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

arXiv: https://arxiv.org/abs/2605.08098 · HTML: https://mlsanity.com/paper/2605.08098/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for energy, networks and operations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 16 of its 57 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Placed in

- Deep reinforcement learning methods / [RL for energy, networks and operations](https://mlsanity.com/deeprl/rl-for-energy-networks-and-operations/)

## Builds on (most cited first, 16 of 16)

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- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Semantic Image Synthesis with Spatially-Adaptive Normalization](https://mlsanity.com/paper/1903.07291/) (2019)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models](https://mlsanity.com/paper/2305.19836/) (2023)
- [Flow Matching for Medical Image Synthesis: Bridging the Gap Between Speed and Quality](https://mlsanity.com/paper/2503.00266/) (2025)
- [Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning](https://mlsanity.com/paper/2401.00003/) (2023)
- [Generative models struggle with kirigami metamaterials](https://mlsanity.com/paper/2402.19196/) (2024)
- [An additive framework for kirigami design](https://mlsanity.com/paper/2207.01810/) (2022)
- [Programming shape using kirigami tessellations](https://mlsanity.com/paper/1812.08644/) (2018)
- [Compact reconfigurable kirigami](https://mlsanity.com/paper/2012.09241/) (2020)
- [Multimodal Limbless Crawling Soft Robot with a Kirigami Skin](https://mlsanity.com/paper/2506.04547/) (2025)

## Abstract (arXiv)

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%~sIoU and outperformed solver baselines while reducing forward simulator evaluations from hundreds to 1. GRPO improved accuracy to 94.91%~sIoU and, with regularity included, reduced TV(x) from 0.95 to 0.81 while maintaining 94.83%~sIoU. Generated layouts were exported to DXF and laser cut in 50~μm polymeric sheets to produce deployable prototypes in 8.0± 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.