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.

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