内容簡介：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.

報告人：李秋齊

報告人簡介：湖南大學數學學院副教授，于湖南大學取得博士學位，并在美國德州農工大學CSC公派博士聯合培養，後先後在北京大學，香港大學，香港中文大學以及新加坡國立大學進行博士後研究。研究方向是不确定性量化和統計建模，多尺度方法，廣義多尺度方法以及大規模問題的代理模型的構造，模型約化方法。發表多篇高水平期刊論文（Journal of Computational Physics, SIAM Journal on Scientific Computing, Computer Methods in Applied Mechanics & Engineeringdent等）以及主持多項國家項目。

時  間：2024年9月14日（周六）下午14：00開始

地  點：騰訊會議号54238559950

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