Navier-Stokes
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| PDE solving | Navier-Stokes 2D | MSE0 | 26 | |
| PDE solving with sparse-in-time observations | Navier-Stokes | PDE Residual0.06 | 24 | |
| PDE Solving | Navier-Stokes Regular Grid (test) | Relative L2 Error0.09 | 16 | |
| 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 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 | |
| Dynamical system modeling | Navier-Stokes (NS) m=4, n=8 (train) | MSE0 | 7 | |
| Operator learning | Navier-Stokes nu=1e-5, T=20, N=1000 1.0 (test) | Relative L2 Error0.1541 | 7 | |
| Operator learning | Navier-Stokes (nu=1e-4, T=30, N=10000) 1.0 (test) | Relative L2 Error0.0667 | 7 | |
| Operator learning | Navier-Stokes (nu=1e-4, T=30, N=1000) 1.0 (test) | Relative L2 Error0.1518 | 7 | |
| Operator learning | Navier-Stokes (nu=1e-3, T=50, N=1000) 1.0 (test) | Relative L2 Error0.0063 | 7 | |
| Inverse PDE Inference | Navier-Stokes 64x64 (test) | Relative L2 Error (%)4.6 | 6 | |
| Forward PDE Inference | Navier-Stokes 64x64 (test) | Relative L2 Error1 | 6 | |
| Inverse Problem | Navier-Stokes 97% Sparse Observation | L2 Relative Error7.91 | 5 | |
| Forward Simulation | Navier-Stokes 97% Sparse Observation | L2 Relative Error7.11 | 5 | |
| Inverse PDE solving | Navier–Stokes Full Observation | L2 Relative Error1.25 | 5 | |
| Forward PDE solving | Navier–Stokes Full Observation | L2 Relative Error0.6 | 5 |
Showing 25 of 36 rows