报告题目：Higher Order Extended Dynamic Mode Decomposition  Based on the Structured Total Least Squares

报 告 人：丁维洋 研究员 复旦大学

报告时间： 2023年6月5日14：00

报告地点：龙洞校区610会议室

主 持 人：常静雅

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 paper. The HOEDMD method, generalizing the extended dynamic mode decomposition, can handle the case when the spectral complexity of the dynamical system exceeds its spatial complexity. Moreover, the proposed method is capable of analyzing 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. Finally, we evaluate the proposed structured total least squares 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 dynamic mode decomposition variants

简介：丁维洋博士现就职于复旦大学类脑智能科学与技术研究院，担任青年研究员。他于2011年和2016年在复旦大学数学科学学院获得理学学士学位和博士学位。2016年10月至2017年8月，他在香港理工大学应用数学系祁力群讲席教授的团队作博士后研究。2017年9月至2020年11月，他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。丁博士近期的主要研究兴趣包括张量计算和优化及其在脑与类脑科学领域中的应用。