Neural Operator Learning on 2D Navier–Stokes ν = 10−5 (test)
7.05Relative L2 LossABLE-HPM
Evaluation Results
| Method | Links | |
|---|---|---|
| ABLE-HPMTraining velocity(s/epoch)=194.19 ± 0.21*, Flops(/step)=49104.81M, Best learning rate=1e-3, Configuration=fixed -> adaptive Laplacian basis2026.05 | 7.05 | |
| HPMTraining velocity(s/epoch)=109.31 ± 0.06, Flops(/step)=46806.34M, Best learning rate=1e-32026.05 | 7.67 | |
| ABLE 2DTraining velocity(s/epoch)=6.08 ± 0.19, Flops(/step)=60.49M, Best learning rate=3e-32026.05 | 9.85 | |
| ABLE-SAOTTraining velocity(s/epoch)=21.78 ± 1.18, Flops(/step)=785.91M, Best learning rate=1e-3, Configuration=FNO -> ABLE2026.05 | 10.05 | |
| GF-NOTraining velocity(s/epoch)=6.93 ± 0.23, Flops(/step)=18.55M, Best learning rate=2.2e-2(1000) †2026.05 | 12.29 | |
| FNO2DTraining velocity(s/epoch)=4.74 ± 0.19, Flops(/step)=32.47M, Best learning rate=3e-32026.05 | 12.37 | |
| FreqMOETraining velocity(s/epoch)=9.13 ± 0.12, Flops(/step)=18.55M, Best learning rate=3e-3(2-stage) †2026.05 | 13.99 | |
| LSMTraining velocity(s/epoch)=10.41 ± 0.31, Flops(/step)=744.58M, Best learning rate=1e-32026.05 | 16.35 | |
| SAOTTraining velocity(s/epoch)=30.41 ± 0.19, Flops(/step)=477.63M, Best learning rate=1e-32026.05 | 24.8 | |
| WNOTraining velocity(s/epoch)=11.54 ± 0.13, Flops(/step)=26.51M, Best learning rate=1e-4(800) †2026.05 | 33.71 |