Learning PDE Solution Operators on Allen-Cahn 1D
0.05Mean L2 Relative ErrorSFO
Evaluation Results
| Method | Links | |
|---|---|---|
| SFOCategory=Ours2026.01 | 0.05 | |
| SVD-NOCategory=SVD Kernel2026.01 | 0.07 | |
| FNOCategory=Fourier2026.01 | 0.08 | |
| PINOCategory=PINN, Fourier2026.01 | 0.08 | |
| UNOCategory=Fourier2026.01 | 0.3 | |
| MPNNCategory=Graph (Local)2026.01 | 0.33 | |
| PIP2 NetArchitectures=seven-layer fully connected, Hidden units=100, Activation=tanh2025.12 | 1.481 | |
| PI-DeepONetArchitectures=seven-layer fully connected, Hidden units=100, Activation=tanh2025.12 | 2.541 | |
| POU-DeepONetArchitectures=seven-layer fully connected, Hidden units=100, Activation=tanh2025.12 | 7.751 | |
| DeepONetArchitectures=seven-layer fully connected, Hidden units=100, Activation=tanh2025.12 | 8.101 | |
| DeepONetCategory=DeepONet2026.01 | 16.53 | |
| UNetCategory=Neural surrogate2026.01 | 68.93 |