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2D Navier-Stokes

Benchmarks

Task NameDataset NameSOTA ResultTrend
Continuum Field Reconstruction (Rollout)2D Navier-Stokes nu=1e-3
MSE0.096
54
Continuum Field Reconstruction (Rollout)2D Navier-Stokes nu=1e-5
MSE1.162
18
Inverse Problem2D Navier-Stokes (test)
Average Relative Error22.71
16
Forward Problem (PtO)2D Navier-Stokes (test)
Average Relative Error1.45
14
Neural Operator Learning2D Navier–Stokes ν = 10−5 (test)
Relative L2 Loss7.05
10
Dynamics modeling2D Navier-Stokes v=1e-5 (test)
Relative L2 Error0.124
7
Dynamics modeling2D Navier-Stokes v=1e-4 (test)
Relative L2 Error0.105
7
Cross-Reynolds prediction2D Navier-Stokes out-of-distribution Re=10,000 (test)
OOD Accuracy61.08
6
2D Navier-Stokes Simulation2D Navier-Stokes (nu=10^-5, T=20, N=1000) 14 (test)
Relative L2 Error0.1556
6
2D Navier-Stokes Simulation2D Navier-Stokes (nu=10^-4, T=30, N=10000) 14 (test)
Relative L2 Error0.082
6
2D Navier-Stokes Simulation2D Navier-Stokes (nu=10^-4, T=30, N=1000) 14 (test)
Relative L2 Error0.1559
6
2D Navier-Stokes Simulation2D Navier-Stokes (nu=10^-3, T=50, N=1000) 14 (test)
Relative L2 Error0.0086
6
Bayesian inverse problem2D Navier-Stokes d=64
Relative Inversion Error (1% Noise)28.79
5
Bayesian inverse problem2D Navier-Stokes d=32
Relative Inversion Error (1% Noise)0.2849
5
Incompressible Flow Prediction2D Navier-Stokes Re=1000 T50-100 (test)
U-MSE0.5
4
Incompressible Flow Prediction2D Navier-Stokes Re=1000 T15-49 (test)
U-MSE1
4
Incompressible Flow Prediction2D Navier-Stokes Re=1000 T101-300 (test)
U-MSE0.007
3
Solving 2D Navier-Stokes equations2D Navier-Stokes nu = 10^-5, T = 20
Relative Test Error0.168
3
Solving 2D Navier-Stokes equations2D Navier-Stokes nu = 10^-4, T = 30
Relative Test Error0.172
3
Incompressible Flow Prediction2D Navier-Stokes Long-term Extrapolation (T151-End) Re=1000 (test)
Total MSE0.0074
2
Incompressible Flow Prediction2D Navier-Stokes Short-term Extrapolation (T51-150) Re=1000 (test)
Total MSE0.0073
2
Incompressible Flow Prediction2D Navier-Stokes Prediction Regime (T15-50) Re=1000 (test)
Total MSE0.0011
2
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