demonstrated by examining a variety of applications at different hierarchical levels, effectively providing a tool for the discovery of shape-shifting Kirigami metamaterials.

    

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4. 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)

   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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5. METASET: An Automated Data Selection Method for Scalable Data-Driven Design of Metamaterials

   https://doi.org/10.1115/DETC2020-22681  

   Chan, Yu-Chin ; Ahmed, Faez ; Wang, Liwei ; Chen, Wei ( October 2020 , International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences)

   null (Ed.)

   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 than others can be detrimental to the efficacy of the approaches and any models built on those sets. 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 space, 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. We also apply METASET to eliminate inherent overlaps in a dataset of 3D unit cells created with symmetry rules, distilling it down to the most unique families. Our diverse subsets are provided publicly for use by any designer.

    

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