PDE solving on Navier-Stokes 2D
0.0027Relative L2 ErrorGC-PINN
Evaluation results
| Method | Links | |||||||
|---|---|---|---|---|---|---|---|---|
| GC-PINNMapping=Torus Mapping2026.02 | 0.0027 | 0 | 0.0012 | — | — | — | — | |
| GC-PINNMapping=Local Stretching2026.02 | 0.0049 | 0 | 0.0019 | — | — | — | — | |
| FNOStep=5, MCL Integration=Model + MCL2026.02 | 0.0052 | 0.0026 | 0.0061 | — | — | — | — | |
| FNOStep=1, MCL Integration=Model + MCL2026.02 | 0.0057 | 0.0031 | 0.0065 | — | — | — | — | |
| FNOStep=10, MCL Integration=Model + MCL2026.02 | 0.0059 | 0.0033 | 0.0072 | — | — | — | — | |
| FNOStep=5, MCL Integration=Model only2026.02 | 0.0066 | 0.0026 | 0.0072 | — | — | — | — | |
| FNOStep=1, MCL Integration=Model only2026.02 | 0.0069 | 0.095 | 0.0073 | — | — | — | — | |
| FNOStep=10, MCL Integration=Model only2026.02 | 0.0072 | 0.0035 | 0.0082 | — | — | — | — | |
| GC-PINNMapping=Radial Mapping2026.02 | 0.0107 | 0.0001 | 0.0046 | — | — | — | — | |
| GINOStep=5, MCL Integration=Model + MCL2026.02 | 0.0116 | 0.0107 | 0.0188 | — | — | — | — | |
| GINOStep=5, MCL Integration=Model only2026.02 | 0.0119 | 0.0116 | 0.0192 | — | — | — | — | |
| GINOStep=10, MCL Integration=Model + MCL2026.02 | 0.013 | 0.013 | 0.0197 | — | — | — | — | |
| GINOStep=10, MCL Integration=Model only2026.02 | 0.0131 | 0.0147 | 0.0197 | — | — | — | — | |
| GINOStep=1, MCL Integration=Model + MCL2026.02 | 0.0132 | 0.0133 | 0.0206 | — | — | — | — | |
| gPINN2026.02 | 0.0133 | 0.0002 | 0.0035 | — | — | — | — | |
| GINOStep=1, MCL Integration=Model only2026.02 | 0.0136 | 0.0144 | 0.0212 | — | — | — | — | |
| SA-PINN2026.02 | 0.0172 | 0.0003 | 0.0044 | — | — | — | — | |
| FF-PINN2026.02 | 0.0213 | 0.0004 | 0.006 | — | — | — | — | |
| U-NOStep=5, MCL Integration=Model + MCL2026.02 | 0.0399 | 0.0443 | 0.0465 | — | — | — | — | |
| U-NOStep=5, MCL Integration=Model only2026.02 | 0.0447 | 0.062 | 0.0523 | — | — | — | — | |
| Vanilla PINNTime (s)=6312026.05 | 0.0506 | — | — | — | — | — | — | |
| U-NOStep=10, MCL Integration=Model + MCL2026.02 | 0.0518 | 0.0516 | 0.0577 | — | — | — | — | |
| U-NOStep=10, MCL Integration=Model only2026.02 | 0.0591 | 0.0649 | 0.0643 | — | — | — | — | |
| PINN+RAR2026.02 | 0.0592 | 0.003 | 0.0188 | — | — | — | — | |
| RAR2026.05 | 0.0651 | — | — | — | — | — | — | |
| U-NOStep=1, MCL Integration=Model + MCL2026.02 | 0.0854 | 0.1178 | 0.0945 | — | — | — | — | |
| U-NOStep=1, MCL Integration=Model only2026.02 | 0.0904 | 0.1216 | 0.099 | — | — | — | — | |
| PINN2026.02 | 0.35 | 0.104 | 0.176 | — | — | — | — | |
| MSAT (no physics)Time (s)=342026.05 | 0.666 | — | — | — | — | — | — | |
| GNOTTime (s)=6,5732026.05 | 0.68 | — | — | — | — | — | — | |
| MSAT (physics)Time (s)=1882026.05 | 0.694 | — | — | — | — | — | — | |
| FNOTime (s)=6342026.05 | 0.821 | — | — | — | — | — | — | |
| DeepONetTime (s)=2,5202026.05 | 0.866 | — | — | — | — | — | — | |
| Mamba-NOTime (s)=120,8122026.05 | 0.926 | — | — | — | — | — | — | |
| BreedStrategy=Breed2026.06 | — | — | — | 0.93 | 1.07 | 1.06 | 1.2 | |
| OGAS-LStrategy=OGAS-L2026.06 | — | — | — | 1.05 | 1.51 | 1.37 | 1.67 | |
| OGAS-UStrategy=OGAS-U2026.06 | — | — | — | 1.03 | 1.55 | 1.34 | 1.64 | |
| SBALStrategy=SBAL2026.06 | — | — | — | 1.02 | 1.03 | 1.02 | 1.02 | |
| SobolStrategy=Sobol2026.06 | — | — | — | 1.04 | 1.04 | 1.02 | 1.01 | |
| Top-KStrategy=Top-K2026.06 | — | — | — | 1.06 | 1.07 | 1.09 | 1.13 |