  Simulations are vital for understanding and predicting the evolution of
complex molecular systems. However, despite advances in algorithms and special
purpose hardware, accessing the timescales necessary to capture the structural
evolution of bio-molecules remains a daunting task. In this work we present a
novel framework to advance simulation timescales by up to three orders of
magnitude, by learning the effective dynamics (LED) of molecular systems. LED
augments the equation-free methodology by employing a probabilistic mapping
between coarse and fine scales using mixture density network (MDN) autoencoders
and evolves the non-Markovian latent dynamics using long short-term memory
MDNs. We demonstrate the effectiveness of LED in the M\"ueller-Brown potential,
the Trp Cage protein, and the alanine dipeptide. LED identifies explainable
reduced-order representations and can generate, at any instant, the respective
all-atom molecular trajectories. We believe that the proposed framework
provides a dramatic increase to simulation capabilities and opens new horizons
for the effective modeling of complex molecular systems.
