We present a novel formulation for mesh-free, reduced-order simulation of deformable hyperelastic objects. Existing work in reduced-order elastodynamic simulation represents the input geometry by either meshes, which can be difficult to obtain due to challenges in scanning and triangulating complex shapes, or by neural fields that require per-shape optimization. We propose to adopt a Reproducing Kernel Particle Method (RKPM) representation, which enables the construction of reduced-order skinning weights by solving a generalized eigensystem on the Hessian matrix of the elastic energy. We demonstrate that this formulation not only leads to a 40x training speedup compared with the per-shape optimization of neural fields, but also achieves lower simulation error when evaluated against the converged results of finite element method. We show our simulation results on a wide variety of objects in different representations including meshes and Gaussian splats, as well as the application of our method in the downstream task of robot simulation.

翻译：摘要：我们提出了一种新颖的无网格降阶仿真公式，用于可变形超弹性物体。现有的降阶弹性动力学仿真工作通过网格（由于复杂形状的扫描和三角剖分存在挑战，这类网格可能难以获得）或需要逐形状优化的神经场来表示输入几何。我们提出采用再生核粒子方法（RKPM）表示，通过求解弹性能量黑塞矩阵上的广义特征系统，来构建降阶蒙皮权重。我们证明，该公式不仅相比神经场的逐形状优化实现了40倍的训练加速，而且在以有限元方法的收敛结果作为评估基准时，实现了更低的仿真误差。我们展示了在不同表示形式（包括网格和高斯泼溅）的各种物体上的仿真结果，以及该方法在机器人仿真下游任务中的应用。