Inverse design of slender elastic structures underlies a wide range of applications in computer graphics, flexible electronics, biomedical devices, and soft robotics. Traditional optimization-based approaches, however, are often orders of magnitude slower than forward dynamic simulations and typically impose restrictive boundary conditions. In this work, we present an inverse discrete elastic rods (inverse-DER) method that enables efficient and accurate inverse design under general loading and boundary conditions. By reformulating the inverse problem as a static equilibrium in the reference configuration, our method attains computational efficiency comparable to forward simulations while preserving high fidelity. This framework allows rapid determination of undeformed geometries for elastic fabrication structures that naturally deform into desired target shapes upon actuation or loading. We validate the approach through both physical prototypes and forward simulations, demonstrating its accuracy, robustness, and potential for real-world design applications.

翻译：细长弹性结构的逆向设计是计算机图形学、柔性电子学、生物医学设备和软体机器人等领域广泛应用的基础。然而，传统的基于优化的方法通常比正向动力学模拟慢数个数量级，且通常施加严格的边界条件。在本研究中，我们提出了一种逆离散弹性杆方法，能够在一般载荷和边界条件下实现高效且精确的逆向设计。通过将逆向问题重新表述为参考构型中的静态平衡问题，我们的方法在保持高保真度的同时，获得了与正向模拟相当的计算效率。该框架能够快速确定弹性制造结构的未变形几何形状，这些结构在驱动或加载时会自然地变形为目标形状。我们通过物理原型和正向模拟验证了该方法的准确性、鲁棒性及其在实际设计应用中的潜力。