FLUIDSPLAT: Reconstructing Physical Fields from Sparse Sensors via Gaussian Primitives

2026-05-15

AI Summary

This work addresses the challenge of reconstructing continuous flow fields from sparse surface sensor measurements by proposing a sensor-conditioned model inspired by 3D Gaussian Splatting. The method employs anisotropic Gaussian primitives to construct a spatially explicit, partition-of-unity-based intermediate representation that balances interpretability and expressiveness. Coupled with a state-conditioned residual decoder, the approach incorporates theoretical insights from Sobolev smoothness analysis to identify a variance bottleneck under sparse sensing and introduces a residual compensation mechanism to enhance reconstruction accuracy. Evaluated on the canonical cylinder flow benchmark, the proposed method achieves the lowest average error across all sensor configurations. On the AirfRANS dataset, it reduces reconstruction error by 11–23% compared to the strongest baseline using only eight surface pressure sensors.

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 $O(σ^{2}K/N)$.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. 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.

Problem

• flow field reconstruction
• sparse sensors
• physical fields
• aerodynamic design
• digital twin

Innovation

• Gaussian Splatting
• Sparse Sensor Reconstruction
• Partition-of-Unity
• Approximation Theory
• Flow Field Reconstruction