i-PhysGaussian: Implicit Physical Simulation for 3D Gaussian Splatting

TL;DR

i-PhysGaussian introduces an implicit simulation framework combining 3D Gaussian Splatting with an MPM integrator, achieving stable, accurate physical simulations at larger time steps for complex scenarios.

Contribution

The paper presents a novel implicit simulation method that reduces time-step sensitivity and improves stability over explicit methods in 3D physical simulations.

Findings

Maintains stability at 20x larger time steps

Preserves structural coherence in complex dynamics

Ensures physical consistency through implicit optimization

Abstract

Physical simulation predicts future states of objects based on material properties and external loads, enabling blueprints for both Industry and Engineering to conduct risk management. Current 3D reconstruction-based simulators typically rely on explicit, step-wise updates, which are sensitive to step time and suffer from rapid accuracy degradation under complicated scenarios, such as high-stiffness materials or quasi-static movement. To address this, we introduce i-PhysGaussian, a framework that couples 3D Gaussian Splatting (3DGS) with an implicit Material Point Method (MPM) integrator. Unlike explicit methods, our solution obtains an end-of-step state by minimizing a momentum-balance residual through implicit Newton-type optimization with a GMRES solver. This formulation significantly reduces time-step sensitivity and ensures physical consistency. Our results demonstrate that i-PhysGaussian maintains stability at up to 20x larger time steps than explicit baselines, preserving structural coherence and smooth motion even in complex dynamic transitions.