论文标题
增强跳跃链 - 稀疏代表时间依赖的马尔可夫跳跃过程
The Augmented Jump Chain -- a sparse representation of time-dependent Markov jump processes
论文作者
论文摘要
模拟分子系统的现代方法基于马尔可夫操作员的数学理论，其重点是自主平衡系统。但是，非自主物理系统或非自治模拟过程变得越来越重要。我们提出了非自主马尔可夫跳跃过程作为时空的自主马尔可夫链的表示。通过相关的跳跃时间的时间信息来增强嵌入式马尔可夫链的空间信息，我们得出了所谓的增强跳跃链。增强的跳跃链继承了原始过程的无限发生器的稀疏性，因此为研究时间依赖性动力学提供了有用的工具，即使在高维度中也是如此。此外，我们讨论了在非自主环境中委员会功能和连贯集的计算计算的可能概括和应用。在得出理论基础之后，我们通过概念验证的Galerkin批准对增强跳跃链的转移操作员的离散化说明了这些概念，该概念应用于简单的示例。
Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non-autonomous physical systems or non-autonomous simulation processes are becoming more and more important. We present a representation of non-autonomous Markov jump processes as autonomous Markov chains on space-time. Augmenting the spatial information of the embedded Markov chain by the temporal information of the associated jump times, we derive the so-called augmented jump chain. The augmented jump chain inherits the sparseness of the infinitesimal generator of the original process and therefore provides a useful tool for studying time-dependent dynamics even in high dimensions. We furthermore discuss possible generalizations and applications to the computation of committor functions and coherent sets in the non-autonomous setting. After deriving the theoretical foundations we illustrate the concepts with a proof-of-concept Galerkin discretization of the transfer operator of the augmented jump chain applied to simple examples.
