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ResearchFormerly WizWand

PDE Solving on 1d Burgers' equation (test)

0.0079Relative ErrorCNN XD
-0.0264640.2054930.437450.669407Mar 29, 2021Jan 19, 2022Nov 11, 2022Sep 4, 2023Jun 26, 2024Apr 18, 2025Feb 9, 2026
Updated 8mo ago

Evaluation results

MethodLinks
CNN XDResolution (s)=5122021.030.0079
CNN XDResolution (s)=20482021.030.0099
CNN XDResolution (s)=81922021.030.0123
FNO-1dResolution (s)=81922021.030.0139
CNN XDResolution (s)=2562021.030.0141
FNO-1dResolution (s)=40962021.030.0142
CNN XDResolution (s)=40962021.030.0145
FNO-1dResolution (s)=20482021.030.0146
FNO-1dResolution (s)=2562021.030.0149
FNO-1d XDResolution (s)=2562021.030.0153
CNN XDResolution (s)=10242021.030.0154
FNO-1d XDResolution (s)=5122021.030.0154
FNO-1d XDResolution (s)=10242021.030.0154
FNO-1d XDResolution (s)=81922021.030.0155
FNO-1dResolution (s)=5122021.030.0158
FNO-1dResolution (s)=10242021.030.016
FNO-1d XDResolution (s)=40962021.030.016
FNO-1d XDResolution (s)=20482021.030.0167
DeepONetTest transformations=none2026.020.017
FNO-1d (reproduced)Resolution (s)=2562021.030.0181
FNO-1d (reproduced)Resolution (s)=40962021.030.0183
FNO-1d (reproduced)Resolution (s)=81922021.030.0183
FNO-1d (reproduced)Resolution (s)=20482021.030.0184
FNO-1d (reproduced)Resolution (s)=10242021.030.0188
LNOResolution (s)=81922021.030.0189
FNO-1d (reproduced)Resolution (s)=5122021.030.0191
LNOResolution (s)=40962021.030.02
LNOResolution (s)=2562021.030.0212
LNOResolution (s)=10242021.030.0217
LNOResolution (s)=20482021.030.0219
LNOResolution (s)=5122021.030.0221
MGNOResolution (s)=2562021.030.0243
MGNOResolution (s)=5122021.030.0355
MGNOResolution (s)=20482021.030.036
MGNOResolution (s)=40962021.030.0364
MGNOResolution (s)=81922021.030.0364
AROMA2024.060.0365
MGNOResolution (s)=10242021.030.0374
PCANNResolution (s)=20482021.030.0383
PCANNResolution (s)=10242021.030.0391
PCANNResolution (s)=40962021.030.0392
PCANNResolution (s)=81922021.030.0393
PCANNResolution (s)=5122021.030.0395
PCANNResolution (s)=2562021.030.0398
OFormer2024.060.0492
FNO2024.060.05
CNNResolution (s)=2562021.030.0518
GNOResolution (s)=2562021.030.0555
GNOResolution (s)=5122021.030.0594
CORAL2024.060.062
GNOResolution (s)=10242021.030.0651
GNOResolution (s)=20482021.030.0663
GNOResolution (s)=40962021.030.0666
GNOResolution (s)=81922021.030.0699
ResNet2024.060.085
FCNResolution (s)=2562021.030.0958
CNNResolution (s)=5122021.030.122
GNOT2024.060.128
FCNResolution (s)=5122021.030.1407
DeepONet + TIEDTest transformations=SL(2, R) ⋉ (R^2, +), Energy=Distance to training domain2026.020.178
CNNResolution (s)=10242021.030.183
DeepONet + LieLACTest transformations=SL(2, R) ⋉ (R^2, +), Energy=Distance to training domain2026.020.187
FCNResolution (s)=10242021.030.1877
DeepONet + FoCalTest transformations=SL(2, R) ⋉ (R^2, +), Energy=Distance to training domain2026.020.202
CNNResolution (s)=20482021.030.228
FCNResolution (s)=20482021.030.2313
CNNResolution (s)=40962021.030.273
FCNResolution (s)=40962021.030.2855
CNNResolution (s)=81922021.030.297
FCNResolution (s)=81922021.030.3238
GCNResolution (s)=2562021.030.3999
GCNResolution (s)=5122021.030.4138
GCNResolution (s)=20482021.030.4157
GCNResolution (s)=10242021.030.4176
GCNResolution (s)=40962021.030.4191
GCNResolution (s)=81922021.030.4198
NNResolution (s)=81922021.030.4452
NNResolution (s)=5122021.030.4561
DINO2024.060.457
NNResolution (s)=20482021.030.4645
NNResolution (s)=2562021.030.4714
NNResolution (s)=40962021.030.4779
NNResolution (s)=10242021.030.4803
DeepONet + Kinetic LangevinTest transformations=SL(2, R) ⋉ (R^2, +), Energy=Distance to training domain2026.020.739
DeepONetTest transformations=SL(2, R) ⋉ (R^2, +)2026.020.867