Published: Sept. 20, 2019

John Harlim

Departments of Mathematics and Meteorology, Penn State University

Manifold learning based computational methods

Recent success of machine learning has drawn tremendous interests in applied mathematics and scientific computations. In this talk, I will discuss recent efforts in using manifold learning algorithms (a branch of machine learning) to do parameter estimation and modeling of dynamical systems. For parameter estimation, I will demonstrate how to use machine learning and existing tools from statistics and functional analysis to perform efficient Bayesian inferences. For modeling application, I will demonstrate how to estimate time-dependent densities of Ito diffusion from time series of the stochastic processes. If time is permitting, I will also demonstrate how to use a manifold learning technique to approximate solutions of elliptic PDE's on smooth manifolds.