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捉复杂的结构-性能关系革新了材料发现领域，然而由于缺乏高效表达能力，将这些方法扩展到三维超材料的逆向设计仍受限于计算复杂度与尚未充分探索的设计空间。本文提出DiffuMeta——一种融合扩散变压器与代数语言表示的生成框架，将三维几何结构编码为数学语句。这种紧凑、统一的参数化方法覆盖多种拓扑结构，使得变压器可直接应用于结构设计。DiffuMeta利用扩散模型生成全新壳结构，在大变形条件下精准实现目标应力-应变响应，在考虑屈曲与接触的同时通过产生多样性解来应对固有的一对多映射问题。独特的是，我们的方法能够同时控制多个力学目标，包括超出训练域的线性和非线性响应。制造结构的实验验证进一步证实了该方法在加速设计具有定制化特性的超材料与结构方面的有效性。