Memory matters: Beyond Markovian models of rare event kinetics

记忆很重要：超越罕见事件动力学的马尔可夫模型

• 批准号: 2729830
• 金额: --
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2729830
• 关键词: Memory; matters; Beyond; Markovian; models

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.

总结：罕见事件涉及系统的两种状态之间的快速但不频繁的转变，例如亚稳母液A和稳定晶体B。该项目将扩展最先进的模型，以了解系统从状态A到状态B的转换频率，并有两个关键的发展：（1）从信号处理到集体动态模型的拟合技术，其中包含内存（2）提交函数的机器学习，即微状态在返回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simulation.Background增强预测：在许多异质系统中，在原子尺度的行为是由罕见的事件，我们的意思是两个状态A和B之间的转换发生迅速，但足够不频繁，他们将永远不会被观察到在可实现的持续时间的模拟。建模这些是具有挑战性的，往往依赖于参数化的简单模型，通过一个单一的集体自由度的动力学来描述罕见的事件。这种描述可以做出准确的预测，但依赖于确定最佳的自由度，并选择一个合适的动力学模型。在大多数情况下，使用粗略（但不昂贵）的近似值。在这个项目中，我们将联合收割机两个国家的最先进的数值技术，以改善这些系统。提交者知道最优集合变量，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）。我们还将使用信号处理文献中的自回归技术来模拟不太理想的集体变量的时间演化，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的晶格模型时进行比较和对比，然后在以后的几年中扩展到原子模拟。该项目将适合对计算方法，统计力学和数据科学感兴趣的学生。