报告题目 (Title)：非线性模型降阶及其应用（Non-linear model reduction and its applications）
报告人 (Speaker)：肖敦辉 教授（同济大学）
报告时间 (Time)：2025年9月25日（周四）14:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：纪丽洁
主办部门：理学院数学系
摘要：This talk will present recent development of reduced order modelling. In addition, a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD) will be presented as well. The PMD provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system into a low-dimensional probabilistic manifold and predicting the dynamics. Through explicit mappings, PMD captures both linearity and non-linearity of the system. A key strength of PMD lies in its predictive capabilities, allowing it to generate stable dynamic states based on embedded representations.
The method also offers a mathematically rigorous approach to analyze the convergence of linear feature matrices and low-dimensional probabilistic manifolds, ensuring that sample-based approximations converge to the true data distributions as sample sizes increase. These properties, combined with its computational efficiency, make PMD a versatile tool for applications requiring high accuracy and scalability, such as fluid dynamics simulations and other engineering problems. By preserving the geometric and probabilistic structures of the high-dimensional system, PMD achieves a balance between computational speed, accuracy, and predictive capabilities, positioning itself as a robust alternative to the traditional model reduction methods such as DMD and POD.
