Shape morphing that transforms morphologies in response to stimuli is crucial for future multifunctional systems. While kirigami holds great promise in enhancing shape-morphing, existing designs primarily focus on kinematics and overlook the underlying physics. This study introduces a differentiable inverse design framework that considers the physical interplay between geometry, materials, and stimuli of active kirigami, made by soft material embedded with magnetic particles, to realize target shape-morphing upon magnetic excitation. We achieve this by combining differentiable kinematics and energy models into a constrained optimization, simultaneously designing the cuts and magnetization orientations to ensure kinematic and physical feasibility. Complex kirigami designs are obtained automatically with unparallel efficiency, which can be remotely controlled to morph into intricate target shapes and even multiple states. The proposed framework can be extended to accommodate various active systems, bridging geometry and physics to push the frontiers in shape-morphing applications, like flexible electronics and minimally invasive surgery.

翻译：形态变形是指结构响应外界刺激而改变其形态的能力，这对于未来多功能系统至关重要。尽管剪纸结构在增强形态变形方面具有巨大潜力，现有设计主要聚焦于运动学，而忽略了底层物理机制。本研究提出了一种可微逆向设计框架，该框架综合考虑了由嵌入磁性颗粒的软材料制成的主动剪纸结构中几何、材料与刺激之间的物理相互作用，以实现磁激励下的目标形态变形。我们通过将可微运动学与能量模型相结合，并纳入约束优化，同时设计切割图案与磁化方向，以确保运动学与物理可行性。复杂剪纸结构的设计能够以无与伦比的效率自动获得，且可通过远程控制实现复杂的预期形态变形，甚至多状态切换。该框架可拓展至多种主动系统，桥接几何与物理，推动形态变形应用的前沿发展，例如柔性电子与微创手术。