About the description of the dataset

[nevoliu]

Thanks for the beautiful work!

I found that the network structure you used is consistent with FNO, just changing the form of the input data. I am having a hard time understanding why Geo-FNO works better than FNO, can you provide some details about the dataset?

[zongyi-li]

Thanks for the question! The new component is when the data is from non-uniform mesh, for example in the elasticity problem https://github.com/neural-operator/Geo-FNO/blob/main/elasticity/elas_geofno.py where we learn a deformation IPHI that map the physical space to latent space.

When the deformation is known/fixed, then we can directly sample the grid based on this deform, which is incorporated into the dataset. The FNO code on the latent space is the same as the standard FNO.