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Seminar on Control Theory and Nonlinear Filtering
Extension of probability flow on matrix Lie group
Extension of probability flow on matrix Lie group
Organizer
Speaker
Time
Tuesday, January 17, 2023 9:30 PM - 10:00 PM
Venue
Online
Abstract
Feedback control for the probability flow is firstly proposed by Prashant G. Mehta et al. Given a smooth path ${p_t^*in mathcal{P}_2(mathbb{R}^d)}$, basic problem is to design stochastic process ${{X}_t}$ such that the probability density ${p}_t$ equals to $p_t^*$ for any time $tge 0$. Note that it acts as a general framework. Solution of probability flow is of interests in many applied areas. Up to 2021, there exist complete formulation under Euclidean space. In this talk, we will discuss the extension to matrix Lie group. We will discuss two cases: deterministic and stochastic probability flow.
Speaker Intro
Xiaopei Jiao received his bachelor's degree from the Zhiyuan College of Shanghai Jiao Tong University and his Ph.D. from the Department of Mathematical Sciences at Tsinghua University. He subsequently worked as a postdoctoral researcher at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) and at the University of Twente in the Netherlands. His current research interests include finite-dimensional filtering theory, Yau-Yau filtering methods, physics-informed neural networks, and bioinformatics. His research focuses primarily on: (1) using geometric tools such as Lie algebras for solving partial differential equations and classifying nonlinear systems; (2) designing novel numerical algorithms based on physics-informed neural networks.