FlowReconBench: Accuracy, calibration and cost of learned and classical flow reconstruction from sparse sensors
Abstract
Reconstructing full flow fields from sparse sensors requires prior assumptions about unmeasured regions and physical variables. Yet it remains unclear when learned models outperform classical estimators and which aspects of their predictions can be trusted. FlowReconBench evaluates ten learned and five classical methods on three regimes: a laminar cylinder wake across Reynolds numbers, two-dimensional Kolmogorov turbulence and a large-scale three-dimensional (3D) isotropic turbulence. Methods share leakage-controlled splits and sensor draws and are scored on per-channel error, ensemble spread, calibration, spectra and cost. The leading method changes for each regime. Classical methods perform strongly in low-order and dense-sensing regimes. On the cylinder wake, linear stochastic estimation and gappy proper orthogonal decomposition lead, including for unobserved pressure. In 3D, inverse-distance weighting matches the best learned methods on observed channels. Data-driven methods become superior at decreasing sensor density or poor sensor observability. On Kolmogorov flow, continuous ranked probability score and error yield different method rankings: generative models offer broader but underdispersed ensembles, while deterministic models prioritize pointwise error. Generative models balance this tradeoff through their sampler budget, with a larger budget improving ensemble quality at higher computational cost. In 3D, scaling tests demonstrate that queryable methods are flat in memory, while full-grid construction methods run out of memory. Observing only 2 of 4 fields leaves the problem kinematically underconstrained, yet a latent model can reproduce structural similarities to the ground truth.
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BibTeX
@misc{tricard2026flowreconbench,
title = {{FlowReconBench: Accuracy, calibration and cost of learned and classical flow reconstruction from sparse sensors}},
author = {Nicolas Tricard and Linzheng Wang and Jason Chen and Sili Deng},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06912},
eprint = {2611.06912},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06912},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - FlowReconBench: Accuracy, calibration and cost of learned and classical flow reconstruction from sparse sensors
AU - Nicolas Tricard
AU - Linzheng Wang
AU - Jason Chen
AU - Sili Deng
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06912
UR - https://arxiv.org/abs/2611.06912
AB - Reconstructing full flow fields from sparse sensors requires prior assumptions about unmeasured regions and physical variables. Yet it remains unclear when learned models outperform classical estimators and which aspects of their predictions can be trusted. FlowReconBench evaluates ten learned and five classical methods on three regimes: a laminar cylinder wake across Reynolds numbers, two-dimensional Kolmogorov turbulence and a large-scale three-dimensional (3D) isotropic turbulence. Methods share leakage-controlled splits and sensor draws and are scored on per-channel error, ensemble spread, calibration, spectra and cost. The leading method changes for each regime. Classical methods perform strongly in low-order and dense-sensing regimes. On the cylinder wake, linear stochastic estimation and gappy proper orthogonal decomposition lead, including for unobserved pressure. In 3D, inverse-distance weighting matches the best learned methods on observed channels. Data-driven methods become superior at decreasing sensor density or poor sensor observability. On Kolmogorov flow, continuous ranked probability score and error yield different method rankings: generative models offer broader but underdispersed ensembles, while deterministic models prioritize pointwise error. Generative models balance this tradeoff through their sampler budget, with a larger budget improving ensemble quality at higher computational cost. In 3D, scaling tests demonstrate that queryable methods are flat in memory, while full-grid construction methods run out of memory. Observing only 2 of 4 fields leaves the problem kinematically underconstrained, yet a latent model can reproduce structural similarities to the ground truth.
ER -