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ResearchFormerly WizWand

PDE Solving on Klein-Gordon equation

0.0009Relative L2 ErrorDBAW-PIKAN
-0.3802762.1925844.7654447.338304Sep 27, 2024Jan 12, 2025Apr 29, 2025Aug 14, 2025Nov 29, 2025Mar 16, 2026Jul 2, 2026
Updated 4mo ago

Evaluation results

MethodLinks
DBAW-PIKANOrder=4, Grid Size=20, Architecture=[2,20,20,1], Parameters=22,360, Optimizer=Adam, Iterations=50,0002025.120.0009
DCGD+LRAloss balancing=LRA2024.090.005
DCGD+NTKloss balancing=NTK2024.090.0055
LRA2024.090.0069
DCGD2024.090.0069
PIKANOrder=4, Grid Size=20, Architecture=[2,20,20,20,1], Parameters=22,360, Optimizer=Adam, Iterations=50,0002025.120.0076
DBAW-PINNOrder=N/A, Grid Size=N/A, Architecture=[2,64,64,64,64,64,64,1], Parameters=21,057, Optimizer=Adam, Iterations=50,0002025.120.008
HARMONIC2026.050.0143
Chebyshev Center-Based Direction Selection2026.050.0218
NTK2024.090.0223
MultiAdam2024.090.0228
Adam2026.050.0267
PCGrad2024.090.0286
PINNOrder=N/A, Grid Size=N/A, Architecture=[2,64,64,64,64,64,64,1], Parameters=21,057, Optimizer=Adam, Iterations=50,0002025.120.0305
ConFIG2026.050.0339
ReLoBRaLo2026.050.0389
PCGrad2026.050.0466
Adam2024.090.0792
IMTL-G2026.050.0871
MGDA2026.050.1494
CAGrad2024.090.185
Aligned-MTL2024.090.5571
MGDA2024.090.669
FS-PIELM-GOptimal frequency range [µmin, µmax]=[10, 100]2026.071.01
LRA2026.051.0174
Vanilladh=128, epochs=20K, seeds=52026.051.5
UAMdh=128, epochs=20K, seeds=52026.051.5
SIREN-PIELMOptimal frequency range [µmin, µmax]=[20, 100]2026.071.78
Tanh-PIELMOptimal frequency range [µmin, µmax]=[5, 50]2026.074.8
FS-PIELM-LOptimal frequency range [µmin, µmax]=[10, 100]2026.074.95
Uncertaintydh=128, epochs=20K, seeds=52026.055.98
SelfAdaptdh=128, epochs=20K, seeds=52026.056.7
FAMO+UAMdh=128, epochs=20K, seeds=52026.057.93
FAMOdh=128, epochs=20K, seeds=52026.058.7
Causaldh=128, epochs=20K, seeds=52026.059.19
GFF-PIELMOptimal frequency range [µmin, µmax]=[25, 100]2026.079.53