FluidGaussian: Propagating Simulation-Based Uncertainty Toward Functionally-Intelligent 3D Reconstruction

Yuqiu Liu; Jialin Song; Marissa Ramirez de Chanlatte; Rochishnu Chowdhury; Rushil Paresh Desai; Wuyang Chen; Daniel Martin; Michael W. Mahoney

cs.CVMar 22, 2026

FluidGaussian: Propagating Simulation-Based Uncertainty Toward Functionally-Intelligent 3D Reconstruction

Authors: Yuqiu Liu, Jialin Song, Marissa Ramirez de Chanlatte, Rochishnu Chowdhury, Rushil Paresh Desai, Wuyang Chen, Daniel Martin, Michael W. Mahoney

Organizations: Simon Fraser University · Lawrence Berkeley National Lab · University of California, Berkeley · International Computer Science Institute

Abstract

Real objects that inhabit the physical world follow physical laws and thus behave plausibly during interaction with other physical objects. However, current methods that perform 3D reconstructions of real-world scenes from multi-view 2D images optimize primarily for visual fidelity, i.e., they train with photometric losses and reason about uncertainty in the image or representation space. This appearance-centric view overlooks body contacts and couplings, conflates function-critical regions (e.g., aerodynamic or hydrodynamic surfaces) with ornamentation, and reconstructs structures suboptimally, even when physical regularizers are added. All these can lead to unphysical and implausible interactions. To address this, we consider the question: How can 3D reconstruction become aware of real-world interactions and underlying object functionality, beyond visual cues? To answer this question, we propose FluidGaussian, a plug-and-play method that tightly couples geometry reconstruction with ubiquitous fluid-structure interactions to assess surface quality at high granularity. We define a simulation-based uncertainty metric induced by fluid simulations and integrate it with active learning to prioritize views that improve both visual and physical fidelity. In an empirical evaluation on NeRF Synthetic (Blender), Mip-NeRF 360, and DrivAerNet++, our FluidGaussian method yields up to +8.6% visual PSNR (Peak Signal-to-Noise Ratio) and -62.3% velocity divergence during fluid simulations. Our code is available at https://github.com/delta-lab-ai/FluidGaussian.

Figures & tables

Figure 1: When only visual fidelity is optimized and physical awareness is excluded [ 46 , 28 ] (left column), reconstructions may look correct visually (top), and yet can fail functionally : fluid simulation exhibits excessive velocity-field divergence (defined in Section 3.2 ), a deficiency that worsens from low to high turbulence (from middle to bottom). With FluidGaussian (right column), both visual fidelity and simulation fidelity are better preserved.

Figure 2: Overview of FluidGaussian. To introduce physics-awareness into 3D reconstruction: (1) start from $K$ candidate camera poses proposed by vision-based NBV methods [ 46 , 28 ] ; and (2) evaluate a physics-informed uncertainty induced from fluid-structure simulations (Section 3.2 ) and select the best next camera pose (Section 3.3 ). The blue block denotes the fluid.

Figure 3: To make our physical uncertainty statistically meaningful, FluidGaussian measures over individual fluid simulations from five initial conditions (i.e., five individual simulations). Blue blocks denote fluids. We use a Y-up coordinate system.

Figure 4: 3D Gaussian accumulates divergence introduced by fluid particles in its neighborhood. Voxelized rigid particles (from 3D Gaussians) are omitted.

Figure 5: Quantification of function-critical region of DrivAerNet++ [ 15 ] : a) Simulation on the $-\mathbf{e}_{x}$ direction to quantify functional-critical regions; b) Examples on function-critical regions in test set. Red arrow shows the direction of flow in the simulation. The rightmost figure indicates the rear of the vehicle.

Figure 6: Visualization of the object from Blender [ 40 ] , MipNeRF360 [ 3 ] , and DrivAerNet++ [ 15 ] . Each column represents different methods, from left to right: ActiveNeRF, ActiveNeRF + FluidGaussian, FisherRF, FisherRF + FluidGaussian, ground truth (GT).

Method	(a) Blender			(b) MipNeRF360			(c) DrivAerNet++
Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
ActiveNeRF	21.1525	0.8527	0.1397	12.9245	0.4331	0.5036	17.3840	0.9079	0.1595
+FluidGaussian	21.7642	0.8613	0.1230	12.4790	0.4248	0.5067	18.8727	0.9297	0.1269
FisherRF	23.4230	0.8761	0.1070	15.3237	0.4704	0.4561	20.1127	0.9339	0.1250
+FluidGaussian	24.7433	0.8907	0.0923	15.5502	0.4717	0.4522	21.0733	0.9462	0.1047

Table 1: Visual reconstruction results on Blender [ 40 ] , MipNeRF360 [ 3 ] , and DrivAerNet++ [ 15 ] datasets. Adding FluidGaussian improves visual quality in most cases, with the largest gains on DrivAerNet++ [ 15 ] when using ActiveNeRF [ 46 ] as the baseline.

Dataset	Blender	MipNeRF360	DrivAerNet++
Training
Resolution	$800\times 800$	$1600\times 1040$	$1600\times 900$
Test views	200	87	100
Opacity ( $\alpha$ ) threshold	0.3	0.4	0.25
Iterations	30000
Initial views	2

Table 2: Training and simulation settings for all datasets.

Datasets	Blender	MipNeRF360	DrivAerNet++
Empty Scene	$5.67\times 10^{-5}$	0.0010	$4.34\times 10^{-4}$
Perfect Geometry	0.0058	0.0014	0.0371
ActiveNeRF	0.0262	0.0130	0.0894
+FluidGaussian	0.0145	0.0049	0.0801
FisherRF	0.0144	0.0025	0.0609
+FluidGaussian	0.0124	0.0022	0.0608

Table 3: Comparison of divergence (

\bar{D}\downarrow

) after optimization. “Empty Scene”: simulation without a rigid body. “Perfect Geometry”: geometry trained with at least 20 views. Value differences in empty-scene divergence are caused by different spatial domains.

Figure 7: PSNR and divergence results on Blender [ 40 ] . FluidGaussian mitigates physical defects increasingly as the fluid transitions from laminar to turbulent. As the fluid velocity rises and the Reynolds number

Re

increases, appearance-only reconstructions exhibit markedly amplified physical errors, whereas FluidGaussian largely preserves physical fidelity and interaction plausibility.

DrivAerNet++	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Divergence $\downarrow$
ActiveNeRF	15.6770	0.8843	0.1896	0.0316
+FluidGaussian	16.8897	0.9086	0.1571	0.0231
FisherRF	18.2988	0.9206	0.1472	0.0213
+FluidGaussian	18.5436	0.9297	0.1312	0.0182

Table 4: Visual and physics-based measures on function-critical regions of the DrivAerNet++ dataset. Adding FluidGaussian gives better reconstruction quality and lower divergence.

Method (fluid direction)	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
$\mathbf{e}_{x}$	24.3862	0.8857	0.0973
$-\mathbf{e}_{x}$	24.5565	0.8875	0.0949
$\mathbf{e}_{z}$	24.0015	0.8842	0.0985
$-\mathbf{e}_{z}$	24.1853	0.8836	0.0986
$\mathbf{e}_{y}$	24.2303	0.8851	0.0985
FisherRF [ 28 ]	23.4230	0.8761	0.1070

Table 5: Results on Blender [ 40 ] under different initial conditions.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Blender	Mip	DrivAer
ActiveNeRF + Random	21.547	12.415	18.770
ActiveNeRF + FluidGaussian	21.764	12.479	18.873
FisherRF + Random	23.631	15.326	20.022
FisherRF + FluidGaussian	24.743	15.550	21.073

Appendix

Table 6: Comparison between random view selection and FluidGaussian under the same reconstruction baseline. PSNR is reported.

Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
ActiveNeRF	24.828	0.961	0.064
ActiveNeRF + FluidGaussian	25.653	0.960	0.063
FisherRF	27.604	0.974	0.041
FisherRF + FluidGaussian	27.807	0.976	0.034

Appendix

Table 7: Comparison between the baseline and FluidGaussian on 7 ShapeNet objects.

Method	Chamfer Distance $\downarrow$
ActiveNeRF	0.0103
ActiveNeRF + FluidGaussian	0.0055
FisherRF	0.0165
FisherRF + FluidGaussian	0.0046

Appendix

Table 8: Chamfer Distance comparison on the Blender dataset. Lower is better.

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Department of Computer Science, Purdue University, West Lafayette, 47907, IN, United States

3D Gaussian Splatting 3D Shape Generation Functional 3D Scene Generation

Open paper AskPDF arXiv

Recent advances in Gaussian Splatting have enabled fast, high-fidelity 3D scene generation, yet these methods remain purely visual and lack an understanding of how shapes behave in the physical world. We introduce Physics-Guided 3D Gaussian Splatting (PG-3DGS), a framework that couples differentiable physics simulation with 3D Gaussian representations to generate 3D structures satisfying physics functionalities. By allowing physical objectives to guide the shape optimization process alongside visual losses, our approach produces geometries that are not only photometrically accurate but also physically functional. The model learns to adjust shapes so that the generated objects exhibit physically meaningful behaviors, for example, teapots that can pour and airplanes that can generate lift, without sacrificing visual quality. Experiments on pouring and aerodynamic lift tasks show that PG-3DGS improves physical functionality while preserving visual quality. In addition to simulation gains, bench-top physical lift tests with 3D-printed aircraft (Cessna, B-2 Spirit, and paper plane) under identical airflow conditions show higher scale-measured lift for PG-3DGS, generated structures than an appearance-matching baseline in all three cases. Our unified framework connects appearance-based reconstruction with physics-based reasoning, enabling end-to-end generation of 3D structures that both look realistic and function correctly.

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