Reinforcement learning for inverse structural design and rapid laser cutting of kirigami prototypes

Kirigami turns stiff sheets into compliant, shape-morphing structures, but its reliance on periodic cut patterns comes at a cost: correlated panel rotations couple extension to shear, so stretching one axis drives a parasitic shear that cannot be suppressed, and also confine anisotropic stiffness to a narrow, discrete set of responses that cannot be tuned independently. Biological tissues overcome an analogous constraint through controlled disorder, such as graded fiber orientations in skin and hierarchical anisotropy in myocardium, achieving direction-dependent mechanics unavailable to regular architectures. Here, we show that engineered disorder is a design degree of freedom for kirigami, with stochastic kirigami accessing a continuous and far broader region of mechanical response than periodic patterns. This includes programmable anisotropy with near-complete elimination of extension-shear coupling. Because disordered patterns lack a simple parameterization, we navigate this design space with a geometry-aware graph neural network (GNN) that maps cut topology to the full nonlinear, bidirectional stress-strain response, coupled to a genetic algorithm that inverse-designs patterns reproducing target responses along two perpendicular axes. The GNN trains an order of magnitude faster and more accurately than image-based models. Fabricated elastomer samples reproduce the predicted nonlinear, anisotropic responses, closing the loop from design to physical component. By turning disorder into a variable to control directional stiffness, this work develops architected materials that stretch without parasitic shear, from soft actuators to tissue-interfacing devices matched to the anisotropy of living tissue.

In semiconductor manufacturing, lithography projects circuit layouts onto silicon wafers through an optical mask. As circuit features shrink below the wavelength of light, optical diffraction causes the printed patterns to deviate from their intended layouts. Inverse Lithography Technology (ILT) addresses this challenge by generating optimized masks that enhance the fidelity of pattern transfer onto wafers. While ILT resembles an image synthesis task, its reliance on explicit physical metrics for mask evaluation limits the applicability of existing generative models. We introduce LithoGRPO, an ILT framework that integrates the flow-matching paradigm with GRPO-based reinforcement learning (RL) fine-tuning, enabling efficient exploration of diverse masks for a given target layout. Unlike purely generative or optimization-based approaches, RL in LithoGRPO exploits the explicitly defined, physics-based reward function of ILT, enabling optimization under complex, process-aware constraints. To the best of our knowledge, this is the first framework that unifies flow matching and RL for mask optimization. To improve RL sampling efficiency, we propose a fast shot-counting algorithm for manufacturability evaluation, achieving over 130x speedup while preserving the mask ranking of the traditional shot-count metric. Extensive experiments demonstrate that LithoGRPO achieves state-of-the-art performance over both optimization-based and learning-based methods, while maintaining efficient mask generation.

Inverse design aims to find design parameters $x$ achieving target performance $y^*$. Generative approaches learn bidirectional mappings between designs and labels, enabling diverse solution sampling. However, standard conditional flow matching (CFM), when adapted to inverse problems by pairing labels with design parameters, exhibits strong sensitivity to their arbitrary ordering and scaling, leading to unstable training. We introduce Diagonal Flow Matching (Diag--CFM), which resolves this through a zero-anchoring strategy that pairs design coordinates with noise and labels with zero, making the learning problem provably invariant to coordinate permutations. This yields substantially lower round-trip error than CFM and invertible neural network baselines across design dimensions up to $P{=}784$, including order-of-magnitude gains on several benchmarks. We develop two architecture-intrinsic uncertainty metrics, Zero-Deviation and Self-Consistency, that enable three practical capabilities: selecting the best candidate among multiple generations, abstaining from unreliable predictions, and detecting out-of-distribution targets; consistently outperforming ensemble and general-purpose alternatives across all tasks. We validate on airfoil, gas turbine combustor, scalable analytical benchmarks, a photonics inverse-design task, and an image-statistics benchmark.