GS-Surrogate: Deformable Gaussian Splatting for Parameter Space Exploration of Ensemble Simulations

Ziwei Li; Rumali Perera; Angus Forbes; Ken Moreland; Dave Pugmire; Scott Klasky; Wei-Lun Chao; Han-Wei Shen

cs.GRApr 7, 2026

GS-Surrogate: Deformable Gaussian Splatting for Parameter Space Exploration of Ensemble Simulations

Authors: Ziwei Li, Rumali Perera, Angus Forbes, Ken Moreland, Dave Pugmire, Scott Klasky, Wei-Lun Chao, Han-Wei Shen

Organizations: The Ohio State University · NVIDIA · Oak Ridge National Laboratory

Abstract

Exploring ensemble simulations is increasingly important across many scientific domains. However, supporting flexible post-hoc exploration remains challenging due to the trade-off between storing the expensive raw data and flexibly adjusting visualization settings. Existing visualization surrogate models have improved this workflow, but they either operate in image space without an explicit 3D representation or rely on neural radiance fields that are computationally expensive for interactive exploration and encode all parameter-driven variations within a single implicit field. In this work, we introduce GS-Surrogate, a deformable Gaussian Splatting-based visualization surrogate for parameter-space exploration. Our method first constructs a canonical Gaussian field as a base 3D representation and adapts it through sequential parameter-conditioned deformations. By separating simulation-related variations from visualization-specific changes, this explicit formulation enables efficient and controllable adaptation to different visualization tasks, such as isosurface extraction and transfer function editing. We evaluate our framework on a range of simulation datasets, demonstrating that GS-Surrogate enables real-time and flexible exploration across both simulation and visualization parameter spaces.

Figures & tables

Figure 1: Overall pipeline of GS-Surrogate. (1) Training images are generated through in situ visualization. (2) A deformable 3DGS-based visualization surrogate is trained offline using the image collection. (3) At inference time, scientists can interactively explore the rendering results across the parameter space.

Figure 2: Overview of the two-stage training pipeline of GS-Surrogate. The first stage optimizes a set of canonical Gaussian primitives. In the second stage, the deformation fields conditioned on simulation and visualization parameters are trained sequentially.

Figure 3: Architecture of the two deformation networks, $F_{\text{sim}}$ and $F_{\text{vis}}$ , trained in the second stage.

Dataset	Volume Resolution	#Views per member	#Simulation Parameters	Image Resolution
Nyx	$512\times 512\times 512$	252	3	$256\times 256$
MPAS-Ocean	$1536\times 768\times 768$	252	4	$512\times 512$
XCompact3D	$256\times 256\times 256$	252	1	$512\times 512$
CloverLeaf3D	$128\times 128\times 128$	252	6	$256\times 256$

Table 1: Ensemble simulation datasets: resolutions, number of images, and parameter dimensionalities. For all datasets, the 252 icosphere viewpoints are split evenly, with 126 for training and 126 reserved for testing.

Simulation	Metric	InSituNet	K-Planes	ViSNeRF	4DGS-HD	GS-Surrogate
Nyx	PSNR $\uparrow$	23.07	32.62	33.56	33.47	37.87
	SSIM $\uparrow$	0.60	0.89	0.91	0.93	0.97
	LPIPS $\downarrow$	0.19	0.14	0.12	0.07	0.03
XCompact3D	PSNR $\uparrow$	24.86	32.27	33.10	34.44	39.10
	SSIM $\uparrow$	0.87	0.94	0.95	0.96	0.98
	LPIPS $\downarrow$	0.12	0.07	0.06	0.03	0.01

Table 2: Quantitative evaluation of all methods on novel viewpoints across training ensemble members.

Figure 4: Visual comparison on a training volume-rendering instance from the Nyx dataset under an unseen viewpoint.

Simulation	Metric	InSituNet	K-Planes	ViSNeRF	4DGS-HD	GS-Surrogate
Nyx	PSNR $\uparrow$	23.11	26.78	33.97	33.39	38.83
	SSIM $\uparrow$	0.61	0.80	0.92	0.93	0.98
	LPIPS $\downarrow$	0.20	0.27	0.12	0.07	0.02
XCompact3D	PSNR $\uparrow$	24.88	33.05	33.81	35.23	41.26
	SSIM $\uparrow$	0.86	0.95	0.95	0.97	0.99
	LPIPS $\downarrow$	0.12	0.07	0.06	0.02	0.01

Table 3: Quantitative evaluation on unseen simulation parameters.

Figure 5: Visual comparison on a representative unseen ensemble member from the XCompact3D dataset.

	Nyx			XCompact3D			CloverLeaf3D
	Size	Train	Test	Size	Train	Test	Size	Train	Test
	(MB)	(hr)	(s/img)	(MB)	(hr)	(s/img)	(MB)	(hr)	(s/img)
InSituNet	232.64	27.30	0.03	232.93	45.47	0.05	232.65	38.70	0.03
K-Planes	76.95	7.25	0.27	69.73	16.67	0.72	88.26	14.50	0.33
ViSNeRF	66.43	5.05	0.18	66.43	8.65	0.73	66.43	6.13	0.37
4DGS-HD	50.75	3.26	0.06	43.70	3.05	0.06	50.53	8.18	0.05

Table 4: Model size, training time, and per-image inference time for all methods. For GS-based methods, the model size includes both the Gaussian primitives and the parameters of the deformation network.

Figure 6: Comparative results of the top three methods on three unseen ensemble members from the CloverLeaf3D dataset. CloverLeaf3D is the most challenging dataset, as its simulation parameters vary substantially across a 6D space.

Metric	InSituNet	K-Planes	ViSNeRF	4DGS-HD	GS-Surrogate
PSNR $\uparrow$	20.96	21.71	23.57	20.97	26.12
SSIM $\uparrow$	0.91	0.87	0.90	0.90	0.94
LPIPS $\downarrow$	0.08	0.15	0.11	0.13	0.06

Table 5: Performance on unseen isovalues for isosurface extraction on the MPAS-Ocean dataset.

Figure 7: Qualitative comparison on the MPAS-Ocean dataset under an unseen isovalue of temperature value 16. The most challenging region to reconstruct is highlighted in red.

Dataset	Nyx	XCompact3D	CloverLeaf3D	MPAS-Ocean	XCompact3D
Resolution	$256\times 256$	$512\times 512$	$256\times 256$	$512\times 512$	$512\times 512$
Task	DVR	DVR	DVR	IR	IR
PSNR $\uparrow$	37.96	39.98	30.64	30.05	30.65
SSIM $\uparrow$	0.97	0.98	0.96	0.95	0.95
LPIPS $\downarrow$	0.02	0.01	0.05	0.05	0.05

Table 6: Evaluation of GS-Surrogate under unseen viewpoints and simulation parameters across three volume rendering tasks and two isosurface extraction tasks.

Figure 8: Visualization results of four different isosurfaces from the XCompact3D dataset under both an unseen viewpoint and unseen simulation parameter.

Figure 9: Zoomed-in views highlighting the visual differences between the ground truth and GS-Surrogate in fine-scale structures.

Figure 10: Interface for interactive parameter space exploration with GS-Surrogate.

Figure 11: Predicted volume renderings varying $\mathit{h}\in\{0.56,0.66,0.76,0.86\}$ on the Nyx dataset, with $\mathit{OmM}$ and $\mathit{OmB}$ fixed.

Figure 12: TF space exploration on the Nyx dataset with fixed simulation parameters. Starting from the base TF, the two interior control points $c1$ and $c2$ are displaced in scalar and opacity to selectively reveal or suppress features.

Scientific Visualization

Scientific visualization turns complex scientific data into visual representations for analysis, exploration, and communication.

See all 53 papers

3D Skew Gaussian Splatting with Any Camera Trajectory Visualization Engine
May 18, 2026Beizhen Zhao, Yifan Zhou, Gaochao Song +23D Gaussian Splatting Novel View Synthesis
The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, 511442, China · Zhejiang University, China · The University of Hong Kong, China
EffGS: Efficient and High-Fidelity Gaussian Splatting
Sep 30, 2026Changbai Li, Shuo Yang, Yichen Yang +23D Gaussian Splatting 3D Gaussian Pruning
Beihang University · Nanyang Technological University
ECoNGS: Efficient Compressive Neural Gaussian Splats for Volume Visualization
Jul 20, 2026Kaiyuan Tang, Chaoli Wang3DGS Compression Scientific Visualization
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA

May 18, 2026J/K move · Enter open · S save

3D Skew Gaussian Splatting with Any Camera Trajectory Visualization Engine

Beizhen Zhao, Yifan Zhou, Gaochao Song, Ziran Yin+1

The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, 511442, China · Zhejiang University, China · The University of Hong Kong, China

3D Gaussian Splatting Novel View Synthesis 3D Scene Representation Gaussian Splatting

Open paper AskPDF arXiv

While 3D Gaussian Splatting (3DGS) has revolutionized real-time photorealistic view synthesis, its fundamental reliance on symmetric Gaussian distributions introduces visual artifacts that hinder accurate spatial data exploration. Specifically, symmetric kernels struggle to capture shape and color discontinuities , which cause blurriness and primitive redundancy that mislead human perception during visual analysis. To address these visualization barriers, we introduce 3D Skew Gaussian Splatting (3DSGS), a novel framework that significantly enhances the structural fidelity and compactness of explicit scene representations. Our key insight lies in extending the standard primitive to a general Skew Gaussian counterpart. This generalized primitive inherits the highly efficient rasterization properties of standard Gaussians while gaining intrinsic asymmetric modeling capabilities. We couple this with an enhanced opacity representation to better handle complex transparency, alongside a depth-aware densification strategy that intelligently manages primitive allocation. Furthermore, to make these advancements actionable for real-world visual analytics, we re-derive the CUDA rasterization pipeline to universally support both symmetric and skew Gaussians, integrating it into a decoupled, free-camera interactive visualization engine. Extensive experiments demonstrate that 3DSGS achieves superior rendering quality and structural compactness, particularly in regions with intricate details, while maintaining the real-time frame rates necessary for fluid interactive exploration. Supplementary derivations and visual results are available at https://3d-skew-gs.github.io/.

Abstract

Scientific Visualization

Explore similar work

3D Skew Gaussian Splatting with Any Camera Trajectory Visualization Engine

EffGS: Efficient and High-Fidelity Gaussian Splatting

ECoNGS: Efficient Compressive Neural Gaussian Splats for Volume Visualization