Memory matters: Beyond Markovian models of rare event kinetics

摘要：罕见事件涉及系统两种状态之间的快速但不频繁的转变，例如亚稳态母液a和稳定晶体B。该项目将通过两个关键发展扩展系统从状态a过渡到状态B的频率模型的最新技术；(1)从信号处理到包含记忆的集体动力学拟合模型的技术(2)提交者函数的机器学习，微观状态在返回到a之前进化到B的概率。结合起来，这两个发展将使我们能够从原子模拟中做出增强的预测。背景：在许多异质系统中，原子尺度上的行为是由罕见事件控制的，我们指的是两种状态A和B之间的转换，这种转换发生得很快，但频率足够低，以至于在可实现的持续时间的模拟中永远不会观察到。建模这些是具有挑战性的，并且通常依赖于简单模型的参数化，这些模型通过单个集体自由度的动力学来描述罕见事件。这样的描述可以做出准确的预测，但依赖于确定最佳自由度和选择适当的动力学模型。在大多数情况下，使用粗糙（但便宜）的近似值。在这个项目中，我们将结合两种最先进的数值技术来系统地改进这些。提交者知道最优的集体变量，即微状态在状态a之前到达状态B的概率。我们将扩展小组中现有的工作，使用机器学习来预测提交者（以及相关的不确定性）。我们还将利用信号处理文献中的自回归技术对非最优集体变量的时间演化进行建模，以建立具有记忆的动力学模型，即超越马尔可夫动力学的通常假设。这两种技术将在应用于由罕见事件控制的简单晶格模型时进行比较和对比，然后在以后的几年扩展到原子模拟。该项目适合对计算方法、统计力学和数据科学感兴趣的学生。

Summary: Rare events involve rapid but infrequent transitions between two states of a system, e.g. a metastable parent liquid A and a stable crystal B. This project will extend the state-of-the-art for models of how often a system transitions from state A to state B with two key developments; (1) techniques from signal processing to fit models of collective dynamics which incorporate memory (2) machine learning of committor functions, the probability that a microstate will evolve to B before returning to A. Combined, these two developments will allow us to make enhanced predictions from atomistic simulations.Background: In many heterogenous systems, behaviour at the atomistic scale is governed by rare events, by which we mean transitions between two states A and B that occur rapidly but sufficiently infrequently that they will never be observed during a simulation of achievable duration. Modelling these is challenging, and often relies on parameterisation of simple models which describe the rare event via the kinetics of a single collective degree of freedom.Such descriptions can make accurate predictions, but rely on identifying the optimal degree of freedom and choosing an appropriate model of its kinetics. In most cases crude (but inexpensive) approximations are used. In this project we will combine two state-of-the-art numerical techniques to improve on these systematically. The optimal collective variable is known to the committor, the probability that a microstate will reach state B before state A. We will extend existing work in the group on using machine learning to predict the committor (and associated uncertainty). We will also model the time evolution of less-optimal collective variables using autoregressive techniques from the signal processing literature to build kinetic models with memory, i.e. beyond the usual assumption of Markovian dynamics.The two techniques will be compared and contrasted when applied to simple on-lattice models governed by rare events, before extending to atomistic simulations in later years. The project would suit a student interested in computational methods, statistical mechanics and data science.