{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/towards-sign-distance-function-based","title":"Towards Signed Distance Function based Metamaterial Design: Neural Operator Transformer for Forward Prediction and Diffusion Model for Inverse Design","arxiv_id":"2504.01195","date":"2025-04-01","proceeding":null,"authors":["Qibang Liu","Seid Koric","Diab Abueidda","Hadi Meidani","Philippe 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 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.","url_abs":"https://arxiv.org/abs/2504.01195v3","url_pdf":"https://arxiv.org/pdf/2504.01195v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"towards-sign-distance-function-based","repo_url":"https://github.com/qibangliu/sdfgeodesign","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}