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This paper introduces a novel approach for mesh-free, reduced-order simulation of deformable hyperelastic objects using the Reproducing Kernel Particle Method (RKPM). By solving a generalized eigensystem on the Hessian matrix of elastic energy, the method achieves a 40x training speedup compared to traditional per-shape optimization of neural fields, while also reducing simulation error relative to finite element methods. The effectiveness of this approach is demonstrated across various object representations, including meshes and Gaussian splats, and its applicability in robot simulation tasks.
Achieving a 40x speedup in training for deformable simulations could revolutionize real-time applications in robotics and animation.
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.
NVIDIA