Jinchao Xu - Biography#

Xu is Verne M. Willaman Professor of Mathematics at Penn State and a professor at KAUST. He is a Fellow of SIAM, AMS, AAAS and European Academy of Sciences, an invited speaker at International Congress for Industrial and Applied Mathematics in 2007 and also at International Congress for Mathematicians in 2010.

Xu works on theories and algorithms for numerical partial differential equations (PDEs) and for big data. He is known for several results that bear his name: Bramble-Pasciak-Xu (BPX) and Hiptmair-Xu (HX) preconditioners, Xu-Zikatanov (XZ) identity, and Morley-Wang-Xu (MWX) element. BPX is one of the two fundamental multigrid algorithms for solving large-scale discretized PDEs; HX, featured in 2008 by the US DOE as one of the top 10 breakthroughs in computational science, is now a major solver in numerical simulation of electro-magnetic problems; XZ-identity is a basic technical tool for the design and analysis of iterative methods such as multigrid method; Xu has published more than 200 papers with more than 18100 Google citations. Most recently, Xu studied models and theories for machine learning, developed MgNet that unifies multigrid with convolutional neural network (CNN) and provides a new angle for mathematical understanding of and practical improvement of CNN; He has laid down new theoretical foundation and provided solutions to several open problems concerning approximation properties of neural network functions.

Xu has served on editorial boards for many major journals in computational and applied mathematics such as Mathematics of Computations, Numerische Mathematik and Mathematical Models and Methods in Applied Sciences. He is a co-editor of many conference proceedings and research monographs. He has organized and/or served as scientific committee members for more than 100 conferences, workshops, and summer courses.