用高斯原语重建稀疏传感器流场，提升精度与可解释性。
FLUIDSPLAT: Reconstructing Physical Fields from Sparse Sensors via Gaussian Primitives
- 基于高斯原语构建空间显式流场表示，支持稀疏传感数据建模。
- 理论证明误差随原语数增长呈幂律下降，实测在4个基准上降低11%-28%误差。
- 适合空气动力学设计、数字孪生等需高可解释性流场重建的场景。
从稀疏表面传感器重建连续流场是气动设计、流动控制和数字孪生仪器的核心任务。现有神经方法通常将传感器读数编码为隐式潜在码，缺乏空间可解释性，且对表征容量如何随观测数量变化缺乏形式化指导。受3D高斯泼溅启发，我们提出FLUIDSPLAT，一种传感器条件模型，可预测K个各向异性高斯原语，形成单位分解骨架，作为流场的空间显式且可解释的中间表示。对于理想化的高斯原语估计器，我们证明了具有Sobolev光滑度s的场逼近率为O(K^{-s/d})；引入N个噪声观测后，平方风险分解为偏差O(K^{-2s/d})和方差O(σ²K/N)。权衡二者得最优原语数K*∼(N/σ²)^{d/(2s+d)}：在稀疏传感下原语数无法自由增长，揭示了方差瓶颈，由此提出结合状态条件残差解码器补充骨架。在涵盖2D与3D的四个基准（圆柱流、AirfRANS、FlowBench LDC-3D、PhySense-Car 3D）上，FLUIDSPLAT相较多个强基线实现11%-28%的误差降低。
原文摘要 · Abstract (English)
Reconstructing continuous flow fields from sparse surface-mounted sensors is central to aerodynamic design, flow control, and digital-twin instrumentation. Existing neural methods for this task typically encode sensor readings into implicit latent codes with little spatial interpretability and limited formal guidance on how representational capacity should scale with observation count. Inspired by 3D Gaussian Splatting, we introduce FLUIDSPLAT, a sensor-conditioned model that predicts K anisotropic Gaussian primitives forming a partition-of-unity scaffold, a spatially explicit and interpretable intermediate representation of the flow. For an idealized Gaussian primitive estimator, we prove an $O(K^{-s/d})$ approximation rate for fields with Sobolev smoothness $s$; incorporating $N$ noisy observations yields a squared-risk decomposition with bias $O(K^{-2s/d})$ and variance $O(σ^{2}K/N)$.Balancing the two yields $K^{*}\!\sim\!(N/σ^{2})^{d/(2s+d)}$: primitive count cannot grow freely under sparse sensing, revealing a variance bottleneck that motivates complementing the scaffold with a state-conditioned residual decoder. Across four benchmarks spanning 2D and 3D, FLUIDSPLAT achieves 11-28% error reduction over several strong baselines on cylinder flow, AirfRANS, FlowBench LDC-3D, and PhySense-Car 3D benchmarks.
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