AI 中文总结
针对传统模型无法捕捉海洋涡旋复杂时空聚类的问题，本文提出时空霍克斯过程模型，结合EM算法与两阶段模拟框架，成功验证了亚中尺度涡旋形成的自激发特性。
AI 中文摘要
海洋涡旋是高度动态的结构，其特征是频繁发生分裂与合并事件，呈现出传统泊松模型无法捕捉的复杂时空聚类特性。本文基于高频海洋流场数据，引入一种新型时空霍克斯（Hawkes）过程来建模自激发涡旋场。我们构建了一个触发核函数，该函数将自激发强度与应变率大小引起的空间变形耦合起来；为表征涡旋场的渐近行为，推导了控制时空涡旋期望强度的沃尔泰拉（Volterra）积分方程。我们开发了一种期望最大化（EM）算法，将未观测到的父子关系视为潜在分支结构以进行参数估计；进一步扩展该框架以适应时变非齐次背景强度，相应修改了EM更新规则与解析沃尔泰拉解。最后，我们提出了一种利用聚类表示算法的两阶段模拟框架，将模拟得到的涡旋形成经验路径与沃尔泰拉方程均值率的数值解进行对比，以验证霍克斯模型的有效性。
英文摘要
Ocean eddies are highly dynamic structures marked by frequent splitting and merging events. They exhibit complex spatio-temporal clustering that traditional Poisson models fail to capture. In this paper, a novel spatio-temporal Hawkes process is introduced to model self-exciting eddy fields on the basis of high-frequency ocean flow data. We formulate a triggering kernel that couples the self-excitation intensity with spatial deformation caused by the strain rate magnitude. To characterize the asymptotic behavior of the eddy field, we derive a Volterra integral equation that governs the expected eddy intensity over time and space. We develop an Expectation-Maximization (EM) algorithm that treats the unobserved parent-child relationships as latent branching structures for parameter estimation. We further extend this framework to accommodate a time-varying, non-homogeneous background intensity, modifying both the EM updates and the analytical Volterra solution accordingly. Finally, we propose a two-stage simulation framework utilizing a cluster representation algorithm. The simulated empirical paths of eddy formation are compared together with numerical solution of the Volterra equation for mean rate as validation of the Hawkes model.
