i-PhysGaussian: Implicit Physical Simulation for 3D Gaussian Splatting
This addresses the need for stable and accurate physical simulators in industry and engineering for risk management, representing a novel method for a known bottleneck.
The paper tackled the problem of physical simulation in 3D reconstruction, which suffers from sensitivity to time steps and accuracy degradation in complex scenarios, by introducing i-PhysGaussian, a framework that couples 3D Gaussian Splatting with an implicit Material Point Method integrator, resulting in stability at up to 20x larger time steps than explicit baselines.
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.