Work

Toward signed distance function based metamaterial design: Neural operator transformer for forward prediction and diffusion model for inverse design

Year: 2025

Type: article

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.

Source: Computer Methods in Applied Mechanics and Engineering

DOI: 10.1016/j.cma.2025.118316

Authors: Qibang Liu, Seid Koric, Diab Abueidda, Hadi Meidani, Philippe Geubelle

Institutions: University of Illinois Urbana-Champaign, Kansas State University, National Center for Supercomputing Applications, New York University Abu Dhabi

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

SDG: Industry, innovation and infrastructure

Open Access status: hybrid

Estimated APC paid: $4,830