Solving time-fractional partial integro-differential equations using tensor neural network

主讲人：阴小波 华中师范大学教授

时间：2026年1月31日9：30

地点：徐汇校区三号楼332室

举办单位：数理学院

主讲人介绍：阴小波，华中师范大学数学与统计学学院教授、博士生导师，副院长。本科毕业于南开大学数学科学学院，博士毕业于中国科学院数学与系统科学研究院，主要研究方向为有限元高精度算法、移动网格方法、非局部问题的数值分析、深度神经网络方法。已在SIAM Journal on Numerical Analysis, Journal of Computational Physics, SIAM Journal on Scientific Computing, IMA Journal on Numerical Analysis等杂志上发表多篇文章。主持四项国家自然科学基金项目，作为主要成员参与一项国家自然科学基金重大研究计划重点支持项目。

内容介绍：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.