Seminar| Institute of Mathematical Sciences
Time: Wednesday, April 22th, 2026,10:00-11:00
Location: IMS, RS506
Speaker: Dunhui Xiao, Tongji University
Abstract: This talk will present a number of data driven model reduction methods. Also, recently developed non-linear model reduction method: Probabilistic Manifold Decomposition (PMD) will be also presented. PMD provides a powerful framework for constructing data driven 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.