Style-constrained inverse design of microstructures with tailored mechanical properties using unconditional diffusion models

2026-01-10

arXiv.org

AI Summary

This work proposes a novel framework for microstructure inverse design by integrating unconditional denoising diffusion models with differentiable programming. Unlike conventional conditional diffusion approaches that rely on large annotated datasets and require retraining when boundary conditions or governing equations change, the proposed method treats the noise input as an optimizable variable and leverages end-to-end gradient backpropagation—implemented via vector-Jacobian product concatenation—to refine the reverse denoising trajectory. This enables direct generation of microstructures that simultaneously satisfy target mechanical properties and stylistic constraints. The approach eliminates the need for labeled data and repeated training, and demonstrates remarkable flexibility and generalization in jointly controlling complex material behaviors, including equivalent stiffness, hyperelasticity, and elastoplasticity, under diverse design constraints.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Neural Architectures and Foundation Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Deep generative models, particularly denoising diffusion models, have achieved remarkable success in high-fidelity generation of architected microstructures with desired properties and styles. Nevertheless, these recent methods typically rely on conditional training mechanisms and demand substantial computational effort to prepare the labeled training dataset, which makes them inflexible since any change in the governing equations or boundary conditions requires a complete retraining process. In this study, we propose a new inverse design framework that integrates unconditional denoising diffusion models with differentiable programming techniques for architected microstructure generation. Our approach eliminates the need for expensive labeled dataset preparation and retraining for different problem settings. By reinterpreting the noise input to the diffusion model as an optimizable design variable, we formulate the design task as an optimization problem over the noise input, enabling control over the reverse denoising trajectory to guide the generated microstructure toward the desired mechanical properties while preserving the stylistic constraints encoded in the training dataset. A unified differentiation pipeline via vector-Jacobian product concatenations is developed to enable end-to-end gradient evaluation through backpropagation. Several numerical examples, ranging from the design of microstructures with specified homogenized properties to those with targeted hyperelastic and elasto-plastic behaviors, showcase the effectiveness of the framework and its potential for advanced design tasks involving diverse performance and style requirements.

Problem

• inverse design
• microstructure
• conditional training
• labeled dataset
• retraining

Innovation

• unconditional diffusion models
• inverse design
• differentiable programming
• microstructure generation
• style-constrained optimization