Toward signed distance function based metamaterial design: Neural operator transformer for forward prediction and diffusion model for inverse design
Qibang Liu, Seid Korić, Diab Abueidda, Hadi Meidani, Philippe H. Geubelle
Abstract
The inverse design of metamaterial architectures presents a significant challenge, particularly for nonlinear mechanical properties involving large deformations, buckling, contact, and plasticity. Traditional methods, such as gradient-based optimization, and recent generative deep-learning approaches often rely on binary pixel-based representations, which introduce jagged edges that hinder finite element (FE) simulations and 3D printing. To overcome these challenges, we propose an inverse design framework that utilizes a signed distance function (SDF) representation combined with a conditional diffusion model. The SDF provides a smooth boundary representation, eliminating the need for post-processing and ensuring compatibility with FE simulations and manufacturing methods. A classifier-free guided diffusion model is trained to generate SDFs conditioned on target macroscopic stress-strain curves, enabling efficient one-shot design synthesis. To assess the mechanical response and the quality of the generated designs, we introduce a forward prediction model based on Neural Operator Transformers (NOT), which accurately predicts homogenized stress-strain curves and local solution fields for arbitrary geometries with irregular query meshes. This approach enables a closed-loop process for general metamaterial design, offering a pathway for the development of advanced functional materials.