题目：Simultaneous identification of the order and potential coefficient in time-fractional diffusion/wave equations by a deep neural networks method

主讲人：魏婷 教授

时间：2025年6月26日（周四） 10：00

地点：理学院楼308

主办单位：理学院

主讲人简介：

魏婷，教授，博导。入选2006年度的教育部新世纪优秀人才支持计划。曾任中国工业与应用数学学会的常务理事和中国计算数学学会常务理事及中国数学会理事。主要研究方向是数学物理方程反问题的计算方法及理论研究，目前主要从事分数阶扩散及扩散波方程反问题的理论与计算方法。已主持完成 4项国家自然科学基金面上项目,  目前正在主持1项面上项目 “反常扩散中多参数同时辨识问题的唯一性理论及算法研究”, 在Inverse Probl, SIAM J Numer Anal, Adv Comput Math等SCI期刊上发表论文110篇，在 Web of Science数据库中他引2900余次。曾多次赴香港、日本、美国作访问学者，并参加了在日本、澳大利亚、中国、斯洛伐克、韩国、芬兰、美国、德国、巴西、新加坡、俄罗斯、马耳他等国家及香港、台湾地区举行的国际会议。 2021-2023年担任《计算数学》杂志编委，为40余种国际高水平期刊的审稿人。已培养博士研究生20余名，硕士研究生40余名。

摘要：

I will talk about two nonlinear inverse problems of identifying simultaneously the order of fractional derivative and a space-dependent potential coefficient in one-dimensional time-fractional diffusion/wave equation from the lateral Cauchy data. For the case of wave equation, the existence and uniqueness of the weak solution for the corresponding direct problem is studied. Based on the solution of direct problem, the uniqueness for the simultaneous determination of fractional order and space-dependent potential coefficient is proved by the analytic continuation, Laplace transformation and Gel’fand-Levitan theory under some suitable conditions to the given data. Moreover, we employ a self-adaptive algorithm combined with a fractional physics-informed method (self-adaptive fPINNs) to find the numerical fractional order and space-dependent potential coefficient simultaneously. The numerical experimental results for a few examples are provided to show the effectiveness of the numerical method. Further, the numerical results solved by a classical iterative method are presented for comparing with the fPINNs method.