Unlike proteins, which have a wealth of validated structural data, experimentally or computationally validated DNA origami datasets are limited. Here we present a graph neural network that can predict the three-dimensional conformation of DNA origami assemblies both rapidly and accurately. We develop a hybrid data-driven and physics-informed approach for model training, designed to minimize not only the data-driven loss but also the physics-informed loss. By employing an ensemble strategy, the model can successfully infer the shape of monomeric DNA origami structures almost in real time. Further refinement of the model in an unsupervised manner enables the analysis of supramolecular assemblies consisting of tens to hundreds of DNA blocks. The proposed model enables an automated inverse design of DNA origami structures for given target shapes. Our approach facilitates the real-time virtual prototyping of DNA origami, broadening its design space.