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Seminar on Control Theory and Nonlinear Filtering
Effective filtering on a random slow manifold
Effective filtering on a random slow manifold
Organizer
Speaker
Time
Wednesday, January 8, 2025 9:00 PM - 10:00 PM
Venue
Online
Abstract
In this talk, we shall introduce a literature about model reduction method and its application in nonlinear filtering. This work is about a slow-fast data assimilation system under Gaussian noisy fluctuations. First, we obtain its low dimensional reduction via an invariant slow manifold. Second, we prove that the low dimensional filter on the slow manifold approximates the original filter in a suitable metric. Finally, we illustrate this approximate filter numerically in an example.
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.