You will get something very similar. Just like you can get something like PCA/SVD using a simple linear autoencoder. But, and this is important, DMD is often applied to data that is so large that a 1-layer network would be prohibitively large, so dimensionality reduction is necessary. This actually got a lot of us in the field thinking about building DMD autoencoders, and after a discussion at a Banff workshop in January 2017, several of us wrote papers on the subject. Our paper on the topic is here: www.nature.com/articles/s41467-018-07210-0 Also, just because you can write something as a neural network, doesn't mean it is a good idea. In the PCA/SVD example, although it is possible to compute this using an autoencoder, in my experience this requires more data and more time, as the SVD optimization has an optimal closed-form solution.

@@Eigensteve Hi Steve. We're working on a Koopman related project in Montreal, so thanks for all the great resources you're putting out on this subject! I read your nature paper, but the continuous spectra part was over my head, so I'd love to ask you this question to clarify something for me if you don't mind: Example 3 in the paper is a "high-dimensional fluid problem", but you are only ever using the analytically derived 3-dimensional reduced model (eq. 8-10), correct? So your argument above about 1-layer networks being prohibitively large wouldn't actually apply in this case, since your data is not actually high dimensional. Is it the continuous spectra here that would break "normal" autoencoders? Or am I missing something?

Seems to me like that would work fine as long as your system is only intermittently driven. For some systems this is the typical scenario, but for other systems, it would be unusual to halt all inputs (e.g. a commercial airplane).