Speaker: Shixiao Willing Jiang (ShanghaiTech)
Time: 2025-Sep-01st 11:00
Location: R1710, SIMIS
Zoom Meeting ID: 844 0594 7424 (Passcode: 076895)
摘要：
In this talk, we first briefly introduce diffusion maps algorithm which is a manifold learning approach. Then, we will show two applications of diffusion maps. First, we show the application of diffusion maps in estimating the diffusion coefficients of second-order elliptic PDEs defined on manifolds. Second, we discuss the application of diffusion maps in missing dynamics problem. In particular, we consider modeling missing dynamics with a nonparametric non-Markovian model, constructed using the theory of kernel embedding of conditional distributions on appropriate reproducing kernel Hilbert spaces (RKHS). The RKHS are equipped with orthonormal basis functions which can be chosen as Hermite polynomials or generated from diffusion maps.
Speaker introduction:
Shixiao Willing Jiang did his PhD at Shanghai Jiaotong University, after which he took postdoctoral positions at both the Courant Institute and Pennsylvania State University. Currently, he is a Professor in ShanghaiTech University. He studies Diffusion Equations, Manifold Learning, Modelling, and the Fermi-Pasta-Ulam Chains (among other topics).
简体中文 
English