Applied Math Seminar | Yuan Gao, From rare events to almost sure events: optimally controlled random walk on point clouds

MS Teams 

Speaker

Yuan Gao |  Duke University

Title

From rare events to almost sure events: optimally controlled random walk on point clouds

Abstract

We focus on analysis and data-driven algorithms for rare events such as essential conformational transitions in biochemical reactions which are modeled by Langevin dynamics on manifolds. We first reinterpret the observed transition paths from the stochastic optimal control viewpoint, which realizes the transitions almost surely. Then based on collected high dimensional point clouds and nonlinear dimension reduction, we construct an approximated Voronoi tessellation for the reduced manifold and design an upwind scheme  for the associated Fokker-Planck equation. The scheme automatically incorporates the manifold structure and enjoys lots of fine properties such as stability and convergence.  An optimally controlled random walk on point clouds is then constructed, which enables efficient Monte Carlo simulation for conformational transitions.