Linear decoder

[agosztolai]

Hello,

I have been playing around with your repository for a few days and have noticed that in the NNDMD example, you are using a non-linear encoder and a linear decoder, e.g., [here](https://pykoopman.readthedocs.io/en/master/tutorial_koopman_nndmd_examples.html).

Some part of the _nndmd.py coder seems to explicitly depend on a linear decoder - it actually crashes if I choose a non-linear decoder because the eigenvectors are mapped back using an 'effective linear transformation'.

Is there a specific reason why this is a good choice? It seems counterintuitive that a linear transformation can invert a non-linear one. For example, in the DeepKoopman code by Lusch et al., a non-linear decoder was used, it seemed to me. Can you point me to a theoretical justification (e.g., a paper) for using a linear decoder?