  Predictive simulations of complex systems are essential for applications
ranging from weather forecasting to drug design. The veracity of these
predictions hinges on their capacity to capture the effective system dynamics.
Massively parallel simulations predict the system dynamics by resolving all
spatiotemporal scales, often at a cost that prevents experimentation while
their findings may not allow for generalisation. On the other hand reduced
order models are fast but limited by the frequently adopted linearization of
the system dynamics and/or the utilization of heuristic closures. Here we
present a novel systematic framework that bridges large scale simulations and
reduced order models to Learn the Effective Dynamics (LED) of diverse complex
systems. The framework forms algorithmic alloys between non-linear machine
learning algorithms and the Equation-Free approach for modeling complex
systems. LED deploys autoencoders to formulate a mapping between fine and
coarse-grained representations and evolves the latent space dynamics using
recurrent neural networks. The algorithm is validated on benchmark problems and
we find that it outperforms state of the art reduced order models in terms of
predictability and large scale simulations in terms of cost. LED is applicable
to systems ranging from chemistry to fluid mechanics and reduces the
computational effort by up to two orders of magnitude while maintaining the
prediction accuracy of the full system dynamics. We argue that LED provides a
novel potent modality for the accurate prediction of complex systems.
