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John Harlim

Departments of Mathematics and Meteorology, Penn State ³Ô¹ÏÍø

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.