FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes

2026-05-27

AI Summary

Traditional simulation of deformable objects relies on mesh-based representations or neural fields requiring per-shape optimization, struggling to balance geometric complexity and computational efficiency. This work proposes a mesh-free reduced-order simulation method that, for the first time, integrates Reproducing Kernel Particle Method (RKPM) with reduced-order elastic dynamics. By employing RKPM to construct a continuous elastic body model and solving the generalized eigenvalue problem of the elastic energy Hessian matrix, the method automatically computes skinning weights without mesh generation or per-shape optimization. The approach achieves a 40× speedup in training compared to neural field–based methods, yields simulation errors lower than those of converged finite element solutions, and demonstrates successful application across diverse geometric representations and robotic simulation tasks.

Abstract

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.

Problem

• reduced-order simulation
• deformable objects
• mesh-free representation
• hyperelasticity
• shape modeling

Innovation

• Reduced-order simulation
• Reproducing Kernel Particle Method
• Eigensystem-based skinning
• Mesh-free deformation
• Hyperelastic modeling