Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation

TL;DR

Simplicits (Modi et al., 2024) is a data-, mesh-, and grid-free formulation for elastic simulation of any 3D object under any representation — meshes, point clouds, SDFs, neural primitives, tomography scans, radiance fields, 3D Gaussian splats. The key observation is that every standard 3D representation reduces to an occupancy function queryable at any point in space, giving a common interface a simulator can be built atop. For each object, a small implicit neural network is fit to encode spatially varying skinning weights that act as a reduced deformation basis; the weights are trained by random perturbations with Monte Carlo elastic-energy evaluation to find a subspace that best minimizes deformation energy. Simulation then runs in the reduced basis with deformations sampled back to the original domain.

Key claims

Any 3D representation (meshes, point clouds, SDFs, neural fields, radiance fields, 3DGS, volume meshes, tomography scans) can be reduced to an occupancy function, letting one simulator run atop all of them via a common query interface [Abstract].
A small per-object implicit neural network encodes spatially varying skinning weights that act as a reduced deformation basis, avoiding the need for meshing or grid construction [Method].
Skinning weights are trained by minimizing elastic energy under random perturbations, with Monte Carlo sampling of the deformation volume through the occupancy function [Method].
The formulation supports a variety of material energies, contact models, and time-integration schemes across the tested representation zoo [Abstract / Results].

Method

Simplicits treats the elastic-simulation problem as agnostic to input representation by requiring only an occupancy query. Given an object in any 3D representation, an implicit MLP is fit to output per-point skinning weights over the volume; these weights parameterize a reduced deformation basis. Training minimizes deformation energy under stochastic perturbations, with elastic energy estimated by Monte Carlo sampling of the deformation volume using the occupancy function to identify inside/outside regions. At simulation time, subspace dynamics run over the reduced coordinates and deformations are sampled back onto the original geometry for rendering.

Results

The project page demonstrates simulation on signed distance functions, point clouds, neural primitives, tomography scans, radiance fields, Gaussian splats, surface meshes, and volume meshes, with variety across material energies, contact models, and time-integration schemes.

Why it’s interesting

Simplicits was, before FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes, the only method offering reduced-order mesh-free hyperelastic simulation across arbitrary object representations — and FreeForm’s benchmark tables directly report ~40× training-time speedup and lower simulation error against Simplicits. The paper matters to Luma as the reference point for what “representation-agnostic physics simulation” means, and as the current production physics backend in NVIDIA Kaolin — A PyTorch Library for Accelerating 3D Deep Learning Research. The occupancy-function interface is also a clean design lesson: it decouples the physics module from the specifics of any one 3D representation, which is the same architectural bet that makes 3DGS+physics pipelines composable at all.