»ã±¨±êÌâ (Title)£º·ÇÏßÐÔÄ£Ðͽµ½×¼°ÆäÀûÓã¨Non-linear model reduction and its applications£©

»ã±¨ÈË (Speaker)£ºÐ¤¶Ø»Ô ½ÌÊÚ£¨Í¬¼Ã´óѧ£©

»ã±¨¹¦·ò (Time)£º2025Äê9ÔÂ25ÈÕ£¨ÖÜËÄ£©14:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

Ô¼ÇëÈË(Inviter)£º¼ÍÀö½à

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ÌáÒª£ºThis 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.