I shall present some mathematical problems encountered in deep learning models. The results include optimal control of selection dynamics for deep neural networks, and gradient methods adaptive with energy. Some of the computational questions that will be addressed have a more general interest in engineering and sciences.
Hailiang Liu received his M.S. in Applied Mathematics from Tsinghua University of China in 1988, and Ph.D from the Chinese Academy in 1995. He received an Alexander von Humboldt-Research Fellowship in 1996 that allowed him to conduct research in Germany from 1997-1999. He joined UCLA as Assistant Professor in Computational and Applied Mathematics (1999-2002). He then joined Iowa State University as Associate Professor in 2002, becoming a full Professor in 2007. Dr. Liu’s primary research interests include analysis of applied partial differential equations, the development of novel, high order algorithms for the approximate solution of these problems, and the interplay between analytical theory and computational aspects of such algorithms with diverse applications. Liu serves on the editorial board of several applied math journals such as the JMAA journal and Numerical Algorithms, and has given many invited lectures, including the invited addresses in the international conference on hyperbolic problems in 2002 and 2018. Liu has published more than 160 research articles, mostly in Numerical Analysis and Applied Partial Differential Equations.