  Finding a reduction of complex, high-dimensional dynamics to its essential,
low-dimensional "heart" remains a challenging yet necessary prerequisite for
designing efficient numerical approaches. Machine learning methods have the
potential to provide a general framework to automatically discover such
representations. In this paper, we consider multiscale stochastic systems with
local slow-fast time scale separation and propose a new method to encode in an
artificial neural network a map that extracts the slow representation from the
system. The architecture of the network consists of an encoder-decoder pair
that we train in a supervised manner to learn the appropriate low-dimensional
embedding in the bottleneck layer. We test the method on a number of examples
that illustrate the ability to discover a correct slow representation.
Moreover, we provide an error measure to assess the quality of the embedding
and demonstrate that pruning the network can pinpoint an essential coordinates
of the system to build the slow representation.
