标题： 分支扩散模型中极端事件的可预测性 显示英文标题

标题： Predictability of extreme events in a branching diffusion model

摘要： 我们提出一个框架，用于研究复杂系统中极端事件的可预测性。 主要概念要素——分层结构、空间动力学和外部驱动——被结合在一个经典的分支扩散与迁入模型中。 新要素——观测空间和观测事件——被引入，以形成一个类似于地球物理和环境应用的预测问题模式。 该问题包括在已知较小事件的观测情况下，估计极端事件发生的可能性，而系统的完整内部动力学是未知的。 我们寻找在极端事件接近时出现的预警模式；这些模式是系统长期平均值的偏离。 我们发现了一个控制参数，它支配着多个时空预警模式。 为此，我们推导出i) 由单个迁入者产生的粒子的时间和空间依赖性大小分布的完整解析描述；ii) 对应于多个迁入者的稳态矩；以及iii) 基于大小和空间的粒子大小分布的渐近形式。 我们的结果表明了一种普遍预警模式的机制，并为其理论和实证研究提供了一个自然框架。 显示英文摘要

摘要： We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with immigration. New elements -- observation space and observed events -- are introduced in order to formulate a prediction problem patterned after the geophysical and environmental applications. The problem consists of estimating the likelihood of occurrence of an extreme event given the observations of smaller events while the complete internal dynamics of the system is unknown. We look for premonitory patterns that emerge as an extreme event approaches; those patterns are deviations from the long-term system's averages. We have found a single control parameter that governs multiple spatio-temporal premonitory patterns. For that purpose, we derive i) complete analytic description of time- and space-dependent size distribution of particles generated by a single immigrant; ii) the steady-state moments that correspond to multiple immigrants; and iii) size- and space-based asymptotic for the particle size distribution. Our results suggest a mechanism for universal premonitory patterns and provide a natural framework for their theoretical and empirical study.