| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Fluid dynamics simulation | Navier-Stokes | nRMSE0.0625 | 60 | |
| PDE Solving | Navier-Stokes Regular Grid (test) | Relative L2 Error0.0319 | 41 | |
| Equation Discovery | Navier–Stokes | MSE0.0799 | 36 | |
| PDE solving | Navier-Stokes 2D | Relative L2 Error0.0027 | 34 | |
| Fluid Dynamics Simulation | Navier-Stokes (NS) nu=10^-5 at 64x64 unified-protocol (test) | Relative L2 Error (Test)2.84 | 31 | |
| 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 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 (NS) problem | Stp201 | 18 | |
| PDE solving | Navier-Stokes 2D (test) | Relative MSE Loss0.0479 | 18 | |
| PDE Solving | Navier-Stokes | Relative L2 Loss8 | 16 | |
| Forward PDE solving | Navier-Stokes | Relative L2 Error0.19 | 15 | |
| 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 | |
| Super-resolution | Navier-Stokes 8^2 to 128^2 | KES-RE0.657 | 14 | |
| PDE dynamics forecasting | Navier-Stokes (NS) OOD | nMSE0.312 | 11 | |
| PDE dynamics forecasting | Navier-Stokes (ID) | nMSE0.0649 | 11 | |
| Inverse PDE solving | Non-bounded Navier-Stokes | Relative Error0.104 | 11 | |
| Forward PDE solving | Non-bounded Navier-Stokes | Relative Error0.043 | 11 | |
| PDE Reconstruction | Navier-Stokes 3% uniformly random measurements | Coefficient Relative L2 Error6.38 | 10 |