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ResearchFormerly WizWand

PDE Solving on Navier-Stokes (Relative L2 Loss)

2.03Relative L2 LossFNO
-1.136820.239141.61562.9909Feb 11, 2025May 5, 2025Jul 28, 2025Oct 20, 2025Jan 11, 2026Apr 5, 2026Jun 28, 2026
Updated 4mo ago

Evaluation results

MethodLinks
FNOTraining time (s)=1150.3, Prediction sequence=t = 11–20, Final predicted time t=202026.062.03
DeepONetTraining time (s)=2000.7, Prediction sequence=t = 11–20, Final predicted time t=202026.062.23
PCA–RaNN-BFGS (ensemble)Training time (s)=88.7, Ensemble size (K)=20, Prediction sequence=t = 11–20, Final predicted time t=202026.062.47
RBFOptimizer=L-BFGS2025.022.56
PCA–RaNN-EM (ensemble)Training time (s)=19.4, Ensemble size (K)=20, Prediction sequence=t = 11–20, Final predicted time t=202026.062.59
RBF-POptimizer=L-BFGS2025.022.98
DNOPInput Context=Uniform Sparse2026.063.23
DANOPInput Context=Uniform Sparse2026.063.26
PCA–NNTraining time (s)=1468.2, Prediction sequence=t = 11–20, Final predicted time t=202026.063.34
RBA-PINNOptimizer=L-BFGS2025.024.86
SAFE-NETOptimizer=L-BFGS2025.025.26
RFFOptimizer=L-BFGS2025.026.76
PINNOptimizer=L-BFGS2025.027.49
FLS-PINNOptimizer=L-BFGS2025.027.91
FUNCATTNArchitecture Category=Attention2026.058
LNOArchitecture Category=Attention2026.058.45
TRANSOLVERArchitecture Category=Attention2026.059.44
DeepONet-FiLMInput Context=Dense Grid2026.0611.21
ONOArchitecture Category=Attention2026.0511.95
FACTFORMERArchitecture Category=Attention2026.0512.14
DeepONet-FlatInput Context=Dense Grid2026.0613.64
GNOTArchitecture Category=Attention2026.0513.8
GALERKINArchitecture Category=Attention2026.0514.01
LSMArchitecture Category=Frequency2026.0515.35
WMTArchitecture Category=Frequency2026.0515.41
FNOArchitecture Category=Frequency2026.0515.56
GEO-FNOArchitecture Category=Frequency2026.0515.56
OFORMERArchitecture Category=Attention2026.0517.05
U-NOArchitecture Category=Frequency2026.0517.13
HT-NETArchitecture Category=Attention2026.0518.47
DeepONet-AttnInput Context=Dense Grid2026.0620.87
RBF-POptimization Schedule=(2)2025.0221.2
U-FNOArchitecture Category=Frequency2026.0522.31
F-FNOArchitecture Category=Frequency2026.0523.22
RBFOptimization Schedule=12025.0225.6
RBFOptimization Schedule=(2)2025.0227.8
RBF-POptimization Schedule=12025.0229.8
SAFE-NETOptimization Schedule=(2)2025.0237.1
RBA-PINNOptimization Schedule=12025.0248.6
RBA-PINNOptimization Schedule=(2)2025.0250.1
SAFE-NETOptimization Schedule=12025.0252.6
RFFOptimization Schedule=12025.0267.6
RFFOptimization Schedule=(2)2025.0268.9
PINNOptimization Schedule=12025.0274.9
PINNOptimization Schedule=(2)2025.0276.7
FLS-PINNOptimization Schedule=12025.0279.1
FLS-PINNOptimization Schedule=(2)2025.0281.2