论文标题
数据驱动的随机减少动力学的构造，编码非马克维亚特征
Data-driven construction of stochastic reduced dynamics encoded with non-Markovian features
论文作者
论文摘要
构建分子系统减少动力学的一个重要问题是，由未解决变量的动力学产生的非马克维亚行为的准确建模。主要的并发症是由于缺乏比例分离而出现的，其中减少的动力学通常表现出明显的记忆和非白噪声项。我们提出了一种数据驱动的方法，以学习忠实保留非马克维亚动力学的多维解决变量的简化模型。与基于内存函数的直接构建的通用方法不同，目前的方法寻求一组非马克维亚特征，这些特征编码已解决变量的历史记录，并根据解决变量和这些特征建立了对扩展的马尔可夫动态的联合学习。训练是基于可以直接从分辨变量的相关变量的相关函数的演变匹配的。构造的模型基本上近似于多维广义朗格文方程，并确保了没有经验处理的数值稳定性。我们通过一维和四维分辨变量来构建分子系统的简化模型来证明该方法的有效性。
One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale separations, where the reduced dynamics generally exhibits pronounced memory and non-white noise terms. We propose a data-driven approach to learn the reduced model of multi-dimensional resolved variables that faithfully retains the non-Markovian dynamics. Different from the common approaches based on the direct construction of the memory function, the present approach seeks a set of non-Markovian features that encode the history of the resolved variables, and establishes a joint learning of the extended Markovian dynamics in terms of both the resolved variables and these features. The training is based on matching the evolution of the correlation functions of the extended variables that can be directly obtained from the ones of the resolved variables. The constructed model essentially approximates the multi-dimensional generalized Langevin equation and ensures numerical stability without empirical treatment. We demonstrate the effectiveness of the method by constructing the reduced models of molecular systems in terms of both one-dimensional and four-dimensional resolved variables.
