FlowReconBench: Accuracy, Calibration and Cost of Learned and Classical Flow Reconstruction
Field: Machine Learning Authors: Nicolas Tricard, Linzheng Wang, Jason Chen, Sili Deng Published: 2026-11-04 arXiv: 2611.06912
Overview
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 addresses this by evaluating ten learned and five classical methods on three flow regimes:
- A laminar cylinder wake across Reynolds numbers
- Two-dimensional Kolmogorov turbulence
- Large-scale three-dimensional (3D) isotropic turbulence
- No universal winner: 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 POD lead (including for unobserved pressure). In 3D, inverse-distance weighting rivals the best learned methods on observed channels.
- Data-driven methods dominate when sensor density decreases or observability worsens.
- CRPS vs. error give different rankings on Kolmogorov flow: generative model ensembles are wider but under-dispersed, while deterministic models favor pointwise error. Generative models balance this trade-off via sampler budget—a larger budget improves ensemble quality at higher computational cost.
- 3D scaling: queryable methods have flat memory overhead, while full-grid construction methods run out of memory.
- Partial observability: observing only 2 of 4 fields makes the problem kinematically under-constrained, yet latent-variable models still reproduce structural similarity with ground truth.
All methods share leakage-controlled data splits and sensor draws, and are scored on per-channel error, ensemble spread, calibration, spectra, and cost.