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报告题目：A new reduced order model for parameterized PDEs based on dynamic mode decomposition
报 告 人：高振 中国海洋大学
报告摘要：Accurately constructing a reduced order model (ROM) of parameterized partial differential equations (PDEs) has always been the challenging problem in engineering and applied sciences. Dynamic mode decomposition (DMD) is a popular and efficient data-driven method for ROM, however, it is proposed for the model order reduction of time-dependent problems that it is invalid for the parameterized problems. In this talk, a new ROM is proposed based on k-nearest neighborhood (KNN) and DMD, namely, KNN-DMD. The KNN can be used to approximate the solution at any given parameter by choosing and averaging the nearest k DMD solutions based on the distance between the given parameter and other parameters. We apply the proposed method to various parameterized PDEs. The results demonstrate the applicability and efficiency of the proposed KNN-DMD as a real-time ROM for parameterized PDEs. Furthermore, KNN-DMD shows better predictive ability than the POD-based ROMs at the outside of the training time region.
报告人简介：高振教授是中国海洋大学数学科学学院副院长、博士生导师、山东省“泰山学者”青年专家、山东省高校优秀青年创新团队带头人，一直从事随机计算、计算流体力学、统计学习方法等的研究工作；主持国家重点研发计划课题、国家某重大科技专项项目、国家自然科学基金等10余项课题。
报告时间：2024年5月18日 9:00-11:30
报告地点：文渊楼 B536
主办单位：数学与统计学院
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