Non-iterative Inverse Design for 4D Printing Via Fabrication-Ready Discrete Material Programming

Four-dimensional (4D) printing enables additively manufactured structures to morph under external stimuli, but its practical use remains limited by the lack of efficient inverse design methods that directly generate manufacturable material layouts. Existing approaches often depend on iterative optimisation or continuous material fields that require post-processing before fabrication. Here, we present a non-iterative inverse design framework that reformulates 4D printing material programming as a segmentation-based discrete assignment problem. After offline training, the model directly converts a prescribed target deformation into a fabrication-ready bilayer orientation map in a single design-inference pass, without target-specific iterative simulation, smoothing, or topology processing. Using temperature-responsive liquid crystal elastomers (LCEs) as a representative system, we construct an experimentally validated finite element dataset and fine-tune a pretrained SegFormer model through a sparse-to-dense training route using an approximately 3,000-sample simulation-data scale. The predicted discrete orientation layouts are directly compatible with direct ink writing (DIW). Across different spatial resolutions and label granularities, the inverse-designed structures achieve mean relative displacement errors below 7% in experimental validation. Demonstrations from simple bending to complex morphing surfaces with void features confirm the scalability of the method under realistic manufacturing constraints. This work provides a route toward automated, fabrication-ready inverse design for 4D printing.