Physics-guided diffusion models for inverse design of disordered metamaterials

2026-03-17

AI Summary

This work addresses the challenges in inverse design of disordered metamaterials—namely, the non-intuitive structure–property relationships, the vast design space, and the need for retraining in existing generative methods when adapting to new tasks. To overcome these limitations, the authors propose a physics-guided diffusion model that embeds a differentiable physics solver into the reverse stochastic differential equation of the diffusion process. During sampling, generation trajectories are dynamically steered via gradient-based guidance toward desired performance criteria. This approach requires only a single unsupervised pretraining phase yet flexibly accommodates diverse design objectives. Demonstrated on foam-like metamaterials, the model efficiently generates microstructures that meet target specifications across three distinct tasks: thermal conductivity tuning, load–displacement response matching, and maximization of fracture energy absorption, thereby significantly enhancing the versatility and adaptability of inverse design.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Disordered metamaterials are promising for programming physical properties across diverse applications, yet their inverse design remains challenging due to the non-intuitive structure-property relationships and large design spaces. Recent generative approaches, particularly diffusion models, have shown potential in high-dimensional inverse design tasks. However, existing methods typically rely on carefully crafted training objectives, such as conditional data-driven or physics-informed loss functions. Because these strategies are inherently task-specific, the model must be retrained from scratch whenever the design problem changes (e.g., different governing equations, boundary conditions, or design objectives), severely limiting their flexibility and generalization ability. In this work, we propose physics-guided diffusion models that leverage differentiable physics-based solvers to instantly guide the generative process for inverse design. Drawing inspiration from classifier guidance, we develop a sampling strategy that directly incorporates physics guidance into the reverse stochastic differential equations. Our approach enables task-adaptive generation using gradients from differentiable solvers, while the diffusion model itself needs to be trained only once on unlabeled data. Focusing on disordered foam metamaterials, we present three representative design tasks: (1) achieving target effective thermal conductivity, (2) matching desired load-displacement response, and (3) maximizing energy absorption involving fractures. In each scenario, the proposed method successfully generates foam-like geometries that fulfill the prescribed physical objectives. These results demonstrate the versatility, efficiency, and practicality of physics-guided diffusion models for tackling complex inverse design problems in disordered metamaterials and beyond.

Problem

• inverse design
• disordered metamaterials
• diffusion models
• physics-guided generation
• structure-property relationship

Innovation

• physics-guided diffusion
• differentiable physics solver
• inverse design
• disordered metamaterials
• task-adaptive generation