Topo-GenMeta: Generative design of metamaterials based on diffusion model with attention to topology

Metamaterials are a family of artificial materials that achieve unique properties by designing the shape of unit cell structures. Expanding the metamaterial unit cell library is a key focus in this field, with the aim of enhancing the design flexibility to meet multifunctional requirements across diverse physical scenarios. Recent advancements in data-driven generative techniques using deep learning have significantly sped up innovations in metamaterial design. However, existing approaches mostly focus on the geometric characteristics of unit structures without considering their topological properties explicitly, which we believe are essential for enhancing design diversity and enriching material properties. In this study, we propose a novel data-driven metamaterial design methodology that combines the denoising diffusion probabilistic model with the persistent homology technique. Our model is capable of generating high-fidelity and functionally effective unit structures. Furthermore, by incorporating topological properties derived from persistent homology into the diffusion process, our method facilitates the generation of a diversity of metamaterial unit structures with richer shapes and properties. To the best of our knowledge, this is the first approach to explicitly consider topological properties in metamaterial design. In addition, our method also supports multi-scale design applications, enabling the generation of metamaterial units that align with the desired properties to achieve the optimization objectives.