| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| PDE forecasting | Kuramoto–Sivashinsky (KS) | nRMSE0.2 | 63 | |
| Data Assimilation | Kuramoto–Sivashinsky long horizon 640 steps | RMSE0.006 | 45 | |
| Data Assimilation | Kuramoto–Sivashinsky short horizon 140 steps | RMSE0.006 | 45 | |
| PDE Solving | 2D Kuramoto-Sivashinsky (test) | Mean Error0.81 | 27 | |
| PDE solving | Kuramoto-Sivashinsky 1D (test) | Relative MSE Loss0.0086 | 18 | |
| PDE Solving | Kuramoto-Sivashinsky (KS) | Rel L2 Error0.0203 | 11 | |
| Filtering | Kuramoto-Sivashinsky L=32π, min(z^4, 10) | RMSE1.15 | 8 | |
| Filtering | Kuramoto-Sivashinsky L=32π arctan | RMSE0.11 | 8 | |
| Filtering | Kuramoto-Sivashinsky L=16π, min(z^4, 10) | RMSE0.11 | 8 | |
| Filtering | Kuramoto-Sivashinsky L=16π, arctan | RMSE0.07 | 8 | |
| 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 | |
| PDE Forecasting | Kuramoto-Sivashinsky (KS) L=66, σ=2.0 | Wasserstein Distance0.226 | 7 | |
| PDE Forecasting | Kuramoto-Sivashinsky (KS) L=66, σ=1.0 | Wasserstein Distance0.15 | 7 | |
| PDE Forecasting | Kuramoto-Sivashinsky (KS) L=66, σ=0.5 | Wasserstein Distance0.13 | 7 | |
| PDE Forecasting | Kuramoto-Sivashinsky (KS) L=22, σ=2.0 | Wasserstein Distance0.514 | 7 | |
| PDE Forecasting | Kuramoto-Sivashinsky (KS) L=22, σ=1.0 | Wasserstein distance0.311 | 7 | |
| PDE Forecasting | Kuramoto-Sivashinsky (KS) L=22, σ=0.5 | Wasserstein Distance0.188 | 7 | |
| 2D Kuramoto-Sivashinsky PDE Simulation | 2D Kuramoto-Sivashinsky | Mean Error4.28 | 7 | |
| 2D Kuramoto-Sivashinsky Prediction | 2D Kuramoto-Sivashinsky | Mean Prediction Error1.11 | 7 | |
| PDE Forecasting | Kuramoto-Sivashinsky (KS) L=66, σ=0.05 | Wasserstein Distance0.123 | 6 | |
| Fluid Dynamics Emulation | Kuramoto-Sivashinsky | 1-step MSE0 | 6 | |
| Online Data Assimilation | Kuramoto-Sivashinsky (KS) (test) | RMSD7.7 | 4 | |
| Spatiotemporal Trajectory Prediction | Kuramoto-Sivashinsky (KS) sigma=2.0 L=66 (test) | Mean CRPS2.17 | 3 |