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Simulations are vital for understanding and predicting the evolution ofcomplex molecular systems. However, despite advances in algorithms and specialpurpose hardware, accessing the timescales necessary to capture the structuralevolution of bio-molecules remains a daunting task. In this work we present anovel framework to advance simulation timescales by up to three orders ofmagnitude, by learning the effective dynamics (LED) of molecular systems. LEDaugments the equation-free methodology by employing a probabilistic mappingbetween coarse and fine scales using mixture density network (MDN) autoencodersand evolves the non-Markovian latent dynamics using long short-term memoryMDNs. We demonstrate the effectiveness of LED in the M\"ueller-Brown potential,the Trp Cage protein, and the alanine dipeptide. LED identifies explainablereduced-order representations and can generate, at any instant, the respectiveall-atom molecular trajectories. We believe that the proposed frameworkprovides a dramatic increase to simulation capabilities and opens new horizonsfor the effective modeling of complex molecular systems.

Accelerated Simulations of Molecular Systems through Learning of their Effective Dynamics