PDE Solving on Klein-Gordon equation
0.0009Relative L2 ErrorDBAW-PIKAN
Evaluation Results
| Method | Links | |
|---|---|---|
| DBAW-PIKANOrder=4, Grid Size=20, Architecture=[2,20,20,1], Parameters=22,360, Optimizer=Adam, Iterations=50,0002025.12 | 0.0009 | |
| DCGD+LRAloss balancing=LRA2024.09 | 0.005 | |
| DCGD+NTKloss balancing=NTK2024.09 | 0.0055 | |
| LRA2024.09 | 0.0069 | |
| DCGD2024.09 | 0.0069 | |
| PIKANOrder=4, Grid Size=20, Architecture=[2,20,20,20,1], Parameters=22,360, Optimizer=Adam, Iterations=50,0002025.12 | 0.0076 | |
| DBAW-PINNOrder=N/A, Grid Size=N/A, Architecture=[2,64,64,64,64,64,64,1], Parameters=21,057, Optimizer=Adam, Iterations=50,0002025.12 | 0.008 | |
| HARMONIC2026.05 | 0.0143 | |
| Chebyshev Center-Based Direction Selection2026.05 | 0.0218 | |
| NTK2024.09 | 0.0223 | |
| MultiAdam2024.09 | 0.0228 | |
| Adam2026.05 | 0.0267 | |
| PCGrad2024.09 | 0.0286 | |
| PINNOrder=N/A, Grid Size=N/A, Architecture=[2,64,64,64,64,64,64,1], Parameters=21,057, Optimizer=Adam, Iterations=50,0002025.12 | 0.0305 | |
| ConFIG2026.05 | 0.0339 | |
| ReLoBRaLo2026.05 | 0.0389 | |
| PCGrad2026.05 | 0.0466 | |
| Adam2024.09 | 0.0792 | |
| IMTL-G2026.05 | 0.0871 | |
| MGDA2026.05 | 0.1494 | |
| CAGrad2024.09 | 0.185 | |
| Aligned-MTL2024.09 | 0.5571 | |
| MGDA2024.09 | 0.669 | |
| FS-PIELM-GOptimal frequency range [µmin, µmax]=[10, 100]2026.07 | 1.01 | |
| LRA2026.05 | 1.0174 | |
| Vanilladh=128, epochs=20K, seeds=52026.05 | 1.5 | |
| UAMdh=128, epochs=20K, seeds=52026.05 | 1.5 | |
| SIREN-PIELMOptimal frequency range [µmin, µmax]=[20, 100]2026.07 | 1.78 | |
| Tanh-PIELMOptimal frequency range [µmin, µmax]=[5, 50]2026.07 | 4.8 | |
| FS-PIELM-LOptimal frequency range [µmin, µmax]=[10, 100]2026.07 | 4.95 | |
| Uncertaintydh=128, epochs=20K, seeds=52026.05 | 5.98 | |
| SelfAdaptdh=128, epochs=20K, seeds=52026.05 | 6.7 | |
| FAMO+UAMdh=128, epochs=20K, seeds=52026.05 | 7.93 | |
| FAMOdh=128, epochs=20K, seeds=52026.05 | 8.7 | |
| Causaldh=128, epochs=20K, seeds=52026.05 | 9.19 | |
| GFF-PIELMOptimal frequency range [µmin, µmax]=[25, 100]2026.07 | 9.53 |