报告题目 (Title)：Multiscale Modeling and Machine Learning Methods for Multiscale Fluid Problems (多尺度流体问题的多尺度建模与机器学习方法)
报告人 (Speaker)：李振 教授(Clemson University)
报告时间 (Time)：2023年11月13日8:30
报告地点 (Place)：腾讯会议 162-216-185
邀请人(Inviter)：李常品、蔡敏
主办部门：永利数学系
报告摘要：Multiscale features in many interesting physical systems originate from hierarchical structures across a wide range of temporal and spatial scales beyond the reach of any single simulation method. Multiscale modeling can seamlessly bridge the gap from microscopic scales to macroscopic scales, and thus become the key scientific approach playing unique roles in research of multiscale problems. In this seminar, I will first introduce mathematical and physical foundations of scale-bridging and derive new governing equations of reduced-order models. I will subsequently present a rigorous theoretical approach of the Mori-Zwanzig (MZ) projection to bridge scales in a soft matter system, by running a molecular dynamics simulation of polymer melts and constructing the MZ-guided coarse-grained model directly from atomistic trajectories, as well as the computation of memory kernels for non-Markovian dynamics. Then, I will introduce three machine-learning approaches applied to scale-bridging in multiscale fluid problems, including supervised parallel-in-time algorithms applied to neural network training, deep neural operators applied in multiphase problems, and physics-informed operator learning for model discovery from data.
