PowerSim: Differentiable Physics Simulation and Rendering with Power Diagrams

Trong-Tung Nguyen; Anand Bhattad

cs.CVSep 29, 2026

PowerSim: Differentiable Physics Simulation and Rendering with Power Diagrams

Authors: Trong-Tung Nguyen, Anand Bhattad

Organizations: Johns Hopkins University

Abstract

We introduce PowerSim, a method to bring physically grounded, differentiable dynamics to PowerFoam's power diagram based 3D representation. PowerSim directly couples a pre-trained PowerFoam scene to the Material Point Method (MPM) by exploiting a natural alignment between the two: the geometric and appearance properties of each primitive correspond closely to the quantities MPM already tracks as an object deforms. Consequently, simulated motion can drive the scene's geometry and appearance directly, without an auxiliary representation in between. Built on this framework, we enable a range of applications on real and synthetic scenes: (1) simulating a static scene under user interaction, (2) recovering spatially varying material fields, (3) compositing primitives from independently captured scenes into a single simulation-ready scene and (4) ray-tracing reflections that update consistently as the object deforms. Our results suggest that PowerSim excels over previous frameworks for physically grounded dynamics, while unlocking unique advantages-such as secondary ray lighting effects on dynamic scenes. Results are best viewed on our project website: https://power-sim.github.io/.

Figures & tables

Figure 2 : PowerSim partitions the reconstructed object volume into explicit cells, while PhysGaussian ( Xie et al., 2023 ) uses Gaussian kernels that tend to concentrate near surfaces and optionally adds interior particles. Under extreme stretching with the same applied force, PAC-NeRF loses texture and develops abrupt cut-like boundaries, while PhysGaussian exhibits pronounced blurring in stretched regions. PowerSim retains more surface detail and sharper boundaries during separation.

Figure 3 : PowerSim overview. After $N$ MPM substeps, we update primitive positions, isotropically scale their radii to match local volume change, and rotate their dipole frames and appearance directions. We then rebuild adjacency for the updated primitives. Insets show two selected primitives before and after deformation.

Figure 4 : Material estimation changes the simulated response. Under the same applied force, random material assignment produces large stem bending, while PhysDreamer produces little bending. PowerSim produces back-and-forth motion with visible stem deformation. The left column shows Young’s modulus; the remaining columns show matching simulation times.

Figure 5 : Scene composition. Our optimization-free primitive selection enables removing the vase from a captured scene (a–b) and selecting a plant from another capture (c, green). We align and insert the selected primitives to create a scene ready for simulation (d).

Figure 6 : Diverse Material Behaviors. Simulation results on different material settings.

Figure 7 : Dynamic reconstruction under deformation and contact. PowerSim preserves the backpack’s texture and Mario’s shape as they fall and contact the ground. PAC-NeRF has blurred textures and distorted silhouettes, while PhysDreamer shows discrepancies in deformation and appearance. Reference frames are shown in the bottom row; time progresses from left to right.

Metrics	Method	backpack	bell	blocks	bus	cream	elephant	grandpa	leather	lion	mario	sofa	turtle	Mean
PSNR $\uparrow$	PAC-NeRF	19.37	25.00	23.36	20.72	23.24	22.27	21.63	20.85	22.66	21.01	22.49	22.19	22.06
	PhysDreamer	18.93	19.54	19.79	18.82	19.83	17.14	16.91	18.27	18.28	17.56	19.58	23.41	19.00
	Ours	23.69	24.39	29.56	26.84	25.82	22.80	22.01	35.33	25.17	20.31	24.72	28.11	25.73
SSIM $\uparrow$	PAC-NeRF	0.887	0.956	0.940	0.908	0.893	0.922	0.939	0.932	0.936	0.921	0.926	0.923	0.924
	PhysDreamer	0.856	0.940	0.917	0.909	0.876	0.892	0.922	0.945	0.910	0.901	0.894	0.939	0.908
	Ours	0.889	0.944	0.953	0.938	0.923	0.908	0.889	0.978	0.930	0.941	0.918	0.953	0.930

Table 1 : Dynamic reconstruction on 12 objects. PowerSim achieves the highest PSNR on 10 objects and SSIM on seven. Bold and underline indicate the best and second-best results, respectively.

Metrics	Method	backpack	bell	blocks	bus	cream	elephant	grandpa	leather	lion	mario	sofa	turtle	Mean
$\log(E)$	PAC-NeRF	3.28	1.08	4.02	3.30	3.22	3.05	2.99	1.20	2.34	3.37	0.20	1.94	2.50
	PhysDreamer	0.10	1.07	0.74	0.40	0.28	0.54	0.43	0.33	1.01	1.18	0.68	0.44	0.60
	Ours	0.06	0.81	0.16	0.60	0.37	0.36	0.47	1.21	0.20	0.60	0.33	0.09	0.44
$\nu$	PAC-NeRF	0.21	0.23	0.33	0.16	0.12	0.06	0.36	0.26	0.14	0.33	0.30	0.01	0.21
	PhysDreamer	0.26	0.01	0.10	0.14	0.14	0.04	0.33	0.11	0.06	0.44	0.05	0.29	0.16
	Ours	0.17	0.18	0.16	0.12	0.17	0.27	0.01	0.11	0.16	0.25	0.09	0.21	0.16

Table 2 : Material estimation on 12 objects. MAE in log Young’s modulus and Poisson’s ratio (lower is better). Bold and underline indicate the best and second-best results, respectively.

Figure 8 : Geometry and appearance updates under large deformation. Fixing dipole orientations produces ragged boundaries, while fixing appearance directions introduces color inconsistencies. The full PowerSim update preserves cleaner surface detail; PhysGaussian shows blurring and fragmentation in stretched regions. Insets highlight these differences. Best viewed on supplementary webpage.

Figure 9 : Ray tracing on dynamic scenes. Independently captured objects are composited and simulated together, with mirror reflections that follow their motion and deformation.

Figure 10 : Disocclusion artifacts. PowerSim can select and move the telephone handset, but its motion exposes poorly reconstructed regions, revealing gaps and visual artifacts.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Scene	Figure	Constitutive Model
Bonsai	Fig. 1	Fixed corotated
Bread roll	Fig. 2	Fixed corotated
Carnation	Fig. 4	Fixed corotated
GSO benchmark	Fig. 7	Fixed corotated
Bread twist	Fig. 8	Fixed corotated
Car	Fig. 9	Fixed corotated

Appendix

Table 3 : List of constitutive models used for simulation.

$\beta$	garden	bonsai	room	counter	kitchen	average
0.1	0.912 / 0.948	0.837 / 0.881	0.604 / 0.953	0.758 / 0.912	0.855 / 0.947	0.793 / 0.928
0.2	0.916 / 0.948	0.833 / 0.877	0.608 / 0.955	0.758 / 0.912	0.855 / 0.947	0.794 / 0.928
0.4	0.922 / 0.948	0.826 / 0.868	0.615 / 0.953	0.759 / 0.912	0.858 / 0.947	0.796 / 0.926
0.5	0.920 / 0.945	0.822 / 0.863	0.619 / 0.953	0.759 / 0.912	0.859 / 0.947	0.796 / 0.924
0.6	0.920 / 0.944	0.819 / 0.860	0.622 / 0.952	0.759 / 0.912	0.859 / 0.947	0.796 / 0.923
0.8	0.917 / 0.940	0.814 / 0.853	0.625 / 0.948	0.759 / 0.912	0.859 / 0.947	0.795 / 0.920

Appendix

Table 4 : Ablation studies on discounting factor

\beta

with mIoU / mAcc per scene.

Method	Opt.-free	Garden	Bonsai	Room	Counter	Kitchen	Average
		mIoU $\uparrow$ / mAcc $\uparrow$	mIoU $\uparrow$ / mAcc $\uparrow$	mIoU $\uparrow$ / mAcc $\uparrow$	mIoU $\uparrow$ / mAcc $\uparrow$	mIoU $\uparrow$ / mAcc $\uparrow$	mIoU $\uparrow$ / mAcc $\uparrow$
LabelGS	✗	0.79 / 0.95	0.70 / 0.92	0.64 / 0.93	0.55 / 0.93	0.82 / 0.96	0.70 / 0.94
Gaussian Grouping	✗	0.88 / 0.92	0.75 / 0.82	0.55 / 0.78	0.74 / 0.92	0.83 / 0.92	0.75 / 0.87
SemanticFoam	✗	0.94 / 0.96	0.90 / 0.94	0.63 / 0.95	0.75 / 0.91	0.90 / 0.94	0.82 / 0.94
Ours	✓	0.92 / 0.95	0.82 / 0.86	0.62 / 0.95	0.76 / 0.91	0.86 / 0.95	0.80 / 0.92

Appendix

Table 5 : Per-scene segmentation result on Mip-NeRF 360. Baseline numbers are taken from the SemanticFoam paper. All baselines optimize a per-scene semantic field; ours requires no optimization .

Figure 11 : We provide qualitative results compared with SemanticFoam on Mip-NeRF 360 scenes

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