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Navier-Stokes

Benchmarks

Task NameDataset NameSOTA ResultTrend
Fluid dynamics simulationNavier-Stokes
nRMSE0.0625
60
PDE SolvingNavier-Stokes Regular Grid (test)
Relative L2 Error0.0319
41
Equation DiscoveryNavier–Stokes
MSE0.0799
36
PDE solvingNavier-Stokes 2D
Relative L2 Error0.0027
34
Fluid Dynamics SimulationNavier-Stokes (NS) nu=10^-5 at 64x64 unified-protocol (test)
Relative L2 Error (Test)2.84
31
Spatiotemporal Field ReconstructionNavier-Stokes 10% Subset
CRPS0.1005
30
Spatiotemporal Field ReconstructionNavier-Stokes (Full)
CRPS0.0968
30
Fluid dynamics simulationNavier-Stokes periodic incompressible (test)
nRMSE5.3
28
PDE solving with sparse-in-time observationsNavier-Stokes
PDE Residual0.06
24
Turbulent field generationNavier-Stokes Equations
KDE R20.9949
20
Super-ResolutionNavier-Stokes (NS) 2x from PDEBench native grid (test)
RMSE0.0209
20
PDE SolvingNavier-Stokes (NS) problem
Stp201
18
PDE solvingNavier-Stokes 2D (test)
Relative MSE Loss0.0479
18
PDE SolvingNavier-Stokes
Relative L2 Loss8
16
Forward PDE solvingNavier-Stokes
Relative L2 Error0.19
15
Operator LearningNavier-Stokes Regular Grid (test)
Relative L2 Error0.0632
15
PDE SolvingNavier-Stokes Point-wise (25% test ratio)
Relative L2 Error0.1274
15
Temporal ExtrapolationNavier-Stokes 1 × 10^-3 (Out-t)
MSE0.0022
15
Temporal ExtrapolationNavier-Stokes 1 × 10^-3 (In-t)
MSE0.0001
15
Super-resolutionNavier-Stokes 8^2 to 128^2
KES-RE0.657
14
PDE dynamics forecastingNavier-Stokes (NS) OOD
nMSE0.312
11
PDE dynamics forecastingNavier-Stokes (ID)
nMSE0.0649
11
Inverse PDE solvingNon-bounded Navier-Stokes
Relative Error0.104
11
Forward PDE solvingNon-bounded Navier-Stokes
Relative Error0.043
11
PDE ReconstructionNavier-Stokes 3% uniformly random measurements
Coefficient Relative L2 Error6.38
10
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