Navier-Stokes
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Fluid dynamics simulation | Navier-Stokes | nRMSE0.0625 | 60 | |
| Spatiotemporal Field Reconstruction | Navier-Stokes 10% Subset | CRPS0.1005 | 30 | |
| Spatiotemporal Field Reconstruction | Navier-Stokes (Full) | CRPS0.0968 | 30 | |
| Fluid dynamics simulation | Navier-Stokes periodic incompressible (test) | nRMSE5.3 | 28 | |
| PDE solving | Navier-Stokes 2D | MSE0 | 26 | |
| PDE Solving | Navier-Stokes Regular Grid (test) | Relative L2 Error0.0484 | 25 | |
| PDE solving with sparse-in-time observations | Navier-Stokes | PDE Residual0.06 | 24 | |
| Turbulent field generation | Navier-Stokes Equations | KDE R20.9949 | 20 | |
| Super-Resolution | Navier-Stokes (NS) 2x from PDEBench native grid (test) | RMSE0.0209 | 20 | |
| PDE solving | Navier-Stokes 2D (test) | Relative MSE Loss0.0479 | 18 | |
| Operator Learning | Navier-Stokes Regular Grid (test) | Relative L2 Error0.0632 | 15 | |
| PDE Solving | Navier-Stokes Point-wise (25% test ratio) | Relative L2 Error0.1274 | 15 | |
| Temporal Extrapolation | Navier-Stokes 1 × 10^-3 (Out-t) | MSE0.0022 | 15 | |
| Temporal Extrapolation | Navier-Stokes 1 × 10^-3 (In-t) | MSE0.0001 | 15 | |
| PDE dynamics forecasting | Navier-Stokes (NS) OOD | nMSE0.312 | 11 | |
| PDE dynamics forecasting | Navier-Stokes (ID) | nMSE0.0649 | 11 | |
| PDE Reconstruction | Navier-Stokes 3% uniformly random measurements | Coefficient Relative L2 Error6.38 | 10 | |
| Spatiotemporal prediction | Navier-Stokes | N-MSE0.1489 | 9 | |
| Fluid Flow Prediction | Navier Stokes (test) | Energy Distance (ED)0.229 | 8 | |
| PDE Solving | Navier-Stokes Point-wise 5% ratio (test) | Relative L2 Error0.1268 | 8 | |
| Steady-state PDE Solving | Navier-Stokes viscosity=0.001 Noisy observations (sigma_max^o)^2 = 0.001 (test) | Test Error0.126 | 8 | |
| Steady-state PDE Solving | Navier-Stokes Noisy inputs (viscosity=0.001) (sigma_max^i)^2 = 0.001 (test) | Test Error0.144 | 8 | |
| Steady-state PDE Solving | Navier-Stokes viscosity=0.001 Clean sigma_max^2 = 0 (test) | Test Error12.8 | 8 | |
| Partial Differential Equation Discovery | Navier-Stokes Taylor-Green Vortex | MSE (True)0.0021 | 7 | |
| Dynamical system modeling | Navier-Stokes (NS) m=4, n=8 (train) | MSE0 | 7 |
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