主講人：陰小波 華中師范大學(xué)教授

時(shí)間：2026年1月31日9：30

地點(diǎn)：徐匯校區(qū)三號(hào)樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：陰小波，華中師范大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)學(xué)院教授、博士生導(dǎo)師，副院長(zhǎng)。本科畢業(yè)于南開(kāi)大學(xué)數(shù)學(xué)科學(xué)學(xué)院，博士畢業(yè)于中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院，主要研究方向?yàn)橛邢拊呔人惴?、移?dòng)網(wǎng)格方法、非局部問(wèn)題的數(shù)值分析、深度神經(jīng)網(wǎng)絡(luò)方法。已在SIAM Journal on Numerical Analysis, Journal of Computational Physics, SIAM Journal on Scientific Computing, IMA Journal on Numerical Analysis等雜志上發(fā)表多篇文章。主持四項(xiàng)國(guó)家自然科學(xué)基金項(xiàng)目，作為主要成員參與一項(xiàng)國(guó)家自然科學(xué)基金重大研究計(jì)劃重點(diǎn)支持項(xiàng)目。

內(nèi)容介紹：In this talk, we report a novel machine learning method based on tensor neural networks (TNNs) and adaptive subspace approximation methods for solving linear and nonlinear time fractional partial integro-differential equations (FPIDEs). In this framework, the Gauss- Jacobi quadrature and TNNs are effectively combined to construct a universal numerical scheme for the Caputo derivative with orders between 0 and 2, depending on time t, the Volterra integral and the Fredholm integral. Specifically, in order to overcome the difficulty of the initial layer, we design the TNN function multiplied by the function tμ when dealing with the initial condition and select the parameter μ according to different cases. Finally, some numerical examples are provided to validate the efficiency and accuracy of the proposed TNN-based machine learning method.