Forward PDE solving on Helmholtz
0.0072Relative ErrorChebyshev Center-Based Direction Selection
Evaluation results
| Method | Links | ||
|---|---|---|---|
| Chebyshev Center-Based Direction Selection2026.05 | 0.0072 | — | |
| PCGrad2026.05 | 0.0075 | — | |
| IMTL-G2026.05 | 0.0086 | — | |
| DCGD2026.05 | 0.0097 | — | |
| SelfAdaptdh=128, epochs=20K, seeds=52026.05 | 0.011 | — | |
| HARMONIC2026.05 | 0.0116 | — | |
| Causaldh=128, epochs=20K, seeds=52026.05 | 0.012 | — | |
| Equi-FunDPSSteps (N)=5002025.05 | 0.0212 | — | |
| FunDPSSteps (N)=5002025.05 | 0.0213 | — | |
| FAMO+UAMdh=128, epochs=20K, seeds=52026.05 | 0.0227 | — | |
| FAMOdh=128, epochs=20K, seeds=52026.05 | 0.0267 | — | |
| Adam2026.05 | 0.0307 | — | |
| Uncertaintydh=128, epochs=20K, seeds=52026.05 | 0.041 | — | |
| ReLoBRaLo2026.05 | 0.057 | — | |
| UAMdh=128, epochs=20K, seeds=52026.05 | 0.067 | — | |
| FM4PDEnumber of steps=1000, number of observations=5002026.05 | 0.0748 | — | |
| Vanilladh=128, epochs=20K, seeds=52026.05 | 0.081 | — | |
| DiffusionPDEObservation mode=Sparse (5/128 points)2024.06 | 0.088 | — | |
| DiffusionPDESteps (N)=20002025.05 | 0.1264 | — | |
| DiffusionPDEnumber of steps=1000, number of observations=5002026.05 | 0.2202 | — | |
| MGDA2026.05 | 0.7542 | — | |
| FNOObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | 0.982 | — | |
| LRA2026.05 | 1 | — | |
| PINOObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | 1.065 | — | |
| DeepONetObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | 1.231 | — | |
| PINNsObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | 1.423 | — | |
| DiffusionPDEObservations=5002026.02 | — | 4,852.36 | |
| DiffusionPDEObservations=10002026.02 | — | 4,690.36 | |
| DiffusionPDEObservations=Full2026.02 | — | 5,600.25 | |
| FunDPSObservations=5002026.02 | — | 3,316.68 | |
| FunDPSObservations=10002026.02 | — | 3,307.42 | |
| FunDPSObservations=Full2026.02 | — | 2,714.46 | |
| PISDObservations=5002026.02 | — | 0.37 | |
| PISDObservations=10002026.02 | — | 0.52 | |
| PISDObservations=Full2026.02 | — | 3.97 |