Reconstructing a dynamical system and forecasting time series by self-consistent deep learning

Understand

We introduce a self-consistent deep-learning framework which, for a noisy deterministic time series, provides unsupervised filtering, state-space reconstruction, identification of the underlying differential equations and forecasting.

• Without a priori information on the signal, we embed the time series in a state space, where deterministic structures, i.e.
• attractors, are revealed.
• Under the assumption that the evolution of solution trajectories is described by an unknown dynamical system, we filter out stochastic outliers.