A hybrid deep learning approach for the design of 2D Auxetic Metamaterials

Mechanical metamaterials feature unique and complex architectures that produce properties not present in their base materials. Traditional design methods often fall short in exploring the vast 2D design space efficiently, necessitating advanced techniques that can accommodate the design of these metamaterials. This paper presents a comprehensive framework for the design and evaluation of 2D metamaterials by integrating data enhancement technology and two novel machine learning (ML) models for design generation and field prediction. One of the primary challenges in designing mechanical metamaterials is the scarcity of data, particularly for non-linear behaviors. To enhance non-linear data, the framework employs data enhancement techniques including domain adaptation (Low-Rank Adaptation (LoRA) and fine-tuning) to adapt knowledge from data-rich linear to non-linear scenarios, and ensemble learning to label designs for generative models. With the enhanced data, a novel hybrid generation model of conditional Variational Autoencoder (CVAE) and Denoising Diffusion Probabilistic Model (DDPM) is introduced. The proposed hybrid model not only achieves high-fidelity design generation but also incorporates a guidance mask module, enabling users to influence the generation process actively and align the output with specific design requirements. Then, to evaluate the generated designs effectively, a novel graph-enhanced convolutional neural network (CNN) model is introduced for field prediction tasks, which has been tested on stress and displacement field prediction. This model excels in predicting stress fields at a nodal level, especially in high-stress regions, and improves the prediction of displacement fields through embedded topological consistency, enhancing both physical fidelity and training efficiency. Based on the predicted stress field, radial basis function (RBF) optimization techniques are applied to fine-tune the designs, particularly at high-stress points, ensuring optimal stress distribution and improved mechanical performance. The results demonstrate that the data enhancement techniques significantly contributed to developing the ML models for non-linear behavior. The proposed CVAE-DDPM hybrid model shows substantial improvements in design robustness and accuracy,compared to the individual CVAE and DDPM models. Additionally, the graph-enhanced CNN outperforms other field prediction models, and the subsequent RBF optimization effectively reduces the maximum von Mises stress in the design, based on predictions from the graph-enhanced CNN.