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1. Textures Synthesis-Based XAI Approach for Designing Periodic Metamaterials Inspired by Stochastic Microstructures

   https://doi.org/10.1115/DETC2025-167879  

   Feng, Zhengkun; Xu, Hongyi (August 2025, American Society of Mechanical Engineers)

   Abstract This paper presents a novel approach for generating metamaterial designs by leveraging texture information learned from stochastic microstructure samples with exceptional mechanical properties. This eXplainable Artificial Intelligence (XAI)-based approach reduces the reliance of brainstorming and trial-and-error in inspiration-driven design practices. The key research question is whether the texture information extracted from stochastic microstructure samples can be used to design metamaterials with periodic structural patterns that surpass the original stochastic microstructures in mechanical properties. The proposed approach employs a pretrained supervised neural network and applies the Activation Maximization Texture Synthesis (AMTS) method to extract representative textures from high-performance stochastic microstructure samples. These textures serve as building blocks for creating novel periodic metamaterial designs. Using three benchmark cases of stochastic microstructure-inspired periodic metamaterial design, we compare the proposed approach with an earlier XAI design approach based on Gradient-weighted Regression Activation Mapping (Grad-RAM). Unlike the proposed approach, Grad-RAM extracts local microstructure patches directly from the original sample images rather than synthesizing representative textures to generate novel periodic metamaterial designs. Both XAI-based design approaches are evaluated based on the mechanical properties of the resulting designs. The relative merits of both approaches in terms of design performance and the need for human intervention are discussed. 

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2. An uncertainty-aware deep learning framework-based robust design optimization of metamaterial units

   https://doi.org/10.1007/s00158-025-03979-z  

   Wang, Zihan; Bhaduri, Anindya; Xu, Hongyi; Wang, Liping (March 2025, Structural and Multidisciplinary Optimization)

   Mechanical metamaterials represent an innovative class of artificial structures, distinguished by their extraordinary mechanical characteristics, which are beyond the scope of traditional natural materials. The use of deep generative models has become increasingly popular in the design of metamaterial units. The effectiveness of using deep generative models lies in their capacity to compress complex input data into a simplified, lower-dimensional latent space, while also enabling the creation of novel optimal designs through sampling within this space. However, the design process does not take into account the effect of model uncertainty due to data sparsity or the effect of input data uncertainty due to inherent randomness in the data. This might lead to the generation of undesirable structures with high sensitivity to the uncertainties in the system. To address this issue, a novel uncertainty-aware deep learning framework-based robust design approach is proposed for the design of metamaterial units with optimal target properties. The proposed approach utilizes the probabilistic nature of the deep learning framework and quantifies both aleatoric and epistemic uncertainties associated with surrogate-based design optimization. We demonstrate that the proposed design approach is capable of designing high-performance metamaterial units with high reliability. To showcase the effectiveness of the proposed design approach, a single-objective design optimization problem and a multi-objective design optimization problem are presented. The optimal robust designs obtained are validated by comparing them to the designs obtained from the topology optimization method as well as the designs obtained from a deterministic deep learning framework-based design optimization where none of the uncertainties in the system are explicitly considered. 

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3. A Generative Graph Neural Network-Based Framework for Designing Connectivity-Guaranteed Porous Metamaterial Units

   https://doi.org/10.1115/DETC2024-143200  

   Wang, Zihan; Bray, Austin; Naghavi_Khanghah, Kiarash; Xu, Hongyi (August 2024, American Society of Mechanical Engineers)

   Abstract Porous metamaterial units filled with fluid have been used in engineering systems due to their ability to achieve desired properties (e.g., effective thermal conductvity). Designing 3D porous metamaterial units while ensuring complete connectivity of both solid and pore phases presents a significant challenge. In this study, we propose a generative graph neural network-based framework for designing the porous metamaterial units infilled with liquid. Firstly, we propose a graph-based metamaterial unit generation approach to generate porous metamaterial samples with complete connectivity in both solid and pore phases. Secondly, we establish and evaluate three distinct variational graph autoencoder (VGAE)-based generative models to assess their effectiveness in generating an accurate latent space representation of metamaterial structures. By choosing the model with the highest reconstruction accuracy, the property-driven design search is conducted to obtain novel metamaterial unit designs with the targeted properties. A case study on designing liquid-filled metamaterials for thermal conductivity properties is carried out. The effectiveness of the proposed graph neural network-based design approach is evaluated by comparing the performances of the obtained designs with those of existing designs in the training database. Merits and shortcomings of the proposed framework are also discussed. 

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4. Designing Connectivity-Guaranteed Porous Metamaterial Units Using Generative Graph Neural Networks

   https://doi.org/10.1115/1.4066128  

   Wang, Zihan; Bray, Austin; Naghavi_Khanghah, Kiarash; Xu, Hongyi (February 2025, Journal of Mechanical Design)

   Abstract Designing 3D porous metamaterial units while ensuring complete connectivity of both solid and pore phases presents a significant challenge. This complete connectivity is crucial for manufacturability and structure-fluid interaction applications (e.g., fluid-filled lattices). In this study, we propose a generative graph neural network-based framework for designing the porous metamaterial units with the constraint of complete connectivity. First, we propose a graph-based metamaterial unit generation approach to generate porous metamaterial samples with complete connectivity in both solid and pore phases. Second, we establish and evaluate three distinct variational graph autoencoder (VGAE)-based generative models to assess their effectiveness in generating an accurate latent space representation of metamaterial structures. By choosing the model with the highest reconstruction accuracy, the property-driven design search is conducted to obtain novel metamaterial unit designs with the targeted properties. A case study on designing liquid-filled metamaterials for thermal conductivity properties is carried out. The effectiveness of the proposed graph neural network-based design framework is evaluated by comparing the performances of the obtained designs with those of known designs in the metamaterial database. Merits and shortcomings of the proposed framework are also discussed. 

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5. 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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