用粒子方法快速模拟变形物体，训练速度提升40倍且更精准。
FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes
- 基于RKPM粒子表示，通过弹性能量海森矩阵求解降维权重
- 相比神经场每形状优化快40倍，仿真误差更低
- 适用于网格、高斯点等多种表示，适合机器人仿真应用
我们提出一种无网格的降维可变形超弹性体模拟新方法。现有降维弹性动力学模拟依赖网格（扫描复杂形状时难获取）或神经场（需每形状优化）。本文采用再生核粒子法（RKPM）表示，通过求解弹性能量海森矩阵的广义特征系统构建降维皮肤权重。实验表明，该方法相比神经场的逐形状优化实现40倍训练加速，且在与有限元收敛结果对比时表现出更低的仿真误差。我们在多种物体（包括网格和高斯点）上验证了模拟效果，并展示了该方法在机器人模拟下游任务中的应用。
原文摘要 · Abstract (English)
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.
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