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ResearchFormerly WizWand

PDE Solving on 1D Burgers

0RelL2 ErrorGC-PINN
-0.0164960.0949360.2063670.317799Aug 28, 2025Oct 16, 2025Dec 5, 2025Jan 24, 2026Mar 14, 2026May 3, 2026Jun 22, 2026
Updated 4mo ago

Evaluation results

MethodLinks
GC-PINNMapping=Radial Mapping2026.02000.0001
GC-PINNMapping=Local Stretching2026.02000.0001
gPINN2026.02000
PINN+RAR2026.02000.0001
GC-PINNMapping=Torus Mapping2026.02000
SA-PINN2026.02000.0001
FF-PINN2026.020.000100.0001
PINN2026.020.000100.0004
FNOTime (s)=6342026.050.0034——
DANOPInput Context=Uniform Sparse2026.060.0047——
Mamba-NOTime (s)=120,8122026.050.005——
DNOPInput Context=Uniform Sparse2026.060.0058——
MSAT (physics)Time (s)=1882026.050.0118——
MSAT (no physics)Time (s)=342026.050.0156——
Gemini-2.5-flashRefinement=review-2, Perspective=Best-of-N, Quantity=u(x, t)2025.080.0182——
Deepseek-R1Refinement=review-2, Perspective=Best-of-N, Quantity=u(x, t)2025.080.0185——
GPT-4.1-miniRefinement=review-2, Perspective=Best-of-N, Quantity=u(x, t)2025.080.0198——
Vanilla PINNTime (s)=6312026.050.0203——
FNOParam=0.001, Step=25, MCL Integration=Model + MCL2026.020.022400.0269
FNOParam=0.001, Step=10, MCL Integration=Model + MCL2026.020.02640.00010.0346
RAR2026.050.0275——
PINN-LRATime (s)=2,5272026.050.0275——
FNOParam=0.001, Step=25, MCL Integration=Model only2026.020.03260.00010.0396
FNOParam=0.001, Step=1, MCL Integration=Model + MCL2026.020.03570.00030.0499
FNOParam=0.001, Step=10, MCL Integration=Model only2026.020.03790.00020.0509
GNOTTime (s)=6,5732026.050.0403——
FNOParam=0.001, Step=1, MCL Integration=Model only2026.020.04660.00060.0689
DeepONetTime (s)=2,5202026.050.066——
GINOParam=0.001, Step=25, MCL Integration=Model + MCL2026.020.08140.00060.1011
GINOParam=0.001, Step=25, MCL Integration=Model only2026.020.08270.00060.1023
DeepONet-FiLMInput Context=Dense Grid2026.060.1025——
GINOParam=0.001, Step=10, MCL Integration=Model + MCL2026.020.10790.00140.1387
GINOParam=0.001, Step=10, MCL Integration=Model only2026.020.10930.00150.1399
GINOParam=0.001, Step=1, MCL Integration=Model + MCL2026.020.14660.00390.1923
GINOParam=0.001, Step=1, MCL Integration=Model only2026.020.14750.0040.1927
DeepONet-FlatInput Context=Dense Grid2026.060.1959——
U-NOParam=0.001, Step=25, MCL Integration=Model + MCL2026.020.33110.00840.3343
DeepONet-AttnInput Context=Dense Grid2026.060.3339——
U-NOParam=0.001, Step=1, MCL Integration=Model + MCL2026.020.35070.03950.3673
U-NOParam=0.001, Step=25, MCL Integration=Model only2026.020.37310.01430.3765
U-NOParam=0.001, Step=10, MCL Integration=Model + MCL2026.020.39860.02040.4048
U-NOParam=0.001, Step=1, MCL Integration=Model only2026.020.39880.04290.4153
U-NOParam=0.001, Step=10, MCL Integration=Model only2026.020.41270.02530.4175