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Kuramoto-Sivashinsky

Benchmarks

Task NameDataset NameSOTA ResultTrend
PDE forecastingKuramoto–Sivashinsky (KS)
nRMSE0.2
63
Data AssimilationKuramoto–Sivashinsky long horizon 640 steps
RMSE0.006
45
Data AssimilationKuramoto–Sivashinsky short horizon 140 steps
RMSE0.006
45
PDE Solving2D Kuramoto-Sivashinsky (test)
Mean Error0.81
27
PDE solvingKuramoto-Sivashinsky 1D (test)
Relative MSE Loss0.0086
18
PDE SolvingKuramoto-Sivashinsky (KS)
Rel L2 Error0.0203
11
FilteringKuramoto-Sivashinsky L=32π, min(z^4, 10)
RMSE1.15
8
FilteringKuramoto-Sivashinsky L=32π arctan
RMSE0.11
8
FilteringKuramoto-Sivashinsky L=16π, min(z^4, 10)
RMSE0.11
8
FilteringKuramoto-Sivashinsky L=16π, arctan
RMSE0.07
8
Data AssimilationKuramoto-Sivashinsky
Total Variation (TV)0.12
8
PDE ModelingKuramoto–Sivashinsky long horizon, 640 steps
HCT (MS-2)243
8
PDE ModelingKuramoto–Sivashinsky short horizon, 140 steps
HCT (MS-2)140
8
PDE ForecastingKuramoto-Sivashinsky (KS) L=66, σ=2.0
Wasserstein Distance0.226
7
PDE ForecastingKuramoto-Sivashinsky (KS) L=66, σ=1.0
Wasserstein Distance0.15
7
PDE ForecastingKuramoto-Sivashinsky (KS) L=66, σ=0.5
Wasserstein Distance0.13
7
PDE ForecastingKuramoto-Sivashinsky (KS) L=22, σ=2.0
Wasserstein Distance0.514
7
PDE ForecastingKuramoto-Sivashinsky (KS) L=22, σ=1.0
Wasserstein distance0.311
7
PDE ForecastingKuramoto-Sivashinsky (KS) L=22, σ=0.5
Wasserstein Distance0.188
7
2D Kuramoto-Sivashinsky PDE Simulation2D Kuramoto-Sivashinsky
Mean Error4.28
7
2D Kuramoto-Sivashinsky Prediction2D Kuramoto-Sivashinsky
Mean Prediction Error1.11
7
PDE ForecastingKuramoto-Sivashinsky (KS) L=66, σ=0.05
Wasserstein Distance0.123
6
Fluid Dynamics EmulationKuramoto-Sivashinsky
1-step MSE0
6
Online Data AssimilationKuramoto-Sivashinsky (KS) (test)
RMSD7.7
4
Spatiotemporal Trajectory PredictionKuramoto-Sivashinsky (KS) sigma=2.0 L=66 (test)
Mean CRPS2.17
3
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