Forward PDE solving on Darcy Flow
0.0127Relative ErrorFM4PDE
Evaluation results
| Method | Links | |||
|---|---|---|---|---|
| FM4PDEnumber of steps=1000, number of observations=5002026.05 | 0.0127 | — | — | |
| DiffusionPDEnumber of steps=1000, number of observations=5002026.05 | 0.1344 | — | — | |
| LNOLayers=4, Dim=128, Size=256, Heads=8, Batch=4, Epoch=500, Loss=rL2, Optimizer=AdamW, Scheduler=OneCycleLR2024.06 | 0.49 | — | — | |
| Transolver2024.06 | 0.58 | — | — | |
| F-FNO2024.06 | 0.75 | — | — | |
| GNOT2024.06 | 1.04 | — | — | |
| U-FNO2024.06 | 1.28 | — | — | |
| DiffusionPDEObservation mode=Sparse (5/128 points)2024.06 | 2.5 | — | — | |
| FNOObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | 28.2 | — | — | |
| PINOObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | 35.2 | — | — | |
| DeepONetObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | 38.3 | — | — | |
| PINNsObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | 48.8 | — | — | |
| DeepONet2026.05 | — | 0.383 | — | |
| Di-BiLPS2026.05 | — | 0.021 | 35.45 | |
| DiffPDE2026.05 | — | 0.025 | 255.74 | |
| FNO2026.05 | — | 0.282 | — | |
| PINNs2026.05 | — | 0.488 | — | |
| PINO2026.05 | — | 0.352 | — |