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ResearchFormerly WizWand

PDE Solving on Darcy

0.0042Relative L2 ErrorFUNCATTN
-0.4888322.8391346.16719.495066May 8, 2026May 16, 2026May 25, 2026Jun 2, 2026Jun 11, 2026Jun 19, 2026Jun 28, 2026
Updated 4mo ago

Evaluation results

MethodLinks
FUNCATTNArchitecture Category=Attention2026.050.0042—
TRANSOLVERArchitecture Category=Attention2026.050.0057—
LNOArchitecture Category=Attention2026.050.006—
LSMArchitecture Category=Frequency2026.050.0065—
ONOArchitecture Category=Attention2026.050.0076—
F-FNOArchitecture Category=Frequency2026.050.0077—
HT-NETArchitecture Category=Attention2026.050.0079—
WMTArchitecture Category=Frequency2026.050.0082—
GALERKINArchitecture Category=Attention2026.050.0084—
GNOTArchitecture Category=Attention2026.050.0105—
FNOArchitecture Category=Frequency2026.050.0108—
GEO-FNOArchitecture Category=Frequency2026.050.0108—
FACTFORMERArchitecture Category=Attention2026.050.0109—
U-NOArchitecture Category=Frequency2026.050.0113—
OFORMERArchitecture Category=Attention2026.050.0124—
U-FNOArchitecture Category=Frequency2026.050.0183—
FNOTraining time (s)=1258.62026.062.43—
PCA–RaNN-BFGS (ensemble)Training time (s)=14.6, Ensemble size (K)=202026.062.94—
PCA–RaNN-EM (ensemble)Training time (s)=10.6, Ensemble size (K)=202026.062.95—
DeepONetTraining time (s)=1740.12026.063.01—
PCA–NNTraining time (s)=1546.32026.063.35—
QuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 128^22026.053.785.9
BlendQuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 128^22026.053.980.9
LayerNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 128^22026.054.01—
QuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 256^22026.054.0723.2
QuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 421^22026.054.1628
BlendQuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 256^22026.055.241
LayerNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 256^22026.055.3—
BlendQuadNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 421^22026.055.711
LayerNormProtocol=Darcy Benchmark, Arch=FNO, Train -> Test=64^2 -> 421^22026.055.77—
QuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 128^22026.056.1937.4
QuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 256^22026.056.6641.1
QuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 421^22026.056.8142.4
QuadNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 128^22026.057.8211.9
QuadNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 256^22026.057.9615.2
QuadNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 128^22026.058.426.3
QuadNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 256^22026.058.6729.6
BlendQuadNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 128^22026.058.830.5
LayerNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 128^22026.058.87—
BlendQuadNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 256^22026.059.320.7
LayerNormProtocol=Darcy Benchmark, Arch=Gal, Train -> Test=64^2 -> 256^22026.059.39—
BlendQuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 128^22026.059.761.4
LayerNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 128^22026.059.9—
BlendQuadNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 128^22026.0511.132.4
BlendQuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 256^22026.0511.141.5
LayerNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 256^22026.0511.31—
LayerNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 128^22026.0511.4—
BlendQuadNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 421^22026.0511.651.5
LayerNormProtocol=Extreme, Arch=FNO, Train -> Test=32^2 -> 421^22026.0511.83—
BlendQuadNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 256^22026.0511.962.9
LayerNormProtocol=Extreme, Arch=Gal, Train -> Test=32^2 -> 256^22026.0512.33—