The 40th Anniversary Celebration of Shenzhen University and the 40th Anniversary Celebration of Mathematics

Liyuan Distinguished Scholar Issue twenty

Title:Scientific Computing and Machine Learning

Speaker: Dr. Jinchao Xu (King Abdullah University of Science and Technology, Penn State University, USA)

Lecture time: 08:30-09:30 a.m., December 11, 2023

Lecture Venue: Lecture Hall 1, School of Finance and Technology Classroom, Hui Xing Building

External version: Classroom No. 1 on the first floor of Huixing Building, Yuehai Campus, SZU

Overview:In this talk, I will report several theoretical and numerical studies of finite element and deep learning methods for partial differential equations and image classification. equations and image classification. Topics include approximation properties of neural network functions, error estimates for the finite neuron method, convergence analysis of training algorithms, finite element versus ReLU deep neuron method, convergence analysis of training algorithms, finite element versus ReLU deep neural networks, multigrid method versus convolutional neural networks, MgNet versus transformational neural networks, and the use of the MgNet method. networks, MgNet versus transformer, subspace correction method versus federated learning.

Speaker Introduction: Academician Xu Jinchao is an international authority in computational mathematics. He is a Professor at King Abdullah University of Science and Technology, Verne M. Willaman Professor of Mathematics at Penn State University, and Director of the Penn State-Peking University Joint Research Center for Computational Mathematics and Applications. He was formerly a Cheung Kong Chair Professor and a "Thousand Talents Program" scholar at Peking University, and Director of the Laboratory of Computational Methods and Applications at the International Center for Mathematical Research in Beijing. Academician Xu received the first Feng Kang Prize for Scientific Computing in 1995, the Humboldt Prize for Senior Scientists in Germany in 2005, the China Outstanding Young Persons' Fund (category B) in 2006, and was invited to give an invited lecture at the 6th Congress of the International Society for Industrial and Applied Mathematics (ISIAAM) in 2007, and a 45-minute lecture at the Congress of the World Mathematicians (WMM) in 2010. In 2010, he was invited to give a 45-minute presentation at the World Congress of Mathematicians. He was elected Fellow of the American Society for Industrial and Applied Mathematics (ASIAM) in 2011, Fellow of the American Mathematical Society (AMS) in 2012, Fellow of the American Association for the Advancement of Science (AAAS) in 2019, Fellow of the European Academy of Sciences in 2022, and Fellow of the Academia Europaea (AEHS) in 2023. Academia Europaea in 2023.

Academician Xu's main research interests are in the design, analysis and application of numerical methods, especially in solving partial differential equations as well as fast algorithms and their applications in big data. He has made a series of seminal scientific achievements in the fields of area decomposition methods, multigrid methods and adaptive finite element methods, and is an internationally recognized academic leader. His representative works include the famous subspace correction algorithms, BPX-preconditioners, HX-preconditioners, and XZ-constant equations, and other works named after his name (Xu). Among them, the BPX-preconditional has become one of the most fundamental algorithms in large-scale scientific computing. The HX-algorithm for solving Maxwell's system of equations has been recognized by the U.S. Department of Energy as one of the top ten breakthroughs in computational science in recent years. Academician Xu has published more than 200 academic papers to date, and his papers have more than 19,000 Google citations. Recently, Dr. Xu has studied the models and theories of machine learning and developed MgNet, which combines multigrid with convolutional neural networks (CNNs) to provide new perspectives on the mathematical understanding and practical improvement of CNNs, and he has laid new theoretical foundations and provided solutions to several open problems on the approximate properties of neural network functions.

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

Students and faculty are welcome to attend!

School of Mathematical Sciences

December 05, 2023