  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.
