Fixed-Budget Gaussian Volume Encoding with Structure-Aware Allocation

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.

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.

Slice-based volumetric imaging is widely applied and it demands representations that compress aggressively while preserving internal structure for analysis. We introduce GaussianPile, unifying 3D Gaussian splatting with an imaging system-aware focus model to address this challenge. Our proposed method introduces three key innovations: (i) a slice-aware piling strategy that positions anisotropic 3D Gaussians to model through-slice contributions, (ii) a differentiable projection operator that encodes the finite-thickness point spread function of the imaging acquisition system, and (iii) a compact encoding and joint optimization pipeline that simultaneously reconstructs and compresses the Gaussian sets. Our CUDA-based design retains the compression and real-time rendering efficiency of Gaussian primitives while preserving high-frequency internal volumetric detail. Experiments on microscopy and ultrasound datasets demonstrate that our method reduces storage and reconstruction cost, sustains diagnostic fidelity, and enables fast 2D visualization, along with 3D voxelization. In practice, it delivers high-quality results in as few as 3 minutes, up to 11x faster than NeRF-based approaches, and achieves consistent 16x compression over voxel grids, offering a practical path to deployable compression and exploration of slice-based volumetric datasets.