Physics-Informed Neural Network-Enabled Forward Prediction and Inverse Design of Ring Origami.

Ring origami, consisting of closed-loop rods, can realize diverse shape-morphing behaviors, including 2D-to-1D, 2D-to-2D, and 2D-to-3D transformations, by harnessing snap-buckling instability. To broaden its application potential in areas such as deployable aerospace structures, soft robotics, and reconfigurable metamaterials, a programmable design framework is highly desired. In this work, we develop a unified framework for the forward prediction and inverse design of ring origami by integrating Kirchhoff rod theory with a physics-informed neural network. The framework can identify the stable states of various segmented rings (e.g., square and hexagonal rings) composed of rod segments with prescribed constant or varying natural curvature (i.e., curvature in the stress-free state). By introducing an additional shape-matching loss, the framework can also determine the natural curvature profile of segmented rings required to achieve stable configurations that can be confined within a target spatial domain or conform to a target curved surface. Its generality and robustness are further demonstrated by extending it to 3D rod systems. This work establishes a powerful strategy for the programmable design of elastic rod systems exemplified by ring origami and opens new opportunities for functional applications that demand shape-morphing structures with simple geometries, high packing capability, and prescribed stable configurations.