標(biāo)題：Simultaneous identification of order and potential coefficient in time-fractional equations by a deep neural networks method
報(bào)告時(shí)間：2025年7月21日（星期一）15：30-16：30
報(bào)告地點(diǎn)：人民大街校區(qū)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院二樓會(huì)議室
主講人：魏婷
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告內(nèi)容簡(jiǎn)介：
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.
主講人簡(jiǎn)介：
魏婷，教授，博導(dǎo)。入選2006年度的教育部新世紀(jì)優(yōu)秀人才支持計(jì)劃。曾任中國(guó)工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)的常務(wù)理事和中國(guó)計(jì)算數(shù)學(xué)學(xué)會(huì)常務(wù)理事及中國(guó)數(shù)學(xué)會(huì)理事。主要研究方向是數(shù)學(xué)物理方程反問(wèn)題的計(jì)算方法及理論研究，目前主要從事分?jǐn)?shù)階擴(kuò)散及擴(kuò)散波方程反問(wèn)題的理論與計(jì)算方法。已主持完成 4項(xiàng)國(guó)家自然科學(xué)基金面上項(xiàng)目, 目前正在主持1項(xiàng)面上項(xiàng)目 “反常擴(kuò)散中多參數(shù)同時(shí)辨識(shí)問(wèn)題的唯一性理論及算法研究”, 在Inverse Probl, SIAM J Numer Anal, Adv Comput Math等SCI期刊上發(fā)表論文110篇。曾多次赴香港、日本、美國(guó)作訪(fǎng)問(wèn)學(xué)者，并參加了在日本、澳大利亞、中國(guó)、斯洛伐克、韓國(guó)、芬蘭、美國(guó)、德國(guó)、巴西、新加坡、俄羅斯、馬耳他等國(guó)家及香港、臺(tái)灣地區(qū)舉行的國(guó)際會(huì)議。 2021-2023年擔(dān)任《計(jì)算數(shù)學(xué)》雜志編委，為40余種國(guó)際高水平期刊的審稿人。已培養(yǎng)博士研究生20余名，碩士研究生40余名。
