Mathematics Colloquium
George Yin
University of Connecticut
Title: Computational Nonlinear Filtering: A Deep Learning Approach
Date: Friday September 22th, 2023
Place and Time: Love 101, 3:05-3:55 pm
Abstract. Nonlinear filtering is a fundamental problem in signal processing, information theory, communication, control and optimization, and systems theory. In the 1960s, celebrated results on nonlinear filtering were obtained. Nevertheless, the computational issues for nonlinear filtering remained to be a long-standing and challenging problem. In this talk, in lieu of treating the stochastic partial differential equations, which is an infinite dimensional problem for obtaining the conditional distribution or conditional measure, we construct finite-dimensional approximations using deep neural networks for the optimal weights. Two recursions are used in the algorithm. One of them is the approximation of the optimal weight and the other is for approximating the optimal learning rate. [This is a joint work with Qing Zhang (University of Georgia), and Hongjiang Qian (University of Connecticut).