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

arXiv: https://arxiv.org/abs/2605.29318 · HTML: https://mlsanity.com/paper/2605.29318/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 51 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 24 of 24)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics](https://mlsanity.com/paper/2311.12198/) (2023)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [PhysDreamer: Physics-Based Interaction with 3D Objects via Video Generation](https://mlsanity.com/paper/2404.13026/) (2024)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [VR-GS: A Physical Dynamics-Aware Interactive Gaussian Splatting System in Virtual Reality](https://mlsanity.com/paper/2401.16663/) (2024)
- [Align Your Gaussians: Text-to-4D with Dynamic 3D Gaussians and Composed Diffusion Models](https://mlsanity.com/paper/2312.13763/) (2023)
- [PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification](https://mlsanity.com/paper/2303.05512/) (2023)
- [Reconstruction and Simulation of Elastic Objects with Spring-Mass 3D Gaussians](https://mlsanity.com/paper/2403.09434/) (2024)
- [Physically Embodied Gaussian Splatting: A Realtime Correctable World Model for Robotics](https://mlsanity.com/paper/2406.10788/) (2024)
- [Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation](https://mlsanity.com/paper/2407.09497/) (2024)
- [Gaussian Garments: Reconstructing Simulation-Ready Clothing with Photorealistic Appearance from Multi-View Video](https://mlsanity.com/paper/2409.08189/) (2024)
- [Neural Stress Fields for Reduced-order Elastoplasticity and Fracture](https://mlsanity.com/paper/2310.17790/) (2023)
- [Data-Free Learning of Reduced-Order Kinematics](https://mlsanity.com/paper/2305.03846/) (2023)
- [Learning 3D Particle-based Simulators from RGB-D Videos](https://mlsanity.com/paper/2312.05359/) (2023)
- [VoMP: Predicting Volumetric Mechanical Property Fields](https://mlsanity.com/paper/2510.22975/) (2025)
- [Fast Complementary Dynamics via Skinning Eigenmodes](https://mlsanity.com/paper/2303.11886/) (2023)
- [LiCROM: Linear-Subspace Continuous Reduced Order Modeling with Neural Fields](https://mlsanity.com/paper/2310.15907/) (2023)
- [Neural Robot Dynamics](https://mlsanity.com/paper/2508.15755/) (2025)
- [Robust Biharmonic Skinning Using Geometric Fields](https://mlsanity.com/paper/2406.00238/) (2024)
- [Accelerate Neural Subspace-Based Reduced-Order Solver of Deformable Simulation by Lipschitz Optimization](https://mlsanity.com/paper/2409.03807/) (2024)
- [Shape Space Spectra](https://mlsanity.com/paper/2408.10099/) (2024)
- [Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domains](https://mlsanity.com/paper/2410.09417/) (2024)

## Built on by (most cited first, 2 of 2)

- [Adaptive Volumetric Mechanical Property Fields Invariant to Resolution](https://mlsanity.com/paper/2606.18231/) (2026)
- [Learning the Right Abstraction: Neural Reduced Dynamics for Complex Robot Control](https://mlsanity.com/paper/2608.19375/) (2026)

## Abstract (arXiv)

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.