PDE Rollout on Allen-Cahn 3D (Accuracy and Timing)
4.1246Relative L2 Error (t=50)HAMNO
Evaluation Results
| Method | Links | ||||
|---|---|---|---|---|---|
| HAMNONtrain=100, lambda=0.25, Tag=Hybrid2026.06 | 4.1246 | 4.1924 | 133.88 | 2.0419 | |
| DeepONetNtrain=100, lambda=0.25, Tag=Hybrid2026.06 | 4.9329 | 5.3365 | 117.05 | 1.7608 | |
| HAMNONtrain=50, lambda=1.0, Tag=Pure Phys.2026.06 | 5.4844 | 5.9834 | 101.72 | 2.0976 | |
| HAMNONtrain=100, lambda=1.0, Tag=Pure Phys.2026.06 | 5.4844 | 5.9834 | 78.4 | 2.0248 | |
| F-FNONtrain=100, lambda=0.25, Tag=Hybrid2026.06 | 5.6584 | 6.4458 | 135.82 | 3.0271 | |
| F-FNONtrain=50, lambda=1.0, Tag=Pure Phys.2026.06 | 6.3913 | 7.6734 | 69.63 | 1.7126 | |
| F-FNONtrain=100, lambda=1.0, Tag=Pure Phys.2026.06 | 6.3913 | 7.6734 | 78.94 | 1.651 | |
| F-FNONtrain=50, lambda=0.25, Tag=Hybrid2026.06 | 6.9923 | 8.388 | 85.43 | 1.6574 | |
| DeepONetNtrain=50, lambda=1.0, Tag=Pure Phys.2026.06 | 7.3443 | 7.9774 | 84.82 | 2.3704 | |
| DeepONetNtrain=100, lambda=1.0, Tag=Pure Phys.2026.06 | 7.3443 | 7.9774 | 90.32 | 2.0546 | |
| DeepONetNtrain=50, lambda=0.25, Tag=Hybrid2026.06 | 7.7465 | 9.2737 | 75.54 | 1.7031 | |
| HAMNONtrain=50, lambda=0.25, Tag=Hybrid2026.06 | 8.8918 | 9.1278 | 79.36 | 2.0526 | |
| HAMNONtrain=100, lambda=0, Tag=Pure Data2026.06 | 9.066 | 13.176 | 103.39 | 2.0185 | |
| DeepONetNtrain=100, lambda=0, Tag=Pure Data2026.06 | 9.6789 | 13.943 | 96.43 | 1.1376 | |
| F-FNONtrain=100, lambda=0, Tag=Pure Data2026.06 | 9.8792 | 15.678 | 97.29 | 1.744 | |
| DeepONetNtrain=50, lambda=0, Tag=Pure Data2026.06 | 12.377 | 16.647 | 52.16 | 1.1335 | |
| HAMNONtrain=50, lambda=0, Tag=Pure Data2026.06 | 13.604 | 24.392 | 90.48 | 2.4845 | |
| F-FNONtrain=50, lambda=0, Tag=Pure Data2026.06 | 15.221 | 27.891 | 52.86 | 1.6857 | |
| FNONtrain=100, lambda=0.25, Tag=Hybrid2026.06 | 22.062 | 23.194 | 45.47 | 0.5179 | |
| FNONtrain=100, lambda=0, Tag=Pure Data2026.06 | 22.467 | 29.233 | 33.34 | 0.5448 | |
| FNONtrain=50, lambda=0.25, Tag=Hybrid2026.06 | 24.041 | 29.039 | 34.51 | 0.6532 | |
| FNONtrain=50, lambda=1.0, Tag=Pure Phys.2026.06 | 24.293 | 27.478 | 27.85 | 0.4426 | |
| FNONtrain=100, lambda=1.0, Tag=Pure Phys.2026.06 | 24.293 | 27.478 | 26.9 | 0.4521 | |
| FNONtrain=50, lambda=0, Tag=Pure Data2026.06 | 31.537 | 46.435 | 20.06 | 0.4304 |