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Reconstructing 3D granular microstructures within volumes of arbitrary geometries from limited 2D image data is crucial for predicting the material properties, as well as performances of structural components accounting for material microstructural effects. We present a novel generative learning framework that enables exascale reconstruction of granular microstructures within complex 3D geometric volumes. Building upon existing transfer learning techniques using pre-trained convolutional neural networks (CNN), we introduce several key innovations to overcome the difficulties inherent in arbitrary geometries. Our framework incorporates periodic boundary conditions using circular padding techniques, ensuring continuity and representativeness of the reconstructed microstructures. We also introduce a novel seamless transition reconstruction (STR) method that creates statistically equivalent transition zones to integrate multiple pre-existing 3D microstructure volumes. Based on STR, we propose a cost-effective strategy for reconstructing microstructures within complex geometric volumes, minimizing computational waste. Validation through numerical experiments using kinetic Monte Carlo simulations demonstrates accurate reproduction of grain statistics, including grain size distributions and morphology. A case study involving the reconstruction of a 4-blade propeller microstructure illustrates the method’s capability to efficiently handle complex geometries. The proposed framework significantly reduces computational demands while maintaining high reconstruction quality, paving the way for scalable microstructure reconstruction in materials design and analysis. 

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. 

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. 

Abstract In this paper, we propose and compare two novel deep generative model-based approaches for the design representation, reconstruction, and generation of porous metamaterials characterized by complex and fully connected solid and pore networks. A highly diverse porous metamaterial database is curated, with each sample represented by solid and pore phase graphs and a voxel image. All metamaterial samples adhere to the requirement of complete connectivity in both pore and solid phases. The first approach employs a Dual Decoder Variational Graph Autoencoder to generate both solid phase and pore phase graphs. The second approach employs a Variational Graph Autoencoder for reconstructing/generating the nodes in the solid phase and pore phase graphs and a Transformer-based Large Language Model (LLM) for reconstructing/generating the connections, i.e., the edges among the nodes. A comparative study was conducted, and we found that both approaches achieved high accuracy in reconstructing node features, while the LLM exhibited superior performance in reconstructing edge features. Reconstruction accuracy is also validated by voxel-to-voxel comparison between the reconstructions and the original images in the test set. Additionally, discussions on the advantages and limitations of using LLMs in metamaterial design generation, along with the rationale behind their utilization, are provided.