  Multiscale stochastic dynamical systems have been widely adopted to a variety
of scientific and engineering problems due to their capability of depicting
complex phenomena in many real world applications. This work is devoted to
investigating the effective dynamics for slow-fast stochastic dynamical
systems. Given observation data on a short-term period satisfying some unknown
slow-fast stochastic systems, we propose a novel algorithm including a neural
network called Auto-SDE to learn invariant slow manifold. Our approach captures
the evolutionary nature of a series of time-dependent autoencoder neural
networks with the loss constructed from a discretized stochastic differential
equation. Our algorithm is also validated to be accurate, stable and effective
through numerical experiments under various evaluation metrics.
