报告题目：Kernel Based Methods for Missing Dynamics and Elliptic Inverse Problems
报告人：蒋诗晓 (上海科技大学 副教授)
会议时间：2022/5/25(周三) 9:30开始
会议地点：线上，腾讯会议号: 837 671 936
报告摘要：In this talk, we review diffusion maps algorithm as a manifold learning technique and discuss its applications in two problems, one being recovery of missing dynamics and the other elliptic inverse problems on Riemannian manifolds. For missing dynamics problem, we propose a framework that reformulates the prediction problem as a supervised learning problem to approximate a map that takes the memories of the resolved and identifiable unresolved variables to the missing components in the resolved dynamics. Supporting numerical results on instructive nonlinear dynamics, including the two-layer Lorenz system, the truncated Burger-Hopf equation, the 57-mode barotropic stress model, and the Kuramoto-Sivashinsky (KS) equation. For elliptic inverse problem, we investigate the formulation and implementation of Bayesian inverse problems to learn the diffusion coefficient of a second-order elliptic PDE on a closed manifold from noisy measurements of the solution. The resulting computational method is mesh-free and easy to implement, and can be applied without full knowledge of the underlying manifold, provided that a point cloud of manifold samples is available. Numerical results validate our graph-based approach and demonstrate the need to design graphical Matérn-type Gaussian field priors that account for boundary conditions when manifolds have boundaries.
报告人简介：蒋诗晓，上海科技大学数学科学研究院副教授。2017年博士毕业于上海交通大学，2017年至2020年，在美国宾州州立大学数学系做博士后，随后担任助研教授， 2020年入职上海科技大学。主要研究方向是非线性色散波，算子估计，流形学习等领域，相关研究成果发表在 J.Fluid Mech., J. Comput. Phys., Inverse Problems, New J. Phys., 等国际知名期刊上，目前主持国家自然科学基金青年项目。
