長(zhǎng)沙理工大學(xué)學(xué)術(shù)活動(dòng)預(yù)告
報(bào)告承辦單位: 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告題目: Bayesian approach to a nonlinear inverse problem for time-space fractional diffusion equation
報(bào)告內(nèi)容:
The inverse problems for fractional differential equations has become a promising research area because of its wide applications in many scientific and engineering fields. Particularly, the correct orders of fractional derivatives are hard to know as they are usually determined by experimental data and contain non-negligible uncertainty, therefore, the research on inverse problems involving the orders are in necessary. Furthermore, the problems involving the inversion of fractional orders are essentially nonlinear, classical methods may hard to provide satisfying approximations and fail to capture the relevant uncertainty, a natural way to solve such inverse problems is through Bayesian approach. In this talk, we consider an inverse problem of simultaneously recovering the source function and the orders of both time and space fractional derivatives for time-space fractional diffusion equation. The problem will be formulated in the Bayesian framework, where the solution is the posterior distribution incorporating the prior information about the unknown and the noisy data. Under the considered infinite dimensional function space setting, we prove that the corresponding Bayesian inverse problem is well-defined based upon proving the continuity of the forward mapping. In addition, we also prove that the posterior distribution depends continuously on the data with respect to the Hellinger distance. Moreover, we adopt the iterative regularizing ensemble Kalman method to provide numerical implementation to the considered inverse problem for one dimensional case, the numerical results shed light on the viability and efficiency of the method.
報(bào)告人姓名: 張遠(yuǎn)祥
報(bào)告人所在單位: 蘭州大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告人職稱/職務(wù)及學(xué)術(shù)頭銜: 副教授
報(bào)告時(shí)間: 2020年10月30日 14:30－15:10
報(bào)告方式: 理科樓A-419
報(bào)告人簡(jiǎn)介: 張遠(yuǎn)祥副教授2012年獲蘭州大學(xué)博士學(xué)位。于2011-2012年赴英國華威大學(xué)數(shù)學(xué)系進(jìn)行博士聯(lián)合培養(yǎng)。張遠(yuǎn)祥副教授研究興趣為偏微分方程反問題的貝葉斯理論及快速算法。主持國家自然科學(xué)基金項(xiàng)目1項(xiàng)，在Inverse Problems等雜志上發(fā)表論文17篇。