Stratton Hall

Department of Mathematical SciencesColloquiumFriday, October 31st, 202511:00AM-11:50AMStratton Hall 202Speaker: George Yin, University of ConnecticutTitle: Computational Nonlinear Filtering: A Deep Learning ApproachAbstract: 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 such the Kushner equation and the Duncan-Motensen-Zakai equation 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 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. Convergence and rates of convergence will be discussed together with some examples. [This is a joint work with Hongjiang Qian (Auburn University) and Qing Zhang (University of Georgia).]