用数学语言建模三维超材料，实现精准逆向设计。
Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers
- 将三维结构编码为数学语句，统一参数化表示复杂拓扑。
- 通过扩散变换器生成满足特定力学响应的新结构，支持大变形与屈曲模拟。
- 可同时控制线性与非线性性能，适合高自由度设计需求。
生成式机器学习模型已推动材料发现，但三维超材料的逆向设计仍受限于计算复杂性和表达能力不足。本文提出DiffuMeta框架，结合扩散变换器与代数语言表示，将三维几何编码为数学语句，实现紧凑统一的参数化。该方法直接应用变换器进行结构设计，利用扩散模型生成具有精确应力-应变响应的壳体结构，能处理大变形、屈曲和接触问题，并通过多样化输出解决一对多映射难题。独特之处在于可同时控制多种力学目标，包括训练域外的非线性响应。实验验证了所制备结构的有效性，证明该方法能加速具有定制性能的超材料与结构的设计。
原文摘要 · Abstract (English)
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.
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