Established methods to approximate dynamical systems, such as Markov State Models or EDMD depend critically on the choice of input features or basis functions. These methods are not directly able to *learn* the featurization from the data because the optimization principles used there - least squares error or maximum likelihood - lead to trivial but useless optima. To this end, we have developed the variational approach for markov processes (VAMP) which turns the search for features of dynamical systems into a well-defined machine learning problem. Using VAMP we define VAMPnets - neural networks for learning optimal featurizations and dynamical models from data.
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