Learning Based on Data and Numerical Solutions for Partial Differential Equations
发布时间：2023年05月08日
浏览次数：2494
发布者: Wenqiong Li
主讲人： 程晋（复旦大学&上海市现代应用数学重点实验室）
活动时间： 从 2023-05-16 16:00 到 17:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室
Abstract: Numerical methods for partial differential equations are powerful and effective tools for solving the engineering problems. But there are still some difficult problems, like high wave number problems and partial differential equations with the interior measurements etc, which could not be effectively solved by the standard well- known business software. It is noticed that the present methods usually do not take account to the exact solutions we have by hand, the experiment data and the numerical solutions we have done before. With the developments of the machine learning and AI, the ideas of learning are widely used in many fields of Sciences and Engineering. In this talk, our recent work on the machine learning based numerical methods for partial differential equations is presented. We also provide a relevant theoretical framework and algorithm. The numerical simulation results indicate that our method has good performance for high wave number problems.
报告人简介：程晋，复旦大学数学科学学院博士导师、教授，2001年晋升教授，现任上海市现代应用数学重点实验室主任；上海市工业与应用数学学会理事长；英国Institute of Physics Fellow、国际反问题联盟执行委员等。曾任中国数学会副理事长，国家基金委数理学部专家评审组成员；美国NSF评审Panel member，多个国际知名期刊编委等。在国内外学术刊物上已发表论文120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。在应用方面，与新日铁、华为等国内外企业进行了有效的合作，取得了突出的成果，得到了业界的好评。
