报告题目： A novel method for solving the inverse spectral problem with the incomplete data

报 告 人：孟品超 教授 长春理工大学

报告时间：2025年 7月4日 10：00—11：00

报告地点：数学楼研讨室6

校内联系人： 吕俊良 [email protected]

报告摘要：In this talk, We propose a novel method for solving the inverse spectral problem of the Dirichlet boundary in a bounded region. We construct a data-driven deep neural network using convolutional and residual layers. The key ingredient of the approach is to extract features from input data, while fully preserving the original features and preventing network degradation. Using incomplete eigenvalue data as input and the Fourier expansion coefficients of the bounded regions as output. The network parameters are updated based on the reciprocal of the error calculated by the smooth L1 function. The incomplete eigenvalues are used to achieve the high-precision inversion of the bounded regions. Numerical experiments demonstrate the effectiveness of our method in solving the inverse spectral problem in both two-dimensional and three dimensional cases.

报告人简介：孟品超，长春理工大学数学与统计学院教授，硕士研究生导师，主要研究兴趣是数学物理反问题、机器学习算法的设计与理论分析等。近年来主要从事反散射问题数值算法和机器学习方法性质研究，尤其是设计有效的反散射问题求解算法并对其进行相应的理论分析。在JCAM，IPI，CICP等国内外重要期刊发表论文20余篇。主持或者参与国家自然科学基金、吉林省科技厅基金和吉林省教育厅基金7项。目前担任中国仿真学会不确定系统分析与仿真专委会委员、吉林省运筹学会理事以及IPIA会员。