Learning Based on Data and Numerical Solutions for Partial Differential Equations
Time: 2023-05-08
Published By: Wenqiong Li
Speaker(s): Jin Cheng (Fudan University & Shanghai Key Laboratory of Contemporary Applied Mathematics)
Time: 16:00-17:00 May 16, 2023
Venue: Room 77201, Jingchunyuan 78, BICMR
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.
Bio-Sketch: Dr. Jin Cheng is a professor in School of Mathematical Sciences at Fudan University. He was promoted to full professor in 2001, and is now director of Shanghai Key Laboratory of Contemporary Applied Mathematics, president of Shanghai SIAM; Prof. Cheng is the Fellow of Institute of Physics (UK). He served for NSF of China and NSF(USA) as a panel member several times and was the vice president of the Chinese Mathematical Society. Prof. Cheng now is in the editorial boards of several international journals. More than 120 papers have been published in the international refereed journals. Prof. Cheng received the first prize of the Shanghai Natural Science Award in 2019 and the second prize of the Shanghai Natural Science Award in 2020. He also received the first prize of the Shanghai Teaching Achievement Award in 2022. Significant progress has been made by Prof. Cheng’s team in the theoretical analysis of inverse problems of partial differential equations and efficient inversion algorithms for general inverse problems. In terms of real application, effective cooperation has been established with domestic and foreign enterprises such as Nippon Steel and Huawei, achieving outstanding results and receiving praise from the industry.
