Inverse Design of Shape‐Programmable Morphing Surfaces With Patterned Limiting Layers via Diffusion‐Based Generative Model

Abstract

Soft morphing surfaces show great potential for adaptive physical interaction, yet their inverse design remains challenging due to strong material nonlinearity and large geometric deformations. Inspired by the differential growth of Acetabularia, we develop shape‐programmable morphing surfaces (SPMS) and establish a generative inverse design framework based on conditional diffusion models (CDMs). SPMS employ patterned limiting layers to regulate local strain under pneumatic actuation, enabling programmable control of spatially varying Gaussian curvature across continuous surfaces. To bridge physical mechanisms with generative models, we construct a high‐fidelity finite element dataset and represent complex 3D geometries as compact 2D Gaussian curvature maps for training. This framework enables end‐to‐end prediction of design patterns from target shapes with high accuracy and rapid inference. We provide a general inverse design strategy that can be transferred to functional soft‐matter systems in specific application scenarios, such as conformal interfaces for robotic mannequins and bio‐inspired swimming robots.