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.

中文翻译：

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通过学习分子系统的有效动力学来加速模拟

模拟对于理解和预测复杂分子系统的演化至关重要。但是，尽管算法和专用硬件有所进步，但获取捕获生物分子结构演变所必需的时间尺度仍然是艰巨的任务。在这项工作中，我们提出了一个新颖的框架，通过学习分子系统的有效动力学（LED），可以将模拟时间尺度提高多达三个数量级。LED通过使用混合密度网络（MDN）自动编码器在粗尺度和精细尺度之间采用概率映射来增强无方程式方法，并使用长短期记忆MDN来发展非马尔可夫潜在动力学。我们证明了LED在M·ueller-Brown电位，Trp笼蛋白和丙氨酸二肽中的有效性。LED识别可解释的降序表示，并可以在任何时候生成各自的全原子分子轨迹。我们认为，提出的框架极大地提高了仿真能力，并为复杂分子系统的有效建模开辟了新的视野。