2D Navier-Stokes
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Continuum Field Reconstruction (Rollout) | 2D Navier-Stokes nu=1e-3 | MSE0.096 | 54 | |
| Conformal Prediction | 2D Navier-Stokes (test) | Coverage98.09 | 25 | |
| Continuum Field Reconstruction (Rollout) | 2D Navier-Stokes nu=1e-5 | MSE1.162 | 18 | |
| Inverse Problem | 2D Navier-Stokes (test) | Average Relative Error22.71 | 16 | |
| Dynamical systems reconstruction | 2D Navier-Stokes (test) | Reconstruction Error (In-t)1.326 | 15 | |
| Dynamical systems reconstruction | 2D Navier-Stokes (train) | In-t Prediction Error1.02 | 15 | |
| Forward Problem (PtO) | 2D Navier-Stokes (test) | Average Relative Error1.45 | 14 | |
| Stochastic PDE Simulation | 2D Navier-Stokes stochastically forced turbulence | Error Energy0.034 | 10 | |
| Neural Operator Learning | 2D Navier–Stokes ν = 10−5 (test) | Relative L2 Loss7.05 | 10 | |
| Operator Learning | 2D Navier-Stokes | Relative L2 Error3.23 | 7 | |
| Fluid Dynamics Prediction | 2D Navier-Stokes Kolmogorov flow (test) | Mean Error0.98 | 7 | |
| Dynamics modeling | 2D Navier-Stokes v=1e-5 (test) | Relative L2 Error0.124 | 7 | |
| Dynamics modeling | 2D Navier-Stokes v=1e-4 (test) | Relative L2 Error0.105 | 7 | |
| Cross-Reynolds prediction | 2D Navier-Stokes out-of-distribution Re=10,000 (test) | OOD Accuracy61.08 | 6 | |
| 2D Navier-Stokes Simulation | 2D Navier-Stokes (nu=10^-5, T=20, N=1000) 14 (test) | Relative L2 Error0.1556 | 6 | |
| 2D Navier-Stokes Simulation | 2D Navier-Stokes (nu=10^-4, T=30, N=10000) 14 (test) | Relative L2 Error0.082 | 6 | |
| 2D Navier-Stokes Simulation | 2D Navier-Stokes (nu=10^-4, T=30, N=1000) 14 (test) | Relative L2 Error0.1559 | 6 | |
| 2D Navier-Stokes Simulation | 2D Navier-Stokes (nu=10^-3, T=50, N=1000) 14 (test) | Relative L2 Error0.0086 | 6 | |
| Bayesian inverse problem | 2D Navier-Stokes d=64 | Relative Inversion Error (1% Noise)28.79 | 5 | |
| Bayesian inverse problem | 2D Navier-Stokes d=32 | Relative Inversion Error (1% Noise)0.2849 | 5 | |
| Incompressible Flow Prediction | 2D Navier-Stokes Re=1000 T50-100 (test) | U-MSE0.5 | 4 | |
| Incompressible Flow Prediction | 2D Navier-Stokes Re=1000 T15-49 (test) | U-MSE1 | 4 | |
| Incompressible Flow Prediction | 2D Navier-Stokes Re=1000 T101-300 (test) | U-MSE0.007 | 3 | |
| Solving 2D Navier-Stokes equations | 2D Navier-Stokes nu = 10^-5, T = 20 | Relative Test Error0.168 | 3 | |
| Solving 2D Navier-Stokes equations | 2D Navier-Stokes nu = 10^-4, T = 30 | Relative Test Error0.172 | 3 |
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