个人介绍： 陈南，复旦本硕（力学/计算数学）纽约大学克朗研究所博士（2016，数学和大气海洋科学博士学位）柯朗所数学系及大气海洋中心博士后（2016-2018） 现在威斯康星大学麦迪逊分校助理教授（tenure-track assistant professor）研究领域：不确定性分析 数据同化 随机模型和预测 复杂系统建模和快速计算 地球物理流体力学 信息论 反问题
Title: A Nonlinear Conditional Gaussian Framework for Extreme Events Prediction, State Estimation and Uncertainty Quantification in Complex Dynamical System
Abstract: A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions. The method is useful for ensemble prediction of complex nonlinear dynamical systems.
