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

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

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

   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. Data-Driven Multiscale Topology Optimization Using Multi-Response Latent Variable Gaussian Process

   https://doi.org/10.1115/DETC2020-22595  

   Wang, Liwei ; Tao, Siyu ; Zhu, Ping ; Chen, Wei ( August 2020 , Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 11A: 46th Design Automation Conference (DAC)

   null (Ed.)

   The data-driven approach is emerging as a promising method for the topological design of the multiscale structure with greater efficiency. However, existing data-driven methods mostly focus on a single class of unit cells without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of inherent ordering or “distance” measure between different classes of unit cells in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) to creating multi-response LVGP (MRLVGP) for the unit cell libraries of metamaterials, taking both qualitative unit cell concepts and quantitative unit cell design variables as mixed-variable inputs. The MRLVGP embeds the mixed variables into a continuous design space based on their collective effect on the responses, providing substantial insights into the interplay between different geometrical classes and unit cell materials. With this model, we can easily obtain a continuous and differentiable transition between different unit cell concepts that can render gradient information for multiscale topology optimization. While the proposed approach has a broader impact on the concurrent topological and material design of engineered systems, we demonstrate its benefits through multiscale topology optimization with aperiodic unit cells. Design examples reveal that considering multiple unit cell types can lead to improved performance due to the consistent load-transferred paths for micro- and macrostructures.

    

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