03_upscaling.md

Upscaling helps more than increasing the number of Fourier layers

To quickly check if increasing the number of Fourier Convolution layers does have a beneficial impact, we consider a FNO model with 2 Fourier Convolution Layers (left) and 4 (right), and show the training and validation loss :

We can observe that using more convolution layers does not impact, which is also visible from the average model errors :

	2 layers	4 layers
v_x	4.0e-05	4.2e-05
v_z	6.4e-05	6.4e-05
b	4.1e-05	4.3e-05
p	1.5e-05	1.4e-05
avg	4.0e-05	4.1e-05

However, the upscaling has a major impact on the accuracy of the model. For instance, if we compare $dv=16$ internal variable put into the Fourier Layer, with $dv=4$, we observe an important impact on the training loss ($dv=16$ on the left, $dv=4$ on the right) :

which is also notable on the model average error, as it's almost divided by 2 :

	dv=16	dv=4
v_x	4.0e-05	8.9e-05
v_z	6.4e-05	1.3e-04
b	4.1e-05	9.6e-05
p	1.5e-05	4.2e-05
avg	4.0e-05	9.0e-05