H.B. Keller Colloquium

Neural Networks and Numerical PDEs

Jinchao Xu, Verne M. Willaman Professor of Mathematics & Director, Center for Computational Mathematics and Applications, Penn State,

Speaker's Bio:
Jinchao Xu is Verne M. Willaman Professor of Mathematics and Director of the Center for Computational Mathematics and Applications at Penn State. His main research interests are in the study of numerical methods, especially multilevel and adaptive finite element methods, for systems of partial differential equations (PDE) and their applications. His other research interests include the analysis, modeling and applications of deep neural networks. He is known, for examples, for the Bramble-Pasciak-Xu preconditioner as one of the two basic multigrid methods for numerical PDEs and also for the Hiptmair-Xu preconditioner featured in 2008 by the DOE as one of the top 10 breakthroughs in computational science in recent years. He was an invited speaker at the International Congress for Industrial and Applied Mathematics in 2007 as well as at the International Congress for Mathematicians in 2010. He is a Fellow of the Society for Industrial and Applied Mathematics (SIAM), the American Mathematical Society (AMS) and the American Association for the Advancement of Science (AAAS).

I will first give a brief introduction to neural network functions, their applications to image classifications, and their relationship with finite element and multigrid methods. I will then present some recent results on the approximation properties of neural network functions, error analysis for numerical PDEs (in view of generalization accuracy in machine learning) and optimization algorithms for the underlying non-convex problems.

Event Sponsors:

Computing and Mathematical Sciences (CMS) - More events from this Sponsor

For more information, please contact Diana Bohler by phone at 6263951768 or by email at [email protected].