Learning PDE Solution Operators on 2D Shallow Water
0.1657Mean L2 Relative ErrorFNO
Evaluation results
| Method | Links | |||
|---|---|---|---|---|
| FNOStep=25, MCL Integration=Model + MCL2026.02 | 0.1657 | 0 | 0.0024 | |
| FNOStep=25, MCL Integration=Model only2026.02 | 0.3055 | 0 | 0.0047 | |
| FNOStep=1, MCL Integration=Model + MCL2026.02 | 0.3084 | 0 | 0.0052 | |
| SFOCategory=Ours2026.01 | 0.38 | — | — | |
| SVD-NOCategory=SVD Kernel2026.01 | 0.39 | — | — | |
| FNOStep=1, MCL Integration=Model only2026.02 | 0.437 | 0 | 0.0083 | |
| PINOCategory=PINN, Fourier2026.01 | 0.46 | — | — | |
| FNOCategory=Fourier2026.01 | 0.49 | — | — | |
| MPNNCategory=Graph (Local)2026.01 | 0.5 | — | — | |
| UNOCategory=Fourier2026.01 | 0.52 | — | — | |
| DeepONetCategory=DeepONet2026.01 | 1.11 | — | — | |
| GINOStep=25, MCL Integration=Model + MCL2026.02 | 8.6314 | 0.0088 | 0.0987 | |
| GINOStep=25, MCL Integration=Model only2026.02 | 8.6397 | 0.0088 | 0.0988 | |
| U-NOStep=25, MCL Integration=Model + MCL2026.02 | 8.9772 | 0.0097 | 0.0927 | |
| U-NOStep=1, MCL Integration=Model + MCL2026.02 | 10.1253 | 0.0124 | 0.1128 | |
| UNetCategory=Neural surrogate2026.01 | 10.93 | — | — | |
| GINOStep=1, MCL Integration=Model + MCL2026.02 | 13.1233 | 0.0203 | 0.1509 | |
| GINOStep=1, MCL Integration=Model only2026.02 | 13.1313 | 0.0203 | 0.1499 | |
| U-NOStep=25, MCL Integration=Model only2026.02 | 13.6177 | 0.0205 | 0.1387 | |
| U-NOStep=1, MCL Integration=Model only2026.02 | 17.2072 | 0.036 | 0.1721 |