3D Field Data Reduction with Adaptive Sample-Based Gaussian-Encoded Reconstruction

Michael R. Martin; Joseph Insley; Victor A. Mateevitsi; Silvio Rizzi; Kwan-Liu Ma

cs.GRSep 10, 2026

3D Field Data Reduction with Adaptive Sample-Based Gaussian-Encoded Reconstruction

Authors: Michael R. Martin, Joseph Insley, Victor A. Mateevitsi, Silvio Rizzi, Kwan-Liu Ma

Organizations: Department of Computer Science, University of California, Davis · Argonne National Laboratory

Abstract

In scientific simulation, regular grids, unstructured meshes, and particle-based formats are chosen to represent field data for computational efficiency, geometry/adaptive flexibility, and following motion/deformation, respectively. Each of these field data formats is often handled through separate data-specific processing pipelines. We present a unified sample-based Gaussian encoding method that represents these data forms under a single fixed-budget formulation. The method initializes and refines Gaussian primitives directly from the input samples while preserving a prescribed primitive count and encoded size to achieve a desired level of data reduction. Across structured, unstructured, and particle data, the sample-based formulation improves reconstruction accuracy with measurably fewer primitives in comparison to prior formulations, achieving up to 4.8 dB higher PSNR with an approximate 44x reduction in primitive count. For time-varying data, warm-starting from the previous timestep reduces the optimization required to reach independently trained reconstruction quality. Together, these results demonstrate a unified fixed-budget Gaussian encoding framework for structured, particle, unstructured, and time-varying scientific data with predictable storage, higher reconstruction accuracy, and improved temporal encoding efficiency.

Figures & tables

Input form	$\mathbf{q}_{j}$	$h_{j}$	$v_{j}$	$m_{j}$	Reference field $V_{\mathrm{ref}}$
HACC SPH particles	particle position	$0.8\,hh$	normalized log density	particle mass	particle deposit
Deep Water Impact cells	cell center	$\tfrac{1}{2}\gamma\,\mathrm{vol}^{1/3}$	normalized cell value	cell volume	volume-weighted cell deposit
Grid voxels	voxel center	$\tfrac{1}{2}$ voxel	normalized voxel value	1	input grid

Table 1: Sample definitions for each input form. All samples are expressed in the index frame of the reference grid;

hh

denotes the SPH smoothing length, and

\gamma

converts Deep Water Impact source-space lengths to reference-grid index units.

Figure 1: HACC rank-0 gas density on the $256^{3}$ reference deposit under a common camera and transfer function. Columns show reference, 300K grid-seeded encoder, implicit neural baselines, and 300K 8-bit sample-based exports with $1024^{3}$ and $256^{3}$ deposit supervision. Labels report on-disk size, reduction factor, supervision lattice, rendered PSNR, and SSIM. Bottom: absolute luminance difference from reference (black, 0; white, 0.25).

Dataset	Input form and extent	Evaluation reference
HACC gas, rank 0 [ 9 ]	1,395,369 SPH particles, $32\,h^{-1}$ Mpc box	particle deposits, $1024^{3}$ supervision / $256^{3}$ evaluation
Deep Water Impact cells, cycle 12,244 [ 28 ]	44,851,632 hexahedral AMR cells, $46{\times}28{\times}24$ km	volume-weighted cell deposit, $1024{\times}624{\times}536$
Deep Water Impact temporal series	26 LANL-distributed $300^{3}$ water-fraction grids	input grid (warm-start evaluation)
Vortex [ 23 ]	$128^{3}$ grid, 8.4 MB	input grid
Bubble, stride 2 [ 23 ]	$128{\times}128{\times}320$ grid, 21.0 MB	input grid
Miranda, stride 3 [ 17 ]	$342^{3}$ grid, 160 MB	input grid

Table 2: Datasets. The input form is consumed by the sample-based encoder; the reference is the lattice on which reconstructed fields are evaluated. Grid sizes give float32 storage of the evaluated lattice.

Model	Size (MB)	Voxel PSNR	Image PSNR	SSIM
Grid-seeded, 300K	14.4	28.06	28.7	0.895
Sample-based, 300K, 8-bit	3.4	32.67	36.5	0.975
Sample-based, 300K, 8-bit ∗	3.5	44.72	42.5	0.992
Sample-based, 650K	31.2	35.24	36.6	0.976
Sample-based, 650K, 8-bit	7.0	35.22	36.6	0.976
Sample-based, 650K ∗	31.2	44.62	41.6	0.990

Table 3: HACC rank-0 gas density evaluated against the exact

256^{3}

particle deposit (PSNR in dB) under one camera and transfer function. The grid-seeded encoder and neural baselines are fitted to the

256^{3}

deposit. All sample-based rows are initialized from the same native SPH particles. Unmarked rows use the

1024^{3}

particle deposit for fidelity supervision, coverage, and relocation; rows marked ∗ use the

256^{3}

deposit fitted by the grid-seeded and neural baselines.

Figure 2: HACC rank-0 gas-density size–fidelity trade-off; Rendered PSNR plotted against model size on disk (log scale); Colors identify implicit neural (blue), grid-seeded Gaussian (orange), and sample-based Gaussian (green) representations; green circles and squares denote $1024^{3}$ and $256^{3}$ supervision, respectively, and hollow markers denote 8-bit exports. Arrow highlights the matched 300K, $256^{3}$ -supervision comparison: sample-based export improves rendered PSNR by 13.8 dB while reducing stored size by $4.1\times$ .

Figure 3: Two further HACC particle properties encoded from the same particles with the sample-based encoder at 300K (4,000 iterations, $256^{3}$ supervision): gas temperature (top) and metal mass fraction (bottom), each as the $256^{3}$ deposit, the float32 model, and its 8-bit export, labeled with size, reduction factor, and rendered PSNR/SSIM under the field’s own transfer function.

Dataset	Budget	MB	Grid-seeded	Sample-based
Vortex ( $128^{3}$ )	32K	1.54	28.32	49.67
Bubble Plume (stride 2)	200K	9.6	40.97	47.15

Table 4: Regular grids: the grid-seeded encoder and the sample-based encoder supplied with the same grid voxels, at identical primitive budget and file size. Both are decoded with Eq. 4 ; values are voxel PSNR in dB. Bubble Plume is evaluated within its saved data window, 1.38–4.27.

Figure 4: Regular grids as samples at identical budget and file size, ray cast from the decoded grids under each dataset’s saved transfer function, camera, and lighting (bar: color over value, line: opacity). Top: Vortex at 32,000 Gaussians (1.54 MB); the grid-seeded panel uses the density mapping saved for that model, and the rendered PSNR rises by 18.3 dB. Bottom: Bubble Plume (stride-2 grid, $128{\times}128{\times}320$ ) at 200,000 Gaussians (9.6 MB) under the saved data window; the rendered PSNR rises by 5.2 dB, and the filaments inside the plume stay separate.

Figure 5: Vortex reconstructions under the saved transfer function, camera, and lighting; grid-seeded panels use that model’s saved density mapping. Top: the reference, W-VEG’s 33K release model, full- and matched-schedule 33K sample-based models, and the 32K grid-seeded model. Bottom: the 32K grid-seeded model and sample-based models at the matched 1,500-iteration schedule, 500-, and 300-iteration short schedules. Panel labels report stored size, schedule, optimization time, rendered PSNR, and SSIM.

Figure 6: Stride-3 Miranda ( $342^{3}$ ) at $\sim$ 200K primitives under the protocol of Figure 5 (top); the grid-seeded panel is the grid-seeded encoder’s stored model, trained on the full grid and decoded on the stride-3 lattice. On this dense field the sample-based encoder renders 1.42 dB above W-VEG.

Method	Primitives	Time (s)	Voxel	Image / SSIM
Vortex, $128^{3}$ , budget 33K
W-VEG, release schedule	33,000	215	37.27	28.0 / 0.885
Sample-based, own	33,000	401	49.72	41.2 / 0.987
Sample-based, matched	33,000	88	45.14	36.6 / 0.971
Grid-seeded	32,000	223	28.32	22.8 / 0.834
Miranda, stride 3 ( $342^{3}$ ), budget 200K

Table 5: Comparison with W-VEG [ 4 ] at its final primitive count (PSNR in dB). W-VEG uses the public implementation under its 16,000-iteration release schedule and is decoded onto the reference lattice with the authors’ renderer. The sample-based and grid-seeded encoders use Eq. 4 . Every reconstructed lattice is scored by the same evaluator; times are wall-clock optimization times on the RTX 5090 laptop GPU. The grid-seeded Vortex row is the published 32K model, whereas the grid-seeded Miranda row is the grid-seeded encoder’s stored model, trained on the full-resolution grid and decoded on the stride-3 lattice.

Figure 7: Deep Water Impact, ray cast with the series’ transfer functions and cropped to the sea surface. Top: cycle 12,244, volume-weighted deposit of the 44.9 M cells and 400K-Gaussian encoding seeded directly from native cells and refined against this deposit, with the splash magnified in the inset. Bottom: cycle 17,260 of the $300^{3}$ series with the water fraction, temperature, and asteroid fraction each encoded at 200K Gaussians (28.8 MB total) and composited: the reference, independent encodes, and warm starts with relocation (bars: color over value, line: opacity).

Coarse stride, no relocation, 1,000 warm iterations
Cycle	Stride (cycles)	Independent final PSNR (dB)	Warm final PSNR (dB)
11,642	1,860	28.93	25.18
13,306	1,664	28.55	26.32
14,509	1,203	28.50	26.65
15,422	913	28.93	27.11
16,118	696	29.62	27.93

Table 6: Water fraction of the Deep Water Impact series on the

300^{3}

grid, 200K Gaussians: sampled PSNR (dB) on the trainer’s validation points. Independent encodes were seeded from the step’s own voxels and ran 3,000 iterations (262–317 s); warm starts were initialized from the previous stored step’s independent model and ran 1,000 iterations without relocation on the coarse stride and 1,500 iterations with relocation on the dense stride (143–163 s).

Dataset, reference	Model	MB	Ratio	Voxel	Image
HACC, $256^{3}$ (67.1 MB)	300K, 8-bit c	3.5	19 $\times$	44.7	42.5
Vortex, $128^{3}$ (8.4 MB)	32K	1.54	5.4 $\times$	49.7	41.1
	10K	0.49	17 $\times$	42.6	34.7
Bubble Plume, stride 2 (21.0 MB)	200K	9.6	2.2 $\times$	47.2 w	28.9
	50K	2.4	8.7 $\times$	44.4 w	25.6
Miranda, $342^{3}$ (160 MB)	200K	9.6	17 $\times$	29.7	35.8

Table 7: Data reduction achieved on every dataset: reference grid and its size on disk, the model, its size, the reduction factor, and that model’s quality (voxel PSNR in dB against the reference grid; rendered PSNR in dB under the saved view). Float32 models unless marked 8-bit; the 8-bit export reduces a float32 model a further

4\times

(measured on HACC, Table 3 ). c

256^{3}

supervision; w windowed voxel PSNR (1.38–4.27); s sampled PSNR.

Figure 8: Warm starts vs. independently encoded water-fraction models at 200K Gaussians: validation-sample PSNR vs. stride to the previous stored cycle, with the encoded cycle beneath each tick. Filled markers show the independent final after 3,000 iterations; hollow markers show the warm-start final after 1,000 iterations without relocation on coarse strides or 1,500 iterations with relocation on dense strides; triangles show dense-stride warm-start peak at iteration 1,100. Dense-stride warm starts reach/exceed the independent final during refinement and finish within 0.17 dB.

Dataset, budget	Encoder	Iter.	Time (s)	PSNR (dB)
Matched protocol
Vortex, 32K	Grid-seeded	1,500	223	28.3
	Sample-based	1,500	128	45.1
Bubble Plume, 200K	Grid-seeded	1,500	387	38.7
	Sample-based	1,500	91	40.0
Own schedules

Table 8: Encoding cost on the RTX 5090 laptop GPU. The matched protocol uses the same budget, 1,500 iterations, and 3,072 points per iteration for both encoders; the HACC rows use each encoder’s own schedule; the short schedules use 8,192 points per iteration. Quality is the sampled PSNR (500,000 random voxels) unless marked.

Aug 14, 2026

Fixed-Budget Gaussian Volume Encoding with Structure-Aware Allocation

Scientific simulations often produce scalar volumes faster than they can be stored, transferred, and loaded, while in situ reduction must use only a limited share of simulation resources. This work encodes scalar fields as anisotropic Gaussian primitives under a fixed budget. The complete primitive set is allocated analytically from local field structure, including position, orientation, and shape, then refined directly against the scalar field without densification, pruning, or count changes. The selected budget determines encoded storage before refinement and, together with the iteration schedule, provides a controllable refinement-time budget. In a controlled benchmark, truncation-aware field evaluation reduces encoding time by up to 51x; 1.4 million Gaussians encode a billion-voxel volume in at most four minutes on one desktop GPU, with reduced-iteration refinement completing in under one minute. Across five datasets spanning 2.1 million to 1.1 billion evaluated voxels, compression-useful configurations achieve 15.0-38.7 dB PSNR at compression ratios from 2.2x to over 40,000x. Pre-encoding structure statistics characterize fields for which one-shot allocation yields limited gains from additional capacity. Because primitives retain scalar attributes rather than baked appearance, a single compact model serves every subsequent visualization state - supporting post-hoc transfer-function, colormap, lighting, and viewpoint changes without re-encoding.

Michael R. Martin, Joseph Insley, Victor A. Mateevitsi +2

Department of Computer Science University of California, Davis · Argonne National Laboratory

Scientific Visualization 3DGS Compression

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Jul 1, 2026

Efficient Compression of Structured and Unstructured Volumes via Learned 3D Gaussian Representation

Recent work has shown that implicit neural representations (INRs) can be trained to effectively compress structured and unstructured volume data, allowing for direct data querying with a reduced memory footprint. However, as existing INRs for unstructured volumes do not encode geometry, they require partial mesh storage for later sampling, limiting achievable compression. At the same time, novel view synthesis methods have shown that explicit collections of 3D Gaussians can be used to accurately visualize volume data. In this work, we introduce an explicit model for volume data compression based on 3D Gaussian primitives. We reinterpret collections of 3D Gaussians as an explicit representation of a scalar field and use a sampling strategy that reconstructs scalar values at spatial locations through weighted aggregation of intersecting Gaussians. We develop optimized CUDA-accelerated pipelines for structured and unstructured model sampling, loss functions that encourage accurate domain encoding by our models, and a novel sampling-error based densification strategy. Our explicit formulation naturally encodes domain geometry, eliminating the need for mesh storage in unstructured volumes and introducing significantly higher compression opportunities. Compared to existing INRs, we demonstrate that our explicit model achieves competitive reconstruction quality with significant training speedups on structured volumes, while markedly outperforming in all metrics on unstructured volumes.

Landon Dyken, Sharmistha Chakrabarti, Nathan Debardeleben +4

3DGS Compression 3D Gaussian Splatting

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Aug 27, 2026

KISS-GS: 3D Gaussian Splatting Compression Kept Simple

Scene reconstruction with 3D Gaussian Splatting (3DGS) has become common, however deployment remains painful as the uncompressed file sizes can be massive. Current 3DGS compression systems combine multiple strategies for file size reduction, which can obscure where gains come from and limit component reuse across training pipelines. To make the gains more transparent, we propose KISS-GS, a modular compression pipeline named after the principle of keeping things simple, designed to decouple compression entirely from training. Given a 3DGS scene reconstructed with vanilla 3DGS, we are able to reduce it through compaction by 15.7x using a combination of state-of-the-art pruning schemes. Then we encode it into an image-based format designed for simple, ubiquitous decoding. With the SOG-XT format, we propose a novel extension to Self-Organizing Gaussians with two main contributions: (i) Self-organizing 2D Codebooks and (ii) Parallel Representative Assignment Smoothing (PRAS), which leverages the symmetry of quaternion and scale parameterizations to produce 2D attribute grids more amenable to encoding. This encoding reduces scene size by 6.6x. We show that optional encoding-aware fine-tuning yields a further 2.2x. Across standard 3DGS benchmarks, our simple and modular approach thus achieves a total of 85x to 319x reductions in the size of the scene over uncompressed vanilla 3DGS, setting new benchmarks for real-world scenes and surpassing tightly integrated methods in rate-distortion. Decoding relies solely on web-native image formats, and the modular design makes each stage easy to combine with future advances in reconstruction and compaction. Code and project page: https://fraunhoferhhi.github.io/KISS-GS/

Wieland Morgenstern, Friedrich Elias Branschke, Florian Fleischmann +5

Fraunhofer HHI, Germany · Humboldt-Universität zu Berlin, Germany · Technische Universität Berlin, Germany

3DGS Compression Gaussian Splatting Compression 3D Gaussian Splatting

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