报告题目：Higher Order Extended Dynamic Mode Decomposition: Algorithms and Applications
报 告 人：丁维洋 博士
报告地点：腾讯会议 588-346-526
报告时间：2025年4月24日 星期四 10: 00--11: 00
报告摘要：We develop a data-driven approach for analyzing the underlying dynamics from snapshots, which is called the higher order extended dynamic mode decomposition (HOEDMD) in this talk. The HOEDMD method, generalizing the extended dynamic mode decomposition (EDMD), can handle the case when the spectral complexity of the dynamical system exceeds its spatial complexity. Moreover, the proposed method is capable to analyze the snapshots taken from multiple trajectories by a mode-frequency-individual decomposition. We also introduce the structured total least squares technique for denoising and debiasing purposes and discuss efficient implementation details.
The ability of our proposed method to accurately retrieve the modes with frequencies in linear dynamical systems is proved, which further provides an empirical choice for an optimal order. We also evaluate the proposed STLS-based HOEDMD algorithm and apply it to four kinds of dynamical systems: a synthetic linear system to show that the proposed algorithm is less sensitive to the noises, a nonlinear dynamical system of iterates from a multilinear PageRank model to illustrate the necessity of introducing higher order cases, real-world signals for time series classification to indicate individual coefficients could parameterize trajectories and kernel tricks can be employed to enhance its performance on nonlinear real-world systems, and a real-world dynamical system of fMRI data to show the proposed algorithm retrieves modes more stably over several other DMD variants. Finally, we develop a randomized algorithm for HOEDMD which further largely reduced the computational cost.
报告人简介：丁维洋博士，复旦大学类脑智能科学与技术研究院青年研究员、博士生导师，长期致力于矩阵、张量计算和优化及其应用研究，曾获得上海市自然科学二等奖、中国计算数学学会优秀青年论文奖等。在复旦大学数学科学学院获得数学与应用数学专业的学士学位和计算数学专业的博士学位，之后在香港理工大学应用数学系作博士后研究。2017年9月至2020年11月，在香港浸会大学数学系担任研究助理教授。其后于2020年11月加入复旦大学类脑智能科学与技术研究院，担任青年研究员。近期的主要研究兴趣包括超复数矩阵理论和计算、时空动力学分析及在脑与类脑科学的应用。
编辑：李朝迁 责任编辑：鲁学伟 审核：徐瑾
