Kuramoto-Sivashinsky
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Data Assimilation | Kuramoto–Sivashinsky long horizon 640 steps | RMSE0.006 | 45 | |
| Data Assimilation | Kuramoto–Sivashinsky short horizon 140 steps | RMSE0.006 | 45 | |
| PDE solving | Kuramoto-Sivashinsky 1D (test) | Relative MSE Loss0.0086 | 18 | |
| PDE Solving | Kuramoto-Sivashinsky (KS) | Rel L2 Error0.0203 | 9 | |
| Data Assimilation | Kuramoto-Sivashinsky | Total Variation (TV)0.12 | 8 | |
| PDE Modeling | Kuramoto–Sivashinsky long horizon, 640 steps | HCT (MS-2)243 | 8 | |
| PDE Modeling | Kuramoto–Sivashinsky short horizon, 140 steps | HCT (MS-2)140 | 8 | |
| Fluid Dynamics Emulation | Kuramoto-Sivashinsky | 1-step MSE0 | 6 | |
| Online Data Assimilation | Kuramoto-Sivashinsky (KS) (test) | RMSD7.7 | 4 | |
| Physics-Informed Neural Network PDE Solving | Kuramoto–Sivashinsky full solution | Relative L2 Error0.0853 | 3 | |
| Physics-Informed Neural Network PDE Solving | Kuramoto–Sivashinsky first time window | Relative L2 Error0 | 3 | |
| Long-term Time-Series Forecasting | Kuramoto-Sivashinsky (K.-S.) synthetic (test) | MSE0.92 | 2 | |
| Operator Learning | Kuramoto-Sivashinsky spatio-temporal chaos | Mean relative L2 Error16.36 | 2 | |
| Inverse parameter identification | Kuramoto-Sivashinsky | Metric- | 0 |
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