汇报标题 (Title)：Efficient Numerical Methods for PDEs with Random Inputs in Multiscale Media
（带有随机输入的PDEs的高效数值步骤）
汇报人 (Speaker)：李秋齐 副教授（湖南大学）
汇报功夫 (Time)：2026年4月25日（周六）10:30-11:00
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：纪丽洁
主办部门：理学院数学系
提要：Partial differential equations (PDEs) with random inputs are widely used to describe complex physical systems with uncertainty, and their efficient numerical solution is an important issue in scientific computing and uncertainty quantification. When the random dimension is high or the system has a complex multi-scale structure, traditional methods often require a large number of computations in the high-dimensional parameter space, leading to a sharp increase in computational cost and the "curse of dimensionality". This report will introduce efficient numerical methods for PDEs with random inputs, focusing on how to explore the potential low-dimensional structures in the random solution space through low-rank structure analysis, model reduction techniques, and data-driven methods, thereby constructing an efficient dimensionality reduction computation and surrogate modeling framework. The related methods can significantly reduce the computational complexity while maintaining computational accuracy, and are applicable to high-dimensional random inputs, complex dynamic systems, and stochastic multi-scale problems.
