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报告题目: Non-linear model reduction via Probabilistic Manifold Decomposition (PMD)
报告人：肖敦辉 教授 同济大学 数学科学学院
报告时间：2025年12月3日 下午13:30-14:30
报告地点：红瓦楼726
报告内容简介：This talk will present a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which 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.
报告人简介：肖敦辉，同济大学数学科学学院教授，国家高层次海外青年人才。同济大学信息办副主任（挂），计算数学教研室主任，中国数学会计算数学分会第十一届常务理事，中国岩石力学与工程协会AI实用化学会第一届常务委员，上海CSIAM委员。曾先后就职于英国帝国理工地球科学系和数据科学所，英国斯旺西大学有限元方法发源地之一的Zienkiewicz工程计算中心。于2013年获帝国理工全奖开始攻读计算流体力学博士，于2016年获博士学位，并且获帝国理工最佳科研博士生奖，一年一个。之后在帝国理工地球科学系和数据科学所从事博士后研究。后加入斯旺西大学辛克维奇工程计算中心从事科研和教学工作，担任讲师和博士生导师。主持过英国基金委如EPSRC， Royal Society和中国国家级项目多项。发表SCI论文50多篇。研究领域包括模型降阶、数据驱动模型、物理与数据混合驱动计算模型、数据同化、区域分解、计算流体力学、流固耦合的降阶模型等。
报告邀请人：方礼冬
