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1. 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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2. Prediction of tensile performance for 3D printed photopolymer gyroid lattices using structural porosity, base material properties, and machine learning

   https://doi.org/10.1016/j.matdes.2023.112126  

   Peloquin, Jacob; Kirillova, Alina; Rudin, Cynthia; Brinson, LC; Gall, Ken (June 2023, Materials & Design)

   Advancements in additive manufacturing (AM) technology and three-dimensional (3D) modeling software have enabled the fabrication of parts with combinations of properties that were impossible to achieve with traditional manufacturing techniques. Porous designs such as truss-based and sheet-based lattices have gained much attention in recent years due to their versatility. The multitude of lattice design possibilities, coupled with a growing list of available 3D printing materials, has provided a vast range of 3D printable structures that can be used to achieve desired performance. However, the process of computationally or experimentally evaluating many combinations of base material and lattice design for a given application is impractical. This research proposes a framework for quickly predicting key mechanical properties of 3D printed gyroid lattices using information about the base material and porosity of the structure. Experimental data was gathered to train a simple, interpretable, and accurate kernel ridge regression machine learning model. The performance of the model was then compared to numerical simulation data and demonstrated similar accuracy at a fraction of the computation time. Ultimately, the model development serves as an advancement in ML-driven mechanical property prediction that can be used to guide extension of current and future models. 

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3. 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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4. Machine Learning–Assisted Design of Material Properties

   https://doi.org/10.1146/annurev-chembioeng-092220-024340  

   Kadulkar, Sanket; Sherman, Zachary M.; Ganesan, Venkat; Truskett, Thomas M. (June 2022, Annual Review of Chemical and Biomolecular Engineering)

   Designing functional materials requires a deep search through multidimensional spaces for system parameters that yield desirable material properties. For cases where conventional parameter sweeps or trial-and-error sampling are impractical, inverse methods that frame design as a constrained optimization problem present an attractive alternative. However, even efficient algorithms require time- and resource-intensive characterization of material properties many times during optimization, imposing a design bottleneck. Approaches that incorporate machine learning can help address this limitation and accelerate the discovery of materials with targeted properties. In this article, we review how to leverage machine learning to reduce dimensionality in order to effectively explore design space, accelerate property evaluation, and generate unconventional material structures with optimal properties. We also discuss promising future directions, including integration of machine learning into multiple stages of a design algorithm and interpretation of machine learning models to understand how design parameters relate to material properties. 

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5. Generative Adversarial Networks for Inverse Design of Two-Dimensional Spinodoid Metamaterials

   https://doi.org/10.2514/1.J063697  

   Liu, Sheng; Acar, Pınar (July 2024, AIAA Journal)

   The geometrical arrangement of metamaterials controls their mechanical properties, such as Young’s modulus and the shear modulus. However, optimizing the geometrical arrangement for user-defined performance criteria leads to an inverse problem that is intractable when considering numerous combinations of properties and underlying geometries. Machine-learning techniques have been proven to be effective and practical to accomplish such nonintuitive design tasks. This paper proposes an inverse design framework using conditional generative adversarial networks (CGANs) to explore and optimize two-dimensional metamaterial designs consisting of spinodal topologies, called spinodoids. CGANs are capable of solving the many-to-many inverse problem, which requires generating a group of geometric patterns of representative volume elements with target combinations of mechanical properties. The performance of the networks was validated by numerical simulations with the finite element method. The proposed inverse design framework vastly improves the efficiency of design exploration and optimization of spinodoid metamaterials. 

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