PDE Solving on Burgers (Relative L2 error)
0.0003Relative L2 ErrorRBF-P
Evaluation Results
| Method | Links | |
|---|---|---|
| RBF-POptimization Schedule=(2)2025.02 | 0.0003 | |
| RBF-POptimization Schedule=12025.02 | 0.0003 | |
| RBA-PINNOptimization Schedule=12025.02 | 0.0004 | |
| RBA-PINNOptimization Schedule=(2)2025.02 | 0.0004 | |
| SAFE-NETOptimization Schedule=(2)2025.02 | 0.001 | |
| SAFE-NETOptimization Schedule=12025.02 | 0.0027 | |
| RBFOptimization Schedule=12025.02 | 0.004 | |
| RBFOptimization Schedule=(2)2025.02 | 0.0041 | |
| SINOCategory=Data-driven methods2025.05 | 0.0097 | |
| PINNOptimization Schedule=12025.02 | 0.0101 | |
| FNOTraining time (s)=13468.72026.06 | 0.0111 | |
| PINNOptimization Schedule=(2)2025.02 | 0.0112 | |
| PCA–RaNN-BFGS (ensemble)Training time (s)=5.5, Ensemble size (K)=202026.06 | 0.0193 | |
| DeepONetTraining time (s)=32330.92026.06 | 0.0228 | |
| PCA–RaNN-EM (ensemble)Training time (s)=2.3, Ensemble size (K)=202026.06 | 0.0228 | |
| FLS-PINNOptimization Schedule=12025.02 | 0.0616 | |
| FLS-PINNOptimization Schedule=(2)2025.02 | 0.0678 | |
| PCA–NNTraining time (s)=2878.82026.06 | 0.0987 | |
| CNextCategory=Data-driven methods2025.05 | 0.3654 | |
| FFNOCategory=Data-driven methods2025.05 | 0.5949 | |
| FactFormerCategory=Data-driven methods2025.05 | 0.9459 | |
| PeRCNNCategory=Physics-aware methods2025.05 | 0.953 | |
| FNOCategory=Data-driven methods2025.05 | 1.0073 | |
| PINNOptimizer=L-BFGS2025.02 | 1.01 | |
| SAFE-NETOptimizer=L-BFGS2025.02 | 2.67 | |
| RBF-POptimizer=L-BFGS2025.02 | 3.47 | |
| RBFOptimizer=L-BFGS2025.02 | 3.95 | |
| RBA-PINNOptimizer=L-BFGS2025.02 | 4.17 | |
| GN+UAMdh=128, epochs=10K, seed count=52026.05 | 4.6 | |
| FAMOdh=128, epochs=10K, seed count=32026.05 | 4.8 | |
| FAMO+UAMdh=128, epochs=10K, seed count=42026.05 | 4.8 | |
| FLS-PINNOptimizer=L-BFGS2025.02 | 6.16 | |
| Vanilladh=128, epochs=10K, seed count=52026.05 | 8.4 |