内容简介：MOR methods aim to construct an approximate model in a low-dimensional subspace of the solution space. The success of these methods relies on the assumption that the solution manifold can be embedded in a low-dimensional space. However, the important class of problems given by parametric dynamical systems usually induce rough solution manifold with slowly decaying Kolmogorov n-widths. This implies that traditional MOR methods are generally not effective. In recent years, there has been a growing interest in the development of MOR techniques for parametric dynamical systems to overcome the limitations of linear global approximations. A large class of methods consider the dynamical low rank approximation  which allows both the deterministic and stochastic basis functions to evolve in time. Other strategies based on deep learning algorithms were proposed to construct the efficient surrogate model for time-dependent parametrized PDEs. In this talk, I will introduce  some nonlinear model reduction methods to construct the efficient and reliable approximation of input-output relationship for parametric systems.

报告人：李秋齐

报告人简介：湖南大学数学学院副教授，于湖南大学取得博士学位，并在美国德州农工大学CSC公派博士联合培养，后先后在北京大学，香港大学，香港中文大学以及新加坡国立大学进行博士后研究。研究方向是不确定性量化和统计建模，多尺度方法，广义多尺度方法以及大规模问题的代理模型的构造，模型约化方法。发表多篇高水平期刊论文（Journal of Computational Physics, SIAM Journal on Scientific Computing, Computer Methods in Applied Mechanics & Engineeringdent等）以及主持多项国家项目。

时  间：2024年9月14日（周六）下午14：00开始

地  点：腾讯会议号54238559950

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信息科学技术学院

2024年8月24日