报告人：张寅玲博士生威斯康星大学麦迪逊分校数学系
报告时间：2025年5月29日下午16:00
报告地点：红瓦楼826
报告内容简介：Discovering the underlying dynamics of high-dimensional complex systems from partial observational data and efficiently carrying out the subsequent data assimilation (DA) and uncertainty quantification (UQ) is computationally challenging. This talk presents two effective mathematical frameworks integrating explainable nonlinear stochastic models with machine learning algorithms to achieve these goals.
The first framework is a causality-based sparse learning algorithm that leverages information theory and DA to discover the underlying nonlinear dynamics with an appropriate UQ using only partial observations. Notably, this approach is robust, efficient, and physics-explainable, ensuring that the identified model structures align with physical constraints even using incomplete data. It can handle systems with relatively high dimensions.
The second framework aims to develop systematic stochastic nonlinear neural differential equations that characterize underlying physics and implement efficient DA and UQ. Notably, the DA is carried out in an augmented latent space that exploits a novel nonlinear extended version of Koopman operator theory assisted by deep learning. Despite the lifted space dimension, the model structure in the latent space allows the use of closed analytic formulae for DA and UQ. Thus, the method is exact, accurate, and computationally efficient. It possesses advantages for systems with intermittency and extreme events.
These two frameworks can adaptively supplement and create general neural dynamical systems for various scientific purposes.
报告人简介：张寅玲本科毕业于上海交通大学数学系，现为美国威斯康辛大学麦迪逊分校数学系博士研究生，师从陈南教授。她的研究兴趣主要集中在应用数学领域，特别专注于随机建模、数据同化、机器学习预测、不确定性量化和信息论等方向。张寅玲的研究工作主要应用于大气海洋科学和材料科学领域，包括厄尔尼诺南方涛动(ENSO)和马登-朱利安振荡(MJO)耦合的随机模型，以及多晶体韧性损伤过程的数据驱动建模。她的研究成果已发表于多个国际期刊并在重要学术会议上展示。
报告邀请人：张晔宇