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

TL;DR

i-PhysGaussian is introduced, a framework that couples 3D Gaussian Splatting with an implicit Material Point Method (MPM) integrator, and maintains stability at up to 20x larger time steps than explicit baselines, preserving structural coherence and smooth motion even in complex dynamic transitions.

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.

Figures (8)

• Figure 1: Overview of i-PhysGaussian. The pipeline starts with (i) a static 3D Gaussian scene and (ii) a configuration file specifying preprocessing, simulation, and rendering options. The scene is first preprocessed (axis alignment, pruning near-transparent Gaussians, and optional particle filling), then enhanced by an implicit MPM solver under the specified material and boundary conditions. The end-of-step state is re-rendered as a Gaussian scene at each time iteratively, which produces a temporally stacked 4D Gaussian representation (4DGS).
• Figure 2: BMF-gated failure rate by scene (and overall). Hatching is used only for visibility; the underlying value remains 0.0%.
• Figure 3: Time-step robustness with the BMF gate. Left column: COMD$\downarrow$; right column: mwRMSD$\downarrow$. Both are plotted versus multiplier $k$ relative to $1\times\Delta t$. Dashed lines mark $k_{\max}$; values beyond $k_{\max}$ may be clamp-dominated.
• Figure 4: Reference-free impulse/torque irregularity at $1\times\Delta t$ (per-frame). Left column: impulse irregularity$\downarrow$; right column: torque irregularity$\downarrow$. Lower values indicate smoother evolution of net impulse/torque (i.e. fewer bursty non-physical jitters).
• Figure 5: Static rendering fidelity at $1\times\Delta t$ (first frame). We compare the first rendered frame against the paired ground-truth image and report PSNR/SSIM/LPIPS (higher is better for PSNR/SSIM; lower is better for LPIPS).