Geometry-Mechanics Compatibility Enables Interpretable Inverse Design of Non-Rigid Origami.

Non-rigid origami offers a geometric route to programmable mechanical and kinematic functions in metamaterials, deployable structures, and robotic mechanisms. Yet, its inverse design remains constrained by a fundamental modeling dilemma: High-fidelity nonlinear simulations become prohibitively expensive when repeatedly applied across large design spaces, whereas reduced models are efficient but often rely on pattern-specific assumptions whose validity is difficult to assess across crease patterns. Here, we introduce a compatibility-guided inverse-design framework that uses a geometry-mechanics test to determine when a parameterized design family can be reliably represented by a single-degree-of-freedom (1-DOF) kinematic model. Once qualified, the reduced model enables rapid and interpretable exploration of the admissible design space, while incompatible cases remain evaluated using high-fidelity analysis. We demonstrate the framework by designing origami metamaterials with programmable multistability and multi-plateau mechanical responses, enabled by the identification and removal of key geometric constraints. Its broader applicability is further illustrated through target-shape morphing and task-specific robotic motion programming. By turning model reduction from an assumed approximation into an explicit design decision, this framework provides a geometry-driven route from target functions to manufacturable non-rigid origami while reducing reliance on simulation-intensive search.