Qualitative Analysis of Molecular Dynamical Systems

研究人员开发了一类严格的方法和工具来分析分子轨迹集，产生易于解释的机械结果，但可以利用现在可能生成的大型数据集。上述模拟引擎生成类似的数据：许多（100到10，000）轨迹，通常在相对较长的时间尺度（100 ns到10 µ s）上。每个轨迹都是原子构型的时间序列。从这个数据集，我们的目标是在一些更宏观的层面上理解模拟过程中所采取的路径的结构。这里的挑战是，虽然有许多自由度，但其中许多并不重要，实际上掩盖了正在进行的潜在相关动态。例如，在研究任何动力系统时，吸引不动点的集合是一个非常重要的不变量。不稳定临界点，以及不变流形，包括吸引子流形，在研究动力学中也有很大的兴趣。即使动力学发生的环境空间在拓扑上是平凡的（例如欧几里得空间），固定集和不变集也经常具有有趣的拓扑结构。此外，存在一套强大的工具（康利指数理论），它往往允许一个得出有用的信息不变的子集，它们之间的相互关系。这种方法已被用来开发计算方法，允许一个描述动态的算法和可证明的方式对低维系统的动态。此外，这些工具允许跟踪参数化系统中的参数变化时的定性行为，从而产生给定物理形式的动力系统行为的"数据库"。这一系列的想法正在迅速发展，并预计将提供非常有用的信息，许多化学动力学系统。研究人员将强调从固有的生物学和化学的角度来看所涉及的挑战。自几十年前起源以来，分子尺度上的生物学模拟已经走过了漫长的道路。 现在，有了强大的单个处理器，以及非常大的分布式处理器集群，人们可以为给定的感兴趣的现象常规地生成非常大量的模拟数据，通常是沿着沿着许多轨迹的全原子细节。 一个日益严峻的挑战是挖掘如此庞大的数据集，以深入了解正在研究的基本现象。研究人员开发了严格的方法来分析这些海量数据集，产生了易于解释的机械结果，但这些结果可以利用现在可能生成的大型数据集。上述模拟引擎生成类似的数据：许多（~100到10，000）轨迹，通常在长时间尺度（100 ns到10 µ s）上。 每个轨迹都是原子构型的时间序列。 根据该数据集，我们的目标是在更宏观的尺度上了解模拟期间所采用的路径的结构。 这里的挑战是，虽然有许多自由度，但其中许多自由度并不重要，实际上掩盖了正在进行的潜在相关动态。

The investigators develop a class of rigorous methods and tools for analyzing sets of molecular trajectories, yielding mechanistic results that are easily interpreted, yet which can take advantage of the large data sets that are now possible to generate. The above simulation engines generate similar data: many (100 to 10,000) trajectories, often on relatively long timescales (100ns to 10µs). Each trajectory is a time series of atomic configurations. From this data set, the goal is to understand at some more macroscopic level the structure of the paths taken during the simulation. The challenge here is that while there are many degrees of freedom, many of these are not important and in fact obscure the potentially relevant dynamics in progress. For example, the collection of attracting fixed points is a primary important invariant when studying any dynamical system. Unstable critical points, as well as invariant manifolds, including attracting submanifolds, are also of a great deal of interest in studying dynamics. Even when the ambient space on which the dynamics is taking place is trivial topologically (Euclidean space, for example), it is well-understood that fixed sets and invariant sets frequently carry interesting topological structure. Moreover, there exists a powerful set of tools (Conley index theory) which often allow one to derive useful information about invariant subsets, and the interrelationship between them. This methodology has been used to develop computational methods which permit one to describe dynamics in an algorithmic and provable way for dynamics on low-dimensional systems. Moreover, these tools permit the tracking of qualitative behavior as parameters in a parametrized system are changed, so as to produce "databases" of dynamical system behavior of a given physical form. This family of ideas is being rapidly developed, and is expected to provide very useful information about many chemical dynamical systems. The investigators will emphasize challenges involved from the point of view of the inherent biology and chemistry.The simulation of biology at the molecular scale has come a long way since its origins decades ago. Now, with powerful individual processors, as well as with very large distributed clusters of processors, one can routinely generate very large quantities of simulation data for a given phenomenon of interest, often in full-atomic detail along many trajectories. A growing challenge is to mine such massive data sets to gain insight into the fundamental phenomena under study. The investigators develop rigorous methods to perform the analysis of these massive data sets, yielding mechanistic results that are easily interpreted, yet which can take advantage of the large data sets that are now possible to generate. The above simulation engines generate similar data: many (~100 to 10,000) trajectories, often on long timescales (100ns to 10µs). Each trajectory is a time series of atomic configurations. From this data set, the goal is to understand at some more macroscopic scale the structure of the paths taken during the simulation. The challenge here is that while there are many degrees of freedom, many of these degrees of freedom are not important and in fact obscure the potentially relevant dynamics in progress.