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1. Data-Driven Topology Optimization With Multiclass Microstructures Using Latent Variable Gaussian Process

   https://doi.org/10.1115/1.4048628  

   Wang, Liwei; Tao, Siyu; Zhu, Ping; Chen, Wei (March 2021, Journal of Mechanical Design)

   null (Ed.)

   Abstract The data-driven approach is emerging as a promising method for the topological design of multiscale structures with greater efficiency. However, existing data-driven methods mostly focus on a single class of microstructures without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of an inherent ordering or “distance” measure between different classes of microstructures in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) models to create multi-response LVGP (MR-LVGP) models for the microstructure libraries of metamaterials, taking both qualitative microstructure concepts and quantitative microstructure design variables as mixed-variable inputs. The MR-LVGP model embeds the mixed variables into a continuous design space based on their collective effects on the responses, providing substantial insights into the interplay between different geometrical classes and material parameters of microstructures. With this model, we can easily obtain a continuous and differentiable transition between different microstructure concepts that can render gradient information for multiscale topology optimization. We demonstrate its benefits through multiscale topology optimization with aperiodic microstructures. Design examples reveal that considering multiclass microstructures can lead to improved performance due to the consistent load-transfer paths for micro- and macro-structures. 

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2. Scalable Gaussian Processes for Data-Driven Design Using Big Data With Categorical Factors

   https://doi.org/10.1115/1.4052221  

   Wang, Liwei; Yerramilli, Suraj; Iyer, Akshay; Apley, Daniel; Zhu, Ping; Chen, Wei (February 2022, Journal of Mechanical Design)

   null (Ed.)

   Abstract Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have difficulties in accommodating big data sets, categorical inputs, and multiple responses, which has become a common challenge for a growing number of data-driven design applications. In this paper, we propose a GP model that utilizes latent variables and functions obtained through variational inference to address the aforementioned challenges simultaneously. The method is built upon the latent-variable Gaussian process (LVGP) model where categorical factors are mapped into a continuous latent space to enable GP modeling of mixed-variable data sets. By extending variational inference to LVGP models, the large training data set is replaced by a small set of inducing points to address the scalability issue. Output response vectors are represented by a linear combination of independent latent functions, forming a flexible kernel structure to handle multiple responses that might have distinct behaviors. Comparative studies demonstrate that the proposed method scales well for large data sets with over 104 data points, while outperforming state-of-the-art machine learning methods without requiring much hyperparameter tuning. In addition, an interpretable latent space is obtained to draw insights into the effect of categorical factors, such as those associated with “building blocks” of architectures and element choices in metamaterial and materials design. Our approach is demonstrated for machine learning of ternary oxide materials and topology optimization of a multiscale compliant mechanism with aperiodic microstructures and multiple materials. 

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3. Connecting Microstructures for Multiscale Topology Optimization With Connectivity Index Constraints

   https://doi.org/10.1115/1.4041176  

   Du, Zongliang; Zhou, Xiao-Yi; Picelli, Renato; Kim, H. Alicia (November 2018, Journal of Mechanical Design)

   Abstract With the rapid developments of advanced manufacturing and its ability to manufacture microscale features, architected materials are receiving ever increasing attention in many physics fields. Such a design problem can be treated in topology optimization as architected material with repeated unit cells using the homogenization theory with the periodic boundary condition. When multiple architected materials with spatial variations in a structure are considered, a challenge arises in topological solutions, which may not be connected between adjacent material architecture. This paper introduces a new measure, connectivity index (CI), to quantify the topological connectivity, and adds it as a constraint in multiscale topology optimization to achieve connected architected materials. Numerical investigations reveal that the additional constraints lead to microstructural topologies, which are well connected and do not substantially compromise their optimalities. 

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4. Design of Polymer Nanodielectrics for Capacitive Energy Storage

   https://doi.org/10.3390/nano13172394  

   Prabhune, Prajakta; Comlek, Yigitcan; Shandilya, Abhishek; Sundararaman, Ravishankar; Schadler, Linda S.; Brinson, Lynda Catherine; Chen, Wei (September 2023, Nanomaterials)

   Polymer nanodielectrics present a particularly challenging materials design problem for capacitive energy storage applications like polymer film capacitors. High permittivity and breakdown strength are needed to achieve high energy density and loss must be low. Strategies that increase permittivity tend to decrease the breakdown strength and increase loss. We hypothesize that a parameter space exists for fillers of modest aspect ratio functionalized with charge-trapping molecules that results in an increase in permittivity and breakdown strength simultaneously, while limiting increases in loss. In this work, we explore this parameter space, using physics-based, multiscale 3D dielectric property simulations, mixed-variable machine learning and Bayesian optimization to identify the compositions and morphologies which lead to the optimization of these competing properties. We employ first principle-based calculations for interface trap densities which are further used in breakdown strength calculations. For permittivity and loss calculations, we use continuum scale modelling and finite difference solution of Poisson’s equation for steady-state currents. We propose a design framework for optimizing multiple properties by tuning design variables including the microstructure and interface properties. Finally, we employ mixed-variable global sensitivity analysis to understand the complex interplay between four continuous microstructural and two categorical interface choices to extract further physical knowledge on the design of nanodielectrics. 

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5. 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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