Generative machine learning models have revolutionized material discovery by capturing complex structure-property relationships, yet extending these approaches to the inverse design of three-dimensional metamaterials remains limited by computational complexity and underexplored design spaces due to the lack of expressive representations. Here we present DiffuMeta, a generative framework integrating diffusion transformers with an algebraic language representation, encoding three-dimensional geometries as mathematical sentences. This compact, unified parameterization spans diverse topologies, enabling the direct application of transformers to structural design. DiffuMeta leverages diffusion models to generate new shell structures with precisely targeted stress-strain responses under large deformations, accounting for buckling and contact while addressing the inherent one-to-many mapping by producing diverse solutions. Uniquely, our approach enables simultaneous control over multiple mechanical objectives, including linear and nonlinear responses beyond training domains. Experimental validation of fabricated structures further confirms the efficacy of our approach for accelerated design of metamaterials and structures with tailored properties.

翻译：生成式机器学习模型通过捕获复杂的结构-性能关系，彻底改变了材料发现领域。然而，由于缺乏高效表达方式，这些方法在三维超材料逆向设计中的应用仍受限于计算复杂度和未充分探索的设计空间。本文提出DiffuMeta框架——一种将扩散变压器与代数语言表示相融合的生成框架，可将三维几何结构编码为数学语句。这种紧凑统一的参数化方式覆盖了多样化的拓扑结构，使变压器能够直接应用于结构设计。DiffuMeta利用扩散模型生成在经历大变形时具有精准靶向应力-应变响应的新型壳结构，在考虑屈曲和接触行为的同时，通过生成多样化解决方案来应对固有的"一对多"映射难题。独特之处在于，本方法可同时控制多个力学目标，包括超越训练域范围的线性和非线性响应。对制备结构的实验验证进一步证实了本方法在加速具有定制性能的超材料和结构设计中的有效性。