Piggy backing here... but this dimension-reduction or system-identification stuff always reminds me of Takens' theorem [0]. He even did some neural network stuff back in the "dark ages" of the topic [1].

[0] https://en.wikipedia.org/wiki/Takens%27s_theorem

[1] https://clgiles.ist.psu.edu/papers/NC-2000-learning-chaos-nn...