报告题目 (Title)：Efficient Numerical Methods for PDEs with Random Inputs in Multiscale Media
中文题目：带有随机输入的PDEs的高效数值方法
报告人 (Speaker)：李秋齐 副教授 湖南大学
报告时间 (Time)：2026年4月25日 (周六) 10：30-11：00
报告地点 (Place)：GJ303
邀请人(Inviter)：纪丽洁
摘要：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.