PDE Solving on Darcy
0.0042Relative L2 ErrorFUNCATTN
Evaluation Results
| Method | Links | ||
|---|---|---|---|
| FUNCATTNArchitecture Category=Attention2026.05 | 0.0042 | — | |
| TRANSOLVERArchitecture Category=Attention2026.05 | 0.0057 | — | |
| LNOArchitecture Category=Attention2026.05 | 0.006 | — | |
| LSMArchitecture Category=Frequency2026.05 | 0.0065 | — | |
| ONOArchitecture Category=Attention2026.05 | 0.0076 | — | |
| F-FNOArchitecture Category=Frequency2026.05 | 0.0077 | — | |
| HT-NETArchitecture Category=Attention2026.05 | 0.0079 | — | |
| WMTArchitecture Category=Frequency2026.05 | 0.0082 | — | |
| GALERKINArchitecture Category=Attention2026.05 | 0.0084 | — | |
| GNOTArchitecture Category=Attention2026.05 | 0.0105 | — | |
| FNOArchitecture Category=Frequency2026.05 | 0.0108 | — | |
| GEO-FNOArchitecture Category=Frequency2026.05 | 0.0108 | — | |
| FACTFORMERArchitecture Category=Attention2026.05 | 0.0109 | — | |
| U-NOArchitecture Category=Frequency2026.05 | 0.0113 | — | |
| OFORMERArchitecture Category=Attention2026.05 | 0.0124 | — | |
| U-FNOArchitecture Category=Frequency2026.05 | 0.0183 | — | |
| FNOTraining time (s)=1258.62026.06 | 2.43 | — | |
| PCA–RaNN-BFGS (ensemble)Training time (s)=14.6, Ensemble size (K)=202026.06 | 2.94 | — | |
| PCA–RaNN-EM (ensemble)Training time (s)=10.6, Ensemble size (K)=202026.06 | 2.95 | — | |
| DeepONetTraining time (s)=1740.12026.06 | 3.01 | — | |
| PCA–NNTraining time (s)=1546.32026.06 | 3.35 | — | |
| QuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 128^22026.05 | 3.78 | 5.9 | |
| BlendQuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 128^22026.05 | 3.98 | 0.9 | |
| LayerNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 128^22026.05 | 4.01 | — | |
| QuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 256^22026.05 | 4.07 | 23.2 | |
| QuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 421^22026.05 | 4.16 | 28 | |
| BlendQuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 256^22026.05 | 5.24 | 1 | |
| LayerNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 256^22026.05 | 5.3 | — | |
| BlendQuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 421^22026.05 | 5.71 | 1 | |
| LayerNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 421^22026.05 | 5.77 | — | |
| QuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 128^22026.05 | 6.19 | 37.4 | |
| QuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 256^22026.05 | 6.66 | 41.1 | |
| QuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 421^22026.05 | 6.81 | 42.4 | |
| QuadNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 128^22026.05 | 7.82 | 11.9 | |
| QuadNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 256^22026.05 | 7.96 | 15.2 | |
| QuadNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 128^22026.05 | 8.4 | 26.3 | |
| QuadNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 256^22026.05 | 8.67 | 29.6 | |
| BlendQuadNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 128^22026.05 | 8.83 | 0.5 | |
| LayerNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 128^22026.05 | 8.87 | — | |
| BlendQuadNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 256^22026.05 | 9.32 | 0.7 | |
| LayerNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 256^22026.05 | 9.39 | — | |
| BlendQuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 128^22026.05 | 9.76 | 1.4 | |
| LayerNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 128^22026.05 | 9.9 | — | |
| BlendQuadNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 128^22026.05 | 11.13 | 2.4 | |
| BlendQuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 256^22026.05 | 11.14 | 1.5 | |
| LayerNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 256^22026.05 | 11.31 | — | |
| LayerNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 128^22026.05 | 11.4 | — | |
| BlendQuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 421^22026.05 | 11.65 | 1.5 | |
| LayerNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 421^22026.05 | 11.83 | — | |
| BlendQuadNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 256^22026.05 | 11.96 | 2.9 | |
| LayerNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 256^22026.05 | 12.33 | — |