What connections between machine learning and dynamical systems?

Question

I have a background of ("pure") dynamical systems and ergodic theory, but I am switching to machine learning.

Can some machine learning questions be treated from a dynamical systems/ergodic theory viewpoint? What literature would you recommend for the intersection of these two fields? What kind of contribution would be possible?

I imagine something around coding of ergodic maps, which is connected with information theory, and seems to have some computer science flavor, but I do not know.

Answer 1

Try searching for topics concerning "Learning Dynamical Systems" and "Predictive State Representation." Here is a possible reference.

I'm not sure Ergodicity in full generality is useful. If you're dealing with a Markov chain with a stationary distribution then there will be some ergodicity involved concerning the visitation of the steady states. Also, there's something called "Ergodic Time Series" which might be interesting to you.