Seminar| Institute of Mathematical Sciences
Time: Monday, March 9th, 2026,15:00-16:00
Location: IMS, RS408
Speaker: Jin Cheng, School of Mathematical Sciences, Fudan University & Shanghai Contemporary Applied Math. Key Lab.
Abstract: The rapid development of Learning theory has opened up a new horizon for scientific research. How to apply the idea of learning in scientific computing and propose new ideas for some difficult problems is currently a research direction of great concern. In this report, we mainly introduce some recent related research results of our team: a method for numerical solution of differential equations based on machine learning. In view of the fact that current numerical solution methods (FEM, FD, BEM etc.) do not consider existing exact solutions (fundamental solutions, series solutions etc.), information from actual engineering measurements, and related results that have already been calculated, we propose a numerical solution method based on learning theory, and provide the relevant theoretical framework and algorithm. The results of numerical simulation show that our method has good effects on high-wavenumber problems.
学习理论的发展日新月异，为科学研究打开了一片新的天地。如何在科学计算中应用学习的思想，针对一些难点问题提出一些新的思路是目前的一个大家关心的研究方向。在本报告，我们主要介绍了我们团队最近的一些相关的研究成果：基于机器学习的微分方程数值解的方法。针对目前数值解方法没有考虑已有精确解（基本解、级数解等）、实际工程测量的信息以及已经计算出的相关结果等信息，我们提出一种基于机器学习的数值解方法，并给出了相关的理论框架和算法。数值解模拟的结果表明我们的方法对于高波数问题有比较好的效果。
About the speaker: 程晋，复旦大学数学科学学院教授，上海市工业与应用数学学会理事长；英国Institute of Physics Fellow、欧亚反问题联盟执行委员等。曾任中国数学会副理事长，多个国际知名期刊编委等。已发表论文130余篇。2019年获得上海市自然科学奖一等奖，2020年获上海市自然科学二等奖，2022年获得上海市教学成果一等奖。在偏微分方程反问题的理论分析和一般反问题的高效反演算法方面取得多项重要进展。
Prof. Cheng Jin is a professor at the School of Mathematical Sciences, Fudan University, and the president of the Shanghai Society of Industrial and Applied Mathematics. He is also a Fellow of the Institute of Physics in the UK and an Executive Committee member of the Eurasian Association of Inverse Problems, among other roles. He has previously served as the Vice President of the Chinese Mathematical Society, a Panel member in the Division of Mathematics and Physics of the National Natural Science Foundation of China, a Panel member for the National Science Foundation (NSF) of the United States, and an editorial board member of multiple internationally renowned journals. He has published over 120 papers in academic journals. In 2019, he received the First Prize of the Shanghai Natural Science Award, the Second Prize of the Shanghai Natural Science Award in 2020, and the First Prize of Shanghai Teaching Achievement Award in 2022. He has made significant progress in theoretical analysis of inverse problems for partial differential equations and efficient inversion algorithms for general inverse problems. In terms of applications, he has effectively collaborated with domestic and foreign enterprises such as Nippon Steel and Huawei, achieving outstanding results and earning praise from the industry.