PDE Solving on 1d Burgers' equation (test)
0.0079Relative ErrorCNN XD
Evaluation Results
| Method | Links | |
|---|---|---|
| CNN XDResolution (s)=5122021.03 | 0.0079 | |
| CNN XDResolution (s)=20482021.03 | 0.0099 | |
| CNN XDResolution (s)=81922021.03 | 0.0123 | |
| FNO-1dResolution (s)=81922021.03 | 0.0139 | |
| CNN XDResolution (s)=2562021.03 | 0.0141 | |
| FNO-1dResolution (s)=40962021.03 | 0.0142 | |
| CNN XDResolution (s)=40962021.03 | 0.0145 | |
| FNO-1dResolution (s)=20482021.03 | 0.0146 | |
| FNO-1dResolution (s)=2562021.03 | 0.0149 | |
| FNO-1d XDResolution (s)=2562021.03 | 0.0153 | |
| CNN XDResolution (s)=10242021.03 | 0.0154 | |
| FNO-1d XDResolution (s)=5122021.03 | 0.0154 | |
| FNO-1d XDResolution (s)=10242021.03 | 0.0154 | |
| FNO-1d XDResolution (s)=81922021.03 | 0.0155 | |
| FNO-1dResolution (s)=5122021.03 | 0.0158 | |
| FNO-1dResolution (s)=10242021.03 | 0.016 | |
| FNO-1d XDResolution (s)=40962021.03 | 0.016 | |
| FNO-1d XDResolution (s)=20482021.03 | 0.0167 | |
| DeepONetTest transformations=none2026.02 | 0.017 | |
| FNO-1d (reproduced)Resolution (s)=2562021.03 | 0.0181 | |
| FNO-1d (reproduced)Resolution (s)=40962021.03 | 0.0183 | |
| FNO-1d (reproduced)Resolution (s)=81922021.03 | 0.0183 | |
| FNO-1d (reproduced)Resolution (s)=20482021.03 | 0.0184 | |
| FNO-1d (reproduced)Resolution (s)=10242021.03 | 0.0188 | |
| LNOResolution (s)=81922021.03 | 0.0189 | |
| FNO-1d (reproduced)Resolution (s)=5122021.03 | 0.0191 | |
| LNOResolution (s)=40962021.03 | 0.02 | |
| LNOResolution (s)=2562021.03 | 0.0212 | |
| LNOResolution (s)=10242021.03 | 0.0217 | |
| LNOResolution (s)=20482021.03 | 0.0219 | |
| LNOResolution (s)=5122021.03 | 0.0221 | |
| MGNOResolution (s)=2562021.03 | 0.0243 | |
| MGNOResolution (s)=5122021.03 | 0.0355 | |
| MGNOResolution (s)=20482021.03 | 0.036 | |
| MGNOResolution (s)=40962021.03 | 0.0364 | |
| MGNOResolution (s)=81922021.03 | 0.0364 | |
| AROMA2024.06 | 0.0365 | |
| MGNOResolution (s)=10242021.03 | 0.0374 | |
| PCANNResolution (s)=20482021.03 | 0.0383 | |
| PCANNResolution (s)=10242021.03 | 0.0391 | |
| PCANNResolution (s)=40962021.03 | 0.0392 | |
| PCANNResolution (s)=81922021.03 | 0.0393 | |
| PCANNResolution (s)=5122021.03 | 0.0395 | |
| PCANNResolution (s)=2562021.03 | 0.0398 | |
| OFormer2024.06 | 0.0492 | |
| FNO2024.06 | 0.05 | |
| CNNResolution (s)=2562021.03 | 0.0518 | |
| GNOResolution (s)=2562021.03 | 0.0555 | |
| GNOResolution (s)=5122021.03 | 0.0594 | |
| CORAL2024.06 | 0.062 | |
| GNOResolution (s)=10242021.03 | 0.0651 | |
| GNOResolution (s)=20482021.03 | 0.0663 | |
| GNOResolution (s)=40962021.03 | 0.0666 | |
| GNOResolution (s)=81922021.03 | 0.0699 | |
| ResNet2024.06 | 0.085 | |
| FCNResolution (s)=2562021.03 | 0.0958 | |
| CNNResolution (s)=5122021.03 | 0.122 | |
| GNOT2024.06 | 0.128 | |
| FCNResolution (s)=5122021.03 | 0.1407 | |
| DeepONet + TIEDTest transformations=SL(2, R) ⋉ (R^2, +), Energy=Distance to training domain2026.02 | 0.178 | |
| CNNResolution (s)=10242021.03 | 0.183 | |
| DeepONet + LieLACTest transformations=SL(2, R) ⋉ (R^2, +), Energy=Distance to training domain2026.02 | 0.187 | |
| FCNResolution (s)=10242021.03 | 0.1877 | |
| DeepONet + FoCalTest transformations=SL(2, R) ⋉ (R^2, +), Energy=Distance to training domain2026.02 | 0.202 | |
| CNNResolution (s)=20482021.03 | 0.228 | |
| FCNResolution (s)=20482021.03 | 0.2313 | |
| CNNResolution (s)=40962021.03 | 0.273 | |
| FCNResolution (s)=40962021.03 | 0.2855 | |
| CNNResolution (s)=81922021.03 | 0.297 | |
| FCNResolution (s)=81922021.03 | 0.3238 | |
| GCNResolution (s)=2562021.03 | 0.3999 | |
| GCNResolution (s)=5122021.03 | 0.4138 | |
| GCNResolution (s)=20482021.03 | 0.4157 | |
| GCNResolution (s)=10242021.03 | 0.4176 | |
| GCNResolution (s)=40962021.03 | 0.4191 | |
| GCNResolution (s)=81922021.03 | 0.4198 | |
| NNResolution (s)=81922021.03 | 0.4452 | |
| NNResolution (s)=5122021.03 | 0.4561 | |
| DINO2024.06 | 0.457 | |
| NNResolution (s)=20482021.03 | 0.4645 | |
| NNResolution (s)=2562021.03 | 0.4714 | |
| NNResolution (s)=40962021.03 | 0.4779 | |
| NNResolution (s)=10242021.03 | 0.4803 | |
| DeepONet + Kinetic LangevinTest transformations=SL(2, R) ⋉ (R^2, +), Energy=Distance to training domain2026.02 | 0.739 | |
| DeepONetTest transformations=SL(2, R) ⋉ (R^2, +)2026.02 | 0.867 |