PDE Solving on Helmholtz equation
0.006Relative L2 ErrorAEH-PINN
Evaluation Results
| Method | Links | |
|---|---|---|
| AEH-PINN2025.12 | 0.006 | |
| DBAW-PIKANOrder=4, Grid Size=20, Architecture=[2,20,20,20,1], Parameters=22,360, Optimizer=Adam, Iterations=50,0002025.12 | 0.0417 | |
| AAPINN2025.12 | 0.0454 | |
| SelectNet2025.12 | 0.0497 | |
| PIKANOrder=4, Grid Size=20, Architecture=[2,20,20,20,1], Parameters=22,360, Optimizer=Adam, Iterations=50,0002025.12 | 0.132 | |
| SAPINN2025.12 | 0.166 | |
| DCGD+LRAloss balancing=LRA2024.09 | 0.23 | |
| DCGD2024.09 | 0.29 | |
| RAD2025.12 | 0.306 | |
| DCGD+NTKloss balancing=NTK2024.09 | 0.57 | |
| LRA2024.09 | 0.66 | |
| Vanilla DNN2026.06 | 1 | |
| DBAW-PINNOrder=Not applicable, Grid Size=Not applicable, Architecture=[2,64,64,64,64,64,64,1], Parameters=21,057, Optimizer=Adam, Iterations=50,0002025.12 | 1.08 | |
| PCGrad2024.09 | 1.09 | |
| CL-Reg2025.12 | 1.47 | |
| PINNOrder=Not applicable, Grid Size=Not applicable, Architecture=[2,64,64,64,64,64,64,1], Parameters=21,057, Optimizer=Adam, Iterations=50,0002025.12 | 1.82 | |
| MultiAdam2024.09 | 2.11 | |
| MFFgamma_x=50, gamma_y=502026.06 | 2.7 | |
| NTK2024.09 | 3.58 | |
| MscaleDNNalpha_scale={1, 2, 4, 8, 16, 32, 64}2026.06 | 4.06 | |
| RepNet2026.06 | 4.18 | |
| SIRENw0=502026.06 | 4.25 | |
| Adam2024.09 | 6.09 | |
| CAGrad2024.09 | 7.35 | |
| DCGD2024.09 | 7.74 | |
| LRA2024.09 | 8.31 | |
| DCGD+LRAloss balancing=LRA2024.09 | 10.45 | |
| PCGrad2024.09 | 25.32 | |
| DCGD+NTKloss balancing=NTK2024.09 | 35.25 | |
| NTK2024.09 | 40.37 | |
| CAGrad2024.09 | 58.54 | |
| Adam2024.09 | 61.09 | |
| Aligned-MTL2024.09 | 65.7 | |
| MGDA2024.09 | 75.9 | |
| MultiAdam2024.09 | 78.09 | |
| Aligned-MTL2024.09 | 91.38 | |
| MGDA2024.09 | 98.83 |