Reinforcement learning for inverse silhouette design and rapid laser cutting of compact parallelogram quad kirigami prototypes

arXiv:2605.08098v2 Announce Type: replace Abstract: Kirigami is an increasingly useful fabrication method to produce shape-programmable metamaterial structures. However, inverse design remains difficult because deployment is nonlinear, and feasible cut layouts must satisfy discrete compatibility rules, avoid overlap, and map one target shape to valid designs. We present RL-Kirigami, an inverse design framework that combines optimal-transport conditional flow matching (OT-CFM) with reinforcement learning to generate compatible ratio fields for compact reconfigurable parallelogram quad kirigami. A marching decoder enforces global geometric compatibility, and Group Relative Policy Optimization (GRPO) aligns the generator with nondifferentiable rewards for silhouette matching, feasibility, and ratio-field regularity. Across procedurally generated target shape instances, a single sample from the pretrained OT-CFM prior reached $94.2\%~\mathrm{sIoU}$ and outperformed solver baselines while reducing forward simulator evaluations from hundreds to $1$. GRPO improved accuracy to $94.91\%~\mathrm{sIoU}$ and, with regularity included, reduced $\mathrm{TV}(\mathbf{x})$ from $0.95$ to $0.81$ while maintaining $94.83\%~\mathrm{sIoU}$. Generated layouts were exported to DXF and laser cut in $50~\mu\mathrm{m}$ polymeric sheets to produce deployable prototypes in $8.0\pm 1.0$ minutes per part. These results support a manufacturing-aware inverse design workflow for deployable kirigami metamaterials under geometric feasibility constraints. Code is available at https://github.com/milad1378yz/RL-Kirigami.