PDE Solving on 1D Burgers
0RelL2 ErrorGC-PINN
Evaluation Results
| Method | Links | |||
|---|---|---|---|---|
| GC-PINNMapping=Radial Mapping2026.02 | 0 | 0 | 0.0001 | |
| GC-PINNMapping=Local Stretching2026.02 | 0 | 0 | 0.0001 | |
| gPINN2026.02 | 0 | 0 | 0 | |
| PINN+RAR2026.02 | 0 | 0 | 0.0001 | |
| GC-PINNMapping=Torus Mapping2026.02 | 0 | 0 | 0 | |
| SA-PINN2026.02 | 0 | 0 | 0.0001 | |
| FF-PINN2026.02 | 0.0001 | 0 | 0.0001 | |
| PINN2026.02 | 0.0001 | 0 | 0.0004 | |
| FNOTime (s)=6342026.05 | 0.0034 | — | — | |
| DANOPInput Context=Uniform Sparse2026.06 | 0.0047 | — | — | |
| Mamba-NOTime (s)=120,8122026.05 | 0.005 | — | — | |
| DNOPInput Context=Uniform Sparse2026.06 | 0.0058 | — | — | |
| MSAT (physics)Time (s)=1882026.05 | 0.0118 | — | — | |
| MSAT (no physics)Time (s)=342026.05 | 0.0156 | — | — | |
| Gemini-2.5-flashRefinement=review-2, Perspective=Best-of-N, Quantity=u(x, t)2025.08 | 0.0182 | — | — | |
| Deepseek-R1Refinement=review-2, Perspective=Best-of-N, Quantity=u(x, t)2025.08 | 0.0185 | — | — | |
| GPT-4.1-miniRefinement=review-2, Perspective=Best-of-N, Quantity=u(x, t)2025.08 | 0.0198 | — | — | |
| Vanilla PINNTime (s)=6312026.05 | 0.0203 | — | — | |
| FNOParam=0.001, Step=25, MCL Integration=Model + MCL2026.02 | 0.0224 | 0 | 0.0269 | |
| FNOParam=0.001, Step=10, MCL Integration=Model + MCL2026.02 | 0.0264 | 0.0001 | 0.0346 | |
| RAR2026.05 | 0.0275 | — | — | |
| PINN-LRATime (s)=2,5272026.05 | 0.0275 | — | — | |
| FNOParam=0.001, Step=25, MCL Integration=Model only2026.02 | 0.0326 | 0.0001 | 0.0396 | |
| FNOParam=0.001, Step=1, MCL Integration=Model + MCL2026.02 | 0.0357 | 0.0003 | 0.0499 | |
| FNOParam=0.001, Step=10, MCL Integration=Model only2026.02 | 0.0379 | 0.0002 | 0.0509 | |
| GNOTTime (s)=6,5732026.05 | 0.0403 | — | — | |
| FNOParam=0.001, Step=1, MCL Integration=Model only2026.02 | 0.0466 | 0.0006 | 0.0689 | |
| DeepONetTime (s)=2,5202026.05 | 0.066 | — | — | |
| GINOParam=0.001, Step=25, MCL Integration=Model + MCL2026.02 | 0.0814 | 0.0006 | 0.1011 | |
| GINOParam=0.001, Step=25, MCL Integration=Model only2026.02 | 0.0827 | 0.0006 | 0.1023 | |
| DeepONet-FiLMInput Context=Dense Grid2026.06 | 0.1025 | — | — | |
| GINOParam=0.001, Step=10, MCL Integration=Model + MCL2026.02 | 0.1079 | 0.0014 | 0.1387 | |
| GINOParam=0.001, Step=10, MCL Integration=Model only2026.02 | 0.1093 | 0.0015 | 0.1399 | |
| GINOParam=0.001, Step=1, MCL Integration=Model + MCL2026.02 | 0.1466 | 0.0039 | 0.1923 | |
| GINOParam=0.001, Step=1, MCL Integration=Model only2026.02 | 0.1475 | 0.004 | 0.1927 | |
| DeepONet-FlatInput Context=Dense Grid2026.06 | 0.1959 | — | — | |
| U-NOParam=0.001, Step=25, MCL Integration=Model + MCL2026.02 | 0.3311 | 0.0084 | 0.3343 | |
| DeepONet-AttnInput Context=Dense Grid2026.06 | 0.3339 | — | — | |
| U-NOParam=0.001, Step=1, MCL Integration=Model + MCL2026.02 | 0.3507 | 0.0395 | 0.3673 | |
| U-NOParam=0.001, Step=25, MCL Integration=Model only2026.02 | 0.3731 | 0.0143 | 0.3765 | |
| U-NOParam=0.001, Step=10, MCL Integration=Model + MCL2026.02 | 0.3986 | 0.0204 | 0.4048 | |
| U-NOParam=0.001, Step=1, MCL Integration=Model only2026.02 | 0.3988 | 0.0429 | 0.4153 | |
| U-NOParam=0.001, Step=10, MCL Integration=Model only2026.02 | 0.4127 | 0.0253 | 0.4175 |