Data-Driven Coarse-Graining using Space-Time Diffusion Maps

具有许多自由度的动力系统在广泛的应用中出现，包括大规模分子动力学，气候和天气研究以及电力网络。模拟中的挑战通常是提取统计信息，例如系统给定状态的平均倾向或某些事件之间经过的平均时间。模拟数据很容易生成，但通常利用率很低。该项目的目标是开发一种数据驱动的方法，用于自动检测基于一组集体变量的系统简化描述，这些变量可以在有效的统计提取程序中使用。这些最慢的自由度通常是最重要的自由度。动力学的特征是在给定状态附近的波动，被描述状态之间转换的相对罕见的事件打断。有效地识别集体变量是设计粗粒度模型的关键第一步，它可以允许在可访问的模拟时间尺度上增加许多数量级。通过自动寻找集体变量，我们可以大大简化许多系统的快速研究和比较。该研究建立在扩散映射技术的基础上，利用扩散算子的特征函数来表征系统的亚稳态（缓慢变化）状态。自动粗粒化的潜在影响将在理性药物设计等领域得到最深刻的感受，在这些领域中，有必要根据药物分子与某些靶标（例如蛋白质）相互作用的性质选择特定的药物分子。生物分子模拟依赖于使用非常专业和高度开发的模拟代码，这些代码是多年发展和政府投资的产物。为了在这一重要领域加速新算法的实施和测试，该项目包括epsrc资助的MIST（分子集成软件工具）平台内的详细软件开发计划。软件方法的测试将通过与化学家和药物化学家的合作进行，包括Rice大学（休斯顿，德克萨斯州）和Memorial Sloan Kettering癌症研究中心（纽约）的研究人员。

Dynamical systems with many degrees of freedom arise in a wide range of applications, including large scale molecular dynamics, climate and weather studies, and electrical power networks. The challenge in simulation is normally to extract statistical information, for example the average propensity of a given state of the system or the average time that elapses between certain events. Simulation data is easy to generate but often poorly utilized. The goal of this project is the development of a data-driven method for the automatic detection of a simplified description of the system based on a set of collective variables which can be used within efficient statistical extraction procedures. These slowest degrees of freedom are typically the most important ones. The dynamics are characterised as fluctuations in the vicinity of given state punctuated by relatively rare events describing transitions between the states. Efficiently identifying collective variables is the crucial first step in the design of coarse-grained models which can allow many order of magnitude increases in the accessible simulation timescale. By automatically finding collective variables, we can greatly simplify rapid study and comparison of many systems. The research builds on the technique of diffusion maps, whereby the eigenfunctions of a diffusion operator are used to characterise the metastable (slowly changing) states of the system. The potential impact of automatic coarse-graining will be felt most profoundly in fields such as rational drug design, where it is necessary to select specific drug molecules for their properties in interaction with some target, e.g. a protein. Bio-molecular simulation depends on the use of very specialised and intensely developed simulation codes which are the products of many years of development and government investment. In order to accelerate the implementation and testing of novel algorithms in this important area, this project includes a detailed plan for software development within the EPSRC-funded MIST (Molecular Integrator Software Tools) platform. Testing of the software methodology will be conducted via collaborations with chemists and pharmaceutical chemists, including researchers at Rice University (Houston, Texas) and Memorial Sloan Kettering Cancer Research Center (New York).