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讲席教授许进超做客线上“自然科学杰出演讲系列讲座” “Distinguished Lecture in Natural Sciences” by Prof. Jinchao Xu

春日未迟,万物复苏。4月17日,第四期“自然科学杰出演讲系列讲座”如约而至,美国宾州大学Verne M. Willaman讲席教授、宾州大学-北京大学计算数学与应用联合研究中心主任许进超应邀以“Numerical PDEs and Deep Learning”为题做学术报告。本次学术报告由自然科学研究院院长金石教授主持,来自数学科学学院、物理与天文学院、致远学院以及海内外其他高校的500多名师生通过线上直播平台共同参会。

本次报告主要介绍如何利用有限元和多层网格法的相关知识来理解、研究和改进深度神经网络的模型结构、数学特性和训练算法。其中,许进超教授着重演示了如何通过对Poisson方程的多重网格方法进行微小的修改,从而衍生出名为“MgNet”的新卷积神经网络(CNN),并讨论“MgNet”的理论和实践潜力。

四月以来,自然科学研究院已举办线上“自然科学杰出演讲系列讲座” 3场,平均每场参会者达500余人。借助在线直播的学术报告形式,来自海内外的学者、师生不受空间限制,共聚“云端”,共享前沿的科研动态和研究成果。

嘉宾介绍:许进超,美国宾州大学Verne M. Willaman讲席教授、宾州大学-北京大学计算数学与应用联合研究中心主任。许教授于1995获得首届冯康科学计算奖,2005年获得德国“洪堡”资深科学家奖,2006年获得中国杰出青年基金(B 类), 2007年应邀在第6届国际工业与应用数学学会大会上作特邀报告,2010年应邀在世界数学家大会上作45分钟报告,2011年当选美国工业与应用数学学会会士,2012年当选美国数学学会会士,2019年当选美国科学促进学会会士。

许教授主要研究方向为数值方法的设计、分析和应用,特别是求解偏微分方程以及大数据中的快速算法及其应用。他在区域分解法、多重网格方法和自适应有限元方法等领域,取得了一系列奠基性的科研成果,是国际知名的学术带头人。其代表作包括著名的子空间校正算法、BPX-预条件子、HX-预条件子以及XZ-恒等式等以他名字(Xu)命名的工作。其中BPX-预条件子已经成为大规模科学计算中最基本的算法之一。用于求解Maxwell方程组的HX-算法,曾被美国能源部评为近年来计算科学领域中的十大突破之一。许教授迄今发表学术论文200余篇,其论文Google引用次数超过14000多次。同时,他还担任了十多种国际计算数学权威期刊的编委。近年来他开始研究深度学习,为传统的统计算法、卷积神经网络(CNN)与稀疏训练算法研发新的算法与数学理论。

Spring is a time for rejuvenation and zest for life. On April 17, the fourth “Distinguished Lecture in Natural Sciences” was held as scheduled. Jinchao Xu, a Verne M. Willaman Professor of the University of Pennsylvania and Director of the PSU-PKU Joint Research Center for Computational Mathematics and Applications, was invited to deliver an academic report on “ Numerical PDEs and Deep Learning “. This lecture was chaired by Professor Shi Jin, Director of the Institute of Natural Sciences. More than 500 teachers and students from the School of Mathematical Sciences, SJTU, the School of Physics and Astronomy, SJTU, Zhiyuan College, SJTU, and other universities at home and abroad participated in the conference through an online live broadcast platform.

Prof. Xu introduced models and algorithms from two different fields: (1) machine learning, including logistic regression, support vector machine and deep neural networks, and (2) numerical PDEs, including finite element and multigrid methods. He demonstrated how a new convolutional neural network (CNN), known as MgNet, can be derived by making very minor modifications of a classic geometric multigrid method for the Poisson equation and then discuss the theoretical and practical potentials of MgNet.

Since April, the Institute of Natural Sciences has held 3 online “Distinguished Lectures in Natural Sciences”, with an average of more than 500 participants. With the form of online live academic reports, domestic and overseas scholars, teachers and students are not restricted by space. They gather together on the “cloud” to share cutting-edge scientific research trends and research results.

Bio
Professor Xu, a Verne M. Willaman professor at The Pennsylvania State University, director of the PSU-PKU Joint Research Center for Computational Mathematics and Applications. Professor Xu won the first Fung Kang Scientific Computing Award in 1995, the German ‘Humboldt’ Senior Scientist Award in 2005, the Outstanding Youth Fund (Type B) in 2006. He was a plenary speaker at the International Congress for Industrial and Applied Mathematics in 2007 and a 45-minute invited speaker at the International Congress for Mathematicians in 2010. In 2011, he was elected as a Fellow of the American Society of Industrial and Applied Mathematics. He is a Fellow of the Society for Industrial and Applied Mathematics (SIAM) and also a fellow in the inaugural class of the American Mathematical Society (AMS). In 2019, Xu was elected as the American Association for the Advancement of Science (AAAS) Fellow.

Xu’s research specialty is numerical methods for partial differential equations that arise from modeling scientific and engineering problems. One major research interest is in multigrid methods for their theoretical analysis, algorithmic developments, and practical application, especially developing, designing, and analyzing fast methods for solving large-scale systems of equations. His work ranges from studying fundamental theoretical questions in numerical analysis to developing and applying numerical algorithms for practical applications. He is, perhaps, best known for the Bramble-Pasciak-Xu preconditioner — an algorithm that is one of the two most fundamental multigrid approaches to solve large-scale discretized partial differential equations. He is also noted for the Hiptmair-Xu preconditioner, which was featured in 2008 by the U.S. Department of Energy as one of the top 10 breakthroughs in computational science in recent years.