FLUIDSPLAT: Reconstructing Physical Fields from Sparse Sensors via Gaussian Primitives

TL;DR

FLUIDSPLAT introduces an interpretable Gaussian primitive-based model for reconstructing flow fields from sparse sensors, outperforming existing methods in accuracy and interpretability.

Contribution

The paper presents FLUIDSPLAT, a novel sensor-conditioned model using Gaussian primitives with theoretical approximation guarantees and improved empirical performance.

Findings

Achieves best mean error on cylinder-flow benchmark.

Reduces error by 11-23% on AirfRANS with 8 sensors.

Provides theoretical analysis of approximation rates and variance-bias trade-offs.

Abstract

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 $O(\sigma^{2}K/N)$.Balancing the two yields $K^{*}\!\sim\!(N/\sigma^{2})^{d/(2s+d)}$: primitive count cannot grow freely under sparse sensing, revealing a variance bottleneck that motivates complementing the scaffold with a state-conditioned residual decoder. On a standard cylinder-flow benchmark, FLUIDSPLAT achieves the best mean error across all surface-sensor layouts; on AirfRANS with 8 surface-pressure sensors, it reduces error by 11-23% over the strongest baseline across three standard splits.