FluidWeave: Reconstructing Physical Fields from Sparse Sensors via Gaussian Primitives

Reconstructing continuous physical fields from sparse surface-mounted sensors is central to scientific monitoring, engineering design, and digital-twin systems. Many neural reconstructors predict queried field values through latent features that do not themselves define a field over the target domain. To make this spatial structure explicit, we introduce FLUIDWEAVE, an end-to-end framework built around a shared spatial state that couples a continuously queryable field proposal with its residual correction. Inspired by 3D Gaussian Splatting, we instantiate this state as K anisotropic Gaussian primitives predicted from the unordered sensor set, whose centers, covariances, and amplitudes encode location, support, and field value, respectively. Their partition-of-unity aggregation forms the normalized proposal, while the full primitive state conditions the correction decoder. To analyze this proposal-correction mechanism, we derive a coverage-amplitude error bound, decompose local sensor sensitivity across the two pathways, and establish an exact identity for the residual's error reduction. Across four complementary benchmarks, from 2D cylinder flow and AirfRANS to 3D FlowBench LDC-3D and PhySense-Car, FLUIDWEAVE outperforms several strong reconstruction baselines.