Fig 1.
The Fourier layer: The internal structure of the Fourier layer.
Fig 2.
Process of pruning: First, pretrained above network framework for findingλ values.
Use data in source domain pre-train the network to get the optimal λ value. Then use the pruning method we proposed to prune the network, cut off the λ parameters that do not contribute much and select the λ parameters that need to be retained. This sparse structure can make our network faster and more compact without losing accuracy. The network below the picture is the pruned network, and we will perform subsequent transfer tasks on this network.
Fig 3.
Target model (TL-λFNO): Transfer the parameters trained on the source model to the target model.
Except for the dimensionality reduction operator (including two fully connected layers inside) and the last fully connected layer (red shaded part), other layer parameters are frozen. The network layers represented by the red shaded part are fine-tuned using the labeled data in target domain
and hybrid loss function
.
Fig 4.
Transfer learning for Darcy Flow: Geometry differences between source and target domains in TL1-TL4.
Table 1.
Relative L2 error (%) on the test set for the source domain (TL1 – TL3).
Table 2.
Relative L2 error (%) on the test set for the target domain (TL1).
Table 3.
Relative L2 error (%) on the test set for the target domain (TL2).
Table 4.
Relative L2 error (%) on the test set for the target domain (TL3).
Table 5.
Relative L2 error (%) on the test set for the source domain (TL4).
Table 6.
Relative L2 error (%) on the test set for the target domain (TL4).
Table 7.
Training cost in seconds (s) for the source domain (TL1-3 and TL4).
Table 8.
Training cost in seconds (s) for the target domain (TL1-TL4).
Fig 5.
Transfer learning for Elasticity model: Geometry differences between source and target domains in TL5-TL6.
Table 9.
Relative L2 error (%) on the test set for the source domain (TL5 – TL6).
Table 10.
Training cost in seconds (s) for the source domain (TL5-6).
Table 11.
Relative L2 error (%) on the test set for the target domain (TL5).
Table 12.
Relative L2 error (%) on the test set for the target domain (TL6).
Table 13.
Training cost in seconds (s) for the target domain (TL5 and TL6).
Table 14.
Relative L2 error (%) on the test set for the source domain (TL7).
Table 15.
Relative L2 error (%) on the test set for the target domain (TL7).
Table 16.
Training cost in seconds (s) for the target domain (TL7).
Fig 6.
Plots of three representative realizations of the initial condition with reference response.
Table 17.
Training hyperparameter.