Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers

TL;DR

DiffuMeta introduces a novel algebraic language and diffusion transformer-based framework for inverse design of 3D metamaterials, enabling diverse, targeted, and multi-objective structural generation with experimental validation.

Contribution

This work presents the first integration of algebraic language representations with diffusion transformers for 3D metamaterial inverse design, expanding design space and control capabilities.

Findings

Generated structures with specific stress-strain responses.

Produced diverse solutions for complex mechanical objectives.

Validated designs through experimental fabrication.

Abstract

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.