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The FlowReconBench study evaluates fifteen reconstruction methods—including ten machine‑learning models and five traditional approaches—across three fluid‑dynamics regimes: a two‑dimensional laminar cylinder wake, two‑dimensional Kolmogorov turbulence, and three‑dimensional isotropic turbulence from the Johns Hopkins database.
| Regime | Dataset | Points | Channels | Split | Primary challenge |
|---|
| 2D laminar periodic | Cylinder wake (new) | 2.4×104 | ux,uy,p | cross-Re | Low-rank observability |
| 2D chaotic | Kolmogorov[65] | 6.6×104 | ω | cross-traj. | Multiscale reconstruction |
| 3D chaotic | JHTDB isotropic[35] | 1.95×106 | Ux,Uy,Uz,p | spatial | Unobserved channels |
For the cylinder wake, the linear stochastic estimation (LSE) method gives the lowest aggregate relative‑L² error of 0.043, while gappy proper orthogonal decomposition (POD) follows with 0.057. Generative models such as SiT‑point achieve higher errors (0.073) and interpolation with inverse‑distance weighting (IDW) performs poorly (0.712). This pattern mirrors the trend that classical methods excel when the flow is low‑rank or sensor coverage is dense, a situation well represented in the cylinder wake.
| Rel. L2 | ||||||||||
| Method | agg. | Re=80 | Re=250 | ux | uy | p | CRPS | Spr/Err | Cov.90 | s/field |
| SiT-point (N=8) | 0.073 | 0.038 | 0.108 | 0.057 | 0.105 | 0.057 | 0.034 | 0.51 | 0.40 | 0.50 |
| Senseiver | 0.134 | 0.118 | 0.150 | 0.115 | 0.192 | 0.095 | 0.082 | — | — | 0.06 |
| MLP-RBF | 0.318 | 0.260 | 0.376 | 0.220 | 0.536 | 0.197 | 0.165 | — | — | 0.07 |
| Geo-FNO | 0.079 | 0.058 | 0.100 | 0.063 | 0.109 | 0.064 | 0.045 | — | — | 0.26 |
| LSE | 0.043 | 0.036 | 0.050 | 0.032 | 0.058 | 0.039 | 0.022 | — | — | — |
| Gappy POD (r=20) | 0.057 | 0.045 | 0.069 | 0.043 | 0.077 | 0.050 | 0.029 | — | — | — |
| IDW (k=8) | 0.712 | 0.674 | 0.751 | 0.522 | 0.615 | 1.000 | 0.441 | — | — | — |
| Nearest neighbor | 0.713 | 0.673 | 0.752 | 0.526 | 0.612 | 1.000 | 0.423 | — | — | — |
| Training mean | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.664 | — | — | — |
In Kolmogorov turbulence, a generative method (S3GM) attains the best mean relative‑L² error of 0.273, outperforming both the SiT‑point variant (0.293) and the deterministic Fourier neural operator (FNO) with 0.380.
For the large‑scale 3D isotropic turbulence, the latent flow‑matching (Latent FM) technique yields the lowest aggregate error of 0.465, better than the learned FNO‑3D‑FM (0.571) and the generative SiT‑point (0.555). This demonstrates that, when reconstructing all physical channels from partial measurements, some learned approaches can surpass classical estimators.
The benchmark also highlights limitations: generative ensembles such as SiT‑point are under‑dispersed, with a spread‑error ratio of 0.51 and only 40 % coverage at the 90 % confidence level in the cylinder wake. Latent FM markedly smooths small‑scale structures, retaining just 21 % of the direct‑numerical‑simulation energy in the dissipation band. Classical grid‑based interpolators like IDW may fail when sensor spacing exceeds the flow’s decorrelation length, yielding errors over twice the training‑mean expectations.
Overall, FlowReconBench shows that the choice of reconstruction method must consider the sensing regime, flow dynamics, and the trade‑off between accuracy and uncertainty calibration.