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ResearchFormerly WizWand

PDE Solving on Helmholtz equation

0.006Relative L2 ErrorAEH-PINN
-3.9469522.73552849.41800576.100482Sep 27, 2024Jan 9, 2025Apr 23, 2025Aug 6, 2025Nov 18, 2025Mar 2, 2026Jun 15, 2026
Updated 4mo ago

Evaluation results

MethodLinks
AEH-PINN2025.120.006
DBAW-PIKANOrder=4, Grid Size=20, Architecture=[2,20,20,20,1], Parameters=22,360, Optimizer=Adam, Iterations=50,0002025.120.0417
AAPINN2025.120.0454
SelectNet2025.120.0497
PIKANOrder=4, Grid Size=20, Architecture=[2,20,20,20,1], Parameters=22,360, Optimizer=Adam, Iterations=50,0002025.120.132
SAPINN2025.120.166
DCGD+LRAloss balancing=LRA2024.090.23
DCGD2024.090.29
RAD2025.120.306
DCGD+NTKloss balancing=NTK2024.090.57
LRA2024.090.66
Vanilla DNN2026.061
DBAW-PINNOrder=Not applicable, Grid Size=Not applicable, Architecture=[2,64,64,64,64,64,64,1], Parameters=21,057, Optimizer=Adam, Iterations=50,0002025.121.08
PCGrad2024.091.09
CL-Reg2025.121.47
PINNOrder=Not applicable, Grid Size=Not applicable, Architecture=[2,64,64,64,64,64,64,1], Parameters=21,057, Optimizer=Adam, Iterations=50,0002025.121.82
MultiAdam2024.092.11
MFFgamma_x=50, gamma_y=502026.062.7
NTK2024.093.58
MscaleDNNalpha_scale={1, 2, 4, 8, 16, 32, 64}2026.064.06
RepNet2026.064.18
SIRENw0=502026.064.25
Adam2024.096.09
CAGrad2024.097.35
DCGD2024.097.74
LRA2024.098.31
DCGD+LRAloss balancing=LRA2024.0910.45
PCGrad2024.0925.32
DCGD+NTKloss balancing=NTK2024.0935.25
NTK2024.0940.37
CAGrad2024.0958.54
Adam2024.0961.09
Aligned-MTL2024.0965.7
MGDA2024.0975.9
MultiAdam2024.0978.09
Aligned-MTL2024.0991.38
MGDA2024.0998.83