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

Yicheng Cao; Zhuo Huang; Yu Yao; Yiming Ying; Daoyi Dong; Tongliang Liu

cs.LGFeb 19, 2026

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

Authors: Yicheng Cao, Zhuo Huang, Yu Yao, Yiming Ying, Daoyi Dong, Tongliang Liu

Organizations: Sydney AI Centre, The University of Sydney · School of Mathematics and Statistics, University of Sydney · Australian Artificial Intelligence Institute, University of Technology Sydney

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 & tables

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).

	Ficus		Pillow2Sofa		Bread
Method	$k_{\max}\uparrow$	fail.% $\downarrow$	$k_{\max}\uparrow$	fail.% $\downarrow$	$k_{\max}\uparrow$	fail.% $\downarrow$
i-PhysGaussian	20	0.0	20	0.0	20	0.0
PhysGaussian	1	90.9	20	0.0	8	54.5
DreamPhysics	2	90.9	14	45.5	1	90.9
Physics3D	0	100.0	2	81.8	0	100.0

Table 1: BMF-gated stability frontier under time-step enlargement. For each scene and method, we report the largest stable multiplier

k_{\max}

and Fail.% (percentage of failed multipliers among all tested

k

values). We use

k_{\max}=0

to indicate that none of the tested multipliers passes the BMF gate.

Figure 2: BMF-gated failure rate by scene (and overall). Hatching is used only for visibility; the underlying value remains 0.0%.

Panel of Figure 3 — 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.

Panel of Figure 4 — 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).

Panel of Figure 5 — 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).

Method	Sat.% mean $\downarrow$	Sat.% std $\downarrow$	Sat.% range $\downarrow$
Alocasia
i-PhysGaussian	0.15	0.0105	0.0805
PhysGaussian	0.15	0.0005	0.0046
DreamPhysics	0.17	0.0003	0.0017
Physics3D	98.14	0.0000	0.0000
Hat

Table 2: Over-exposure diagnostic at

1\times\Delta t

. We report saturation ratio statistics (mean/std/range), where SatRatio t is the percentage of pixels whose luminance satisfies

Y_{t}(\mathbf{p})\geq 0.98

. Lower values indicate fewer over-exposed regions.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

	time			boundary_conditions: particle_impulse
time-size	substep_dt	frame_dt	frame_num	$f_{x}$	num_dt	start_time
$1\times\Delta t$	$1.0\mathrm{e}{-4}$	$4.0\mathrm{e}{-2}$	125	$-1.8\mathrm{e}{-1}$	1	0.0
$2\times\Delta t$	$2.0\mathrm{e}{-4}$	$4.0\mathrm{e}{-2}$	125	$-9.0\mathrm{e}{-2}$	1	0.0
$4\times\Delta t$	$4.0\mathrm{e}{-4}$	$4.0\mathrm{e}{-2}$	125	$-4.5\mathrm{e}{-2}$	1	0.0
$6\times\Delta t$	$6.0\mathrm{e}{-4}$	$4.0\mathrm{e}{-2}$	125	$-3.0\mathrm{e}{-2}$	1	0.0
$8\times\Delta t$	$8.0\mathrm{e}{-4}$	$4.0\mathrm{e}{-2}$	125	$-2.25\mathrm{e}{-2}$	1	0.0

Appendix

Table 3: Ficus scene: time-step schedule and particle-impulse boundary condition. We sweep

k\in\{1,2,4,6,8,10,12,14,16,18,20\}

by setting substep_dt =

k\times 10^{-4}

while keeping frame_dt =

4.0\mathrm{e}{-2}

and frame_num =125 fixed. The particle impulse uses force = [

f_{x}

,0,0 ] , num_dt =1, and start_time =0.0.

	time
time-size	substep_dt	frame_dt	frame_num
$1\times\Delta t$	$1.0\mathrm{e}{-4}$	$2.0\mathrm{e}{-2}$	300
$2\times\Delta t$	$2.0\mathrm{e}{-4}$	$2.0\mathrm{e}{-2}$	300
$4\times\Delta t$	$4.0\mathrm{e}{-4}$	$2.0\mathrm{e}{-2}$	300
$6\times\Delta t$	$6.0\mathrm{e}{-4}$	$2.0\mathrm{e}{-2}$	300
$8\times\Delta t$	$8.0\mathrm{e}{-4}$	$2.0\mathrm{e}{-2}$	300

Appendix

Table 4: Pillow2Sofa scene: time-step schedule. We sweep

k\in\{1,2,4,6,8,10,12,14,16,18,20\}

by setting substep_dt =

k\times 10^{-4}

while keeping frame_dt =

2.0\mathrm{e}{-2}

and frame_num =300 fixed.

	time
time-size	substep_dt	frame_dt	frame_num
$1\times\Delta t$	$1.0\mathrm{e}{-4}$	$1.0\mathrm{e}{-2}$	300
$2\times\Delta t$	$2.0\mathrm{e}{-4}$	$1.0\mathrm{e}{-2}$	300
$4\times\Delta t$	$4.0\mathrm{e}{-4}$	$1.0\mathrm{e}{-2}$	300
$6\times\Delta t$	$6.0\mathrm{e}{-4}$	$1.0\mathrm{e}{-2}$	300
$8\times\Delta t$	$8.0\mathrm{e}{-4}$	$1.0\mathrm{e}{-2}$	300

Appendix

Table 5: Bread scene: time-step schedule. We sweep

k\in\{1,2,4,6,8,10,12,14,16,18,20\}

by setting substep_dt =

k\times 10^{-4}

while keeping frame_dt =

1.0\mathrm{e}{-2}

and frame_num =300 fixed.

Material	Type	Model
jelly	Elastic	Neo-Hookean
metal	Plastic	J2 (von Mises)
foam	Damage	J2 + softening
snow/sand	Frictional	Drucker–Prager
plasticine	Viscoplastic	Rate-dependent J2

Appendix

Table 6: Material scope and constitutive models.

Figure 6: Stability heatmaps across time-step multipliers. Color indicates exceedance ratio $r=\frac{1}{T}\sum_{t=1}^{T}\mathbb{I}[\mathrm{BMF}_{t}>0.5]$ (lower is better); $\times$ marks runs that fail the gate ( $r>0.5$ ).

Method	COMD AUC $\downarrow$	mwRMSD AUC $\downarrow$
Ficus
i-PhysGaussian	0.0184	0.0279
PhysGaussian	0.5975	0.8509
DreamPhysics	0.0556	0.8539
Physics3D	0.0000	0.8539
Pillow2Sofa

Appendix

Table 7: Normalized AUC of drift curves (lower is better), computed over

k\in\{1,2,4,\dots,20\}

on BMF-valid runs.

Panel of Figure 7 — Figure 7: Reference-free mass conservation at $1\times\Delta t$ (per-frame). We plot MassDrift ${}_{t}=\frac{|M_{t}-M_{1}|}{M_{1}+\varepsilon}$ over frames for each scene (lower is better).

Panel of Figure 8 — Figure 8: Trajectory overlays at a key simulation moment. Near-flat irregularity curves can correspond to kinematic degeneration (suppressed motion), as visualized here.

Scene	$\Delta t$	Success $\uparrow$ base/noLS $\Delta$ pp	Speedup $\uparrow$	RelEnd $\downarrow$ base noLS
pillow2sofa	1x	63.3 / 62.6 $-0.7$	1.02 $\times$	6.28e-4 6.28e-4
	10x	71.2 / 72.4 $+1.2$	1.00 $\times$	3.09e-4 2.94e-4
	20x	66.4 / 62.6 $-3.8$	0.99 $\times$	6.20e-4 5.53e-4
bread	1x	0.3 / 0.0 $-0.3$	1.74 $\times$	1.57e-5 1.59e-5
	10x	99.3 / 0.0 $-99.3$	0.99 $\times$	4.19e-5 5.72e-5
	20x	99.3 / 0.0 $-99.3$	1.50 $\times$	5.24e-5 –

Appendix

Table 8: Line-search ablation on the i-PhysGaussian implicit MPM solver. Success is the frame-level success rate (a frame is successful only if all substeps converge). Speedup is computed as

\sum t_{\text{Newton}}^{\text{base}}/\sum t_{\text{Newton}}^{\text{noLS}}

. RelEnd is the mean Newton residual ratio

R_{\text{end}}/R_{0}

averaged over converged substeps .

Scene	$\Delta t$	Success $\uparrow$ base/fixed	Speedup $\uparrow$	GMRES iters (mean/max) base/fixed	RelEnd $\downarrow$ base/fixed
pillow2sofa	1x	63.3 / 63.3	1.22 $\times$	7.0 / 18 4.0 / 22	1.53e-6 1.55e-6
	10x	70.3 / 70.3	0.99 $\times$	4.1 / 18 4.1 / 18	2.66e-5 1.92e-5
	20x	71.0 / 71.0	1.01 $\times$	6.1 / 19 5.3 / 32	8.49e-5 6.58e-5
bread	1x	0.3 / 0.3	0.99 $\times$	11.0 / 21 14.3 / 46	6.63e-6 6.65e-6
	10x	99.3 / 99.3	1.00 $\times$	14.5 / 39 20.0 / 54	4.21e-5 4.22e-5
	20x	99.3 / 99.3	0.89 $\times$	28.3 / 57 44.3 / 84	5.26e-5 5.24e-5

Appendix

Table 9: Fixed forcing-term ablation for the i-PhysGaussian implicit MPM solver ( base : Eisenstat–Walker adaptive forcing term; fixed : constant GMRES tolerance shared across scenes). Success is the frame-level success rate (a frame is successful only if all substeps converge). Speedup is computed as

\sum t_{\text{Newton}}^{\text{base}}/\sum t_{\text{Newton}}^{\text{fixed}}

(larger is faster for fixed ). GMRES iters reports mean/max GMRES iterations aggregated over converged Newton solves. RelEnd is the mean Newton residual ratio

R_{\text{end}}/R_{0}

averaged over converged substeps .

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Physics-based simulation models physical systems with equations and numerical solvers, increasingly augmented by learned models for speed and control.

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3D Gaussian Splatting has evolved from static reconstruction toward physics-integrated representations meant to predict how scenes change under interaction. This creates an evaluation problem: a rollout can look plausible while relying on incorrect internal mechanics, and visual agreement with observed motion does not establish a correct response to a new force, material edit, contact, or thermal intervention. We introduce GaussianBench, a physics-fidelity evaluation suite for physics-integrated Gaussian scene representations. It uses frozen file-based scenes, simulator-independent scorers, and analytical or measured references. The benchmark tests conservation, continuum response, heterogeneous-material coupling, Gaussian covariance transport and rendering, thermal phase change, and counterfactual response. Each reference declares its regime of validity, and outcomes distinguish PASS, FAIL, NA, and INVALID, separating physical failures from unsupported capabilities and invalid comparisons. We also provide GaussianFlesh, a thermomechanical reference entrant in which persistent 3D Gaussians act as both rendering primitives and continuum material points, advanced by a shared-grid MPM solver with per-particle constitutive dispatch and persistent thermal and phase state. We evaluate six released external systems: PhysGaussian, GaussianFluent, OmniPhysGS, PhysDreamer, Physics3D, and GASP. Testing every system the same way reveals failures that their original evaluations missed: a system can simulate a single material correctly but fail where two materials meet, or update its Gaussians correctly for a deformation it never produced. Matched faults and tolerance audits confirm these distinctions arise from the intended tests. Physics-integrated Gaussian systems must therefore be tested on their internal physical state, not just on whether their rollouts look plausible.

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Physics-Based Simulation

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