PDE Solving on Navier-Stokes (Relative L2 Loss)
2.03Relative L2 LossFNO
Evaluation Results
| Method | Links | |
|---|---|---|
| FNOTraining time (s)=1150.3, Prediction sequence=t = 11–20, Final predicted time t=202026.06 | 2.03 | |
| DeepONetTraining time (s)=2000.7, Prediction sequence=t = 11–20, Final predicted time t=202026.06 | 2.23 | |
| PCA–RaNN-BFGS (ensemble)Training time (s)=88.7, Ensemble size (K)=20, Prediction sequence=t = 11–20, Final predicted time t=202026.06 | 2.47 | |
| RBFOptimizer=L-BFGS2025.02 | 2.56 | |
| PCA–RaNN-EM (ensemble)Training time (s)=19.4, Ensemble size (K)=20, Prediction sequence=t = 11–20, Final predicted time t=202026.06 | 2.59 | |
| RBF-POptimizer=L-BFGS2025.02 | 2.98 | |
| DNOPInput Context=Uniform Sparse2026.06 | 3.23 | |
| DANOPInput Context=Uniform Sparse2026.06 | 3.26 | |
| PCA–NNTraining time (s)=1468.2, Prediction sequence=t = 11–20, Final predicted time t=202026.06 | 3.34 | |
| RBA-PINNOptimizer=L-BFGS2025.02 | 4.86 | |
| SAFE-NETOptimizer=L-BFGS2025.02 | 5.26 | |
| RFFOptimizer=L-BFGS2025.02 | 6.76 | |
| PINNOptimizer=L-BFGS2025.02 | 7.49 | |
| FLS-PINNOptimizer=L-BFGS2025.02 | 7.91 | |
| FUNCATTNArchitecture Category=Attention2026.05 | 8 | |
| LNOArchitecture Category=Attention2026.05 | 8.45 | |
| TRANSOLVERArchitecture Category=Attention2026.05 | 9.44 | |
| DeepONet-FiLMInput Context=Dense Grid2026.06 | 11.21 | |
| ONOArchitecture Category=Attention2026.05 | 11.95 | |
| FACTFORMERArchitecture Category=Attention2026.05 | 12.14 | |
| DeepONet-FlatInput Context=Dense Grid2026.06 | 13.64 | |
| GNOTArchitecture Category=Attention2026.05 | 13.8 | |
| GALERKINArchitecture Category=Attention2026.05 | 14.01 | |
| LSMArchitecture Category=Frequency2026.05 | 15.35 | |
| WMTArchitecture Category=Frequency2026.05 | 15.41 | |
| FNOArchitecture Category=Frequency2026.05 | 15.56 | |
| GEO-FNOArchitecture Category=Frequency2026.05 | 15.56 | |
| OFORMERArchitecture Category=Attention2026.05 | 17.05 | |
| U-NOArchitecture Category=Frequency2026.05 | 17.13 | |
| HT-NETArchitecture Category=Attention2026.05 | 18.47 | |
| DeepONet-AttnInput Context=Dense Grid2026.06 | 20.87 | |
| RBF-POptimization Schedule=(2)2025.02 | 21.2 | |
| U-FNOArchitecture Category=Frequency2026.05 | 22.31 | |
| F-FNOArchitecture Category=Frequency2026.05 | 23.22 | |
| RBFOptimization Schedule=12025.02 | 25.6 | |
| RBFOptimization Schedule=(2)2025.02 | 27.8 | |
| RBF-POptimization Schedule=12025.02 | 29.8 | |
| SAFE-NETOptimization Schedule=(2)2025.02 | 37.1 | |
| RBA-PINNOptimization Schedule=12025.02 | 48.6 | |
| RBA-PINNOptimization Schedule=(2)2025.02 | 50.1 | |
| SAFE-NETOptimization Schedule=12025.02 | 52.6 | |
| RFFOptimization Schedule=12025.02 | 67.6 | |
| RFFOptimization Schedule=(2)2025.02 | 68.9 | |
| PINNOptimization Schedule=12025.02 | 74.9 | |
| PINNOptimization Schedule=(2)2025.02 | 76.7 | |
| FLS-PINNOptimization Schedule=12025.02 | 79.1 | |
| FLS-PINNOptimization Schedule=(2)2025.02 | 81.2 |