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ResearchFormerly WizWand

PDE Solving on Burgers (Relative L2 error)

0.0003Relative L2 ErrorRBF-P
-0.3356991.9322234.2001456.468066Feb 11, 2025May 5, 2025Jul 28, 2025Oct 20, 2025Jan 11, 2026Apr 5, 2026Jun 28, 2026
Updated 4mo ago

Evaluation results

MethodLinks
RBF-POptimization Schedule=(2)2025.020.0003
RBF-POptimization Schedule=12025.020.0003
RBA-PINNOptimization Schedule=12025.020.0004
RBA-PINNOptimization Schedule=(2)2025.020.0004
SAFE-NETOptimization Schedule=(2)2025.020.001
SAFE-NETOptimization Schedule=12025.020.0027
RBFOptimization Schedule=12025.020.004
RBFOptimization Schedule=(2)2025.020.0041
SINOCategory=Data-driven methods2025.050.0097
PINNOptimization Schedule=12025.020.0101
FNOTraining time (s)=13468.72026.060.0111
PINNOptimization Schedule=(2)2025.020.0112
PCA–RaNN-BFGS (ensemble)Training time (s)=5.5, Ensemble size (K)=202026.060.0193
DeepONetTraining time (s)=32330.92026.060.0228
PCA–RaNN-EM (ensemble)Training time (s)=2.3, Ensemble size (K)=202026.060.0228
FLS-PINNOptimization Schedule=12025.020.0616
FLS-PINNOptimization Schedule=(2)2025.020.0678
PCA–NNTraining time (s)=2878.82026.060.0987
CNextCategory=Data-driven methods2025.050.3654
FFNOCategory=Data-driven methods2025.050.5949
FactFormerCategory=Data-driven methods2025.050.9459
PeRCNNCategory=Physics-aware methods2025.050.953
FNOCategory=Data-driven methods2025.051.0073
PINNOptimizer=L-BFGS2025.021.01
SAFE-NETOptimizer=L-BFGS2025.022.67
RBF-POptimizer=L-BFGS2025.023.47
RBFOptimizer=L-BFGS2025.023.95
RBA-PINNOptimizer=L-BFGS2025.024.17
GN+UAMdh=128, epochs=10K, seed count=52026.054.6
FAMOdh=128, epochs=10K, seed count=32026.054.8
FAMO+UAMdh=128, epochs=10K, seed count=42026.054.8
FLS-PINNOptimizer=L-BFGS2025.026.16
Vanilladh=128, epochs=10K, seed count=52026.058.4