Kolmogorov flow
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Data Assimilation | Kolmogorov flow short horizon 60 steps | RMSE0.016 | 63 | |
| Data Assimilation | Kolmogorov flow long horizon 180 steps | RMSE0.016 | 45 | |
| Fluid Flow Generative Modeling | Kolmogorov Flow | KDE R^20.9995 | 20 | |
| Autoregressive Super-Resolution (64 to 256) | KF256 (2D Kolmogorov Flow) (test) | RL20.309 | 13 | |
| Energy spectrum decay fitting | Kolmogorov flow | Decay Rate Exponent-2.712 | 12 | |
| 3D Spatiotemporal Regression | Kolmogorov Flow (test) | Log-Likelihood1.89 | 8 | |
| Data Assimilation | Kolmogorov flow | Dissipation0.0003 | 8 | |
| PDE Modeling | Kolmogorov flow long horizon, 180 steps | HCT (MS, Res=2)180 | 8 | |
| PDE Modeling | Kolmogorov flow short horizon 60 steps | HCT (MS-2)38 | 8 | |
| Fluid Simulation | 2D Kolmogorov flow | w Avg Error0.1486 | 8 | |
| PDE Forecasting | Kolmogorov Flow ν=1e-4 | Wasserstein Distance0.0007 | 7 | |
| PDE Forecasting | Kolmogorov Flow ν=5e-4 | Wasserstein Distance0.0006 | 7 | |
| PDE Forecasting | Kolmogorov Flow ν=1e-3 | Wasserstein Distance0.0011 | 7 | |
| Active Learning for Fluid Dynamics | Kolmogorov flow 2D Navier-Stokes | Mean1.72 | 7 | |
| Forward prediction | Kolmogorov flow 40 frames Super-resolution (test) | L2 Relative Error0.0198 | 6 | |
| Forward prediction | Kolmogorov flow 40 frames Forcing-shift (test) | L2 Relative Error0.0206 | 6 | |
| Forward prediction | Kolmogorov flow 40 frames Viscosity-shift (test) | L2 Relative Error0.0342 | 6 | |
| Forward prediction | Kolmogorov flow 40 frames In-distribution (test) | L2 Relative Error0.808 | 6 | |
| Fluid Dynamics Emulation | Kolmogorov Flow | MSE (1-step)0 | 6 | |
| Dense field reconstruction | Kolmogorov Flow PhysBR |S| = 256 (test) | Mean Relative L2 Error45 | 5 | |
| Dense field reconstruction | Kolmogorov Flow PhysBR |S| = 3,200 (test) | Mean Rel L2 Error0.12 | 5 | |
| Statistical Emulation of Chaotic Systems | Kolmogorov Flow single-traj Clean (sigma = 0.0) | L1 Histogram Distance0.178 | 4 | |
| Data Assimilation | Kolmogorov Flow | Encoder Training Time (s)0 | 4 | |
| Generative Flow Modeling | Kolmogorov Flow (test) | IT6,431 | 4 | |
| Spatiotemporal Trajectory Prediction | Kolmogorov Flow nu=1e-4 standard (test) | Mean CRPS1.8 | 3 |
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