报告人：Prof. YangQuan Chen, ( University of California,Merced)
报告时间：2023年5月17日（星期三） 上午9:00-10:00
报告地点：数学与信息学院数学系715会议室
摘要：In the 1st part of this talk, I will introduce a triangle that connects “complexity”, “inverse power law” (IPL) and “fractional calculus” (FC). The key message is that, to better understand complexity one has to use FC. Based on this foundation, in the 2nd part of this talk, I will mainly discuss how FC, renormalization group (RG) theory and machine learning (ML) are connected. FC has been shown to help us better understand complex systems, improve the processing of complex signals, enhance the control of complex networks, increase optimization performance, and even extend the enabling of the potential for creativity. RG allows one to investigate the changes of a dynamical system at different scales. Although extensive research has been carried out on the three topics separately, few studies have investigated the association triangle between the FC, RG, and ML. In the FC and RG, scaling laws reveal the complexity of the phenomena discussed. It is emphasized that the FC's and RG's critical connection is the form of inverse power laws (IPL), and the IPL index provides a measure of the level of complexity. For FC and ML, the critical connections in big data, wherein variability, optimization, and non-local models are described. In the end, the association between the RG and ML is also explained. The mutual information, feature extraction, and locality are also discussed. Many of the cross-sectional studies suggest a connection between the RG and ML. It is shown that the new triangle between FC, RG, and ML, forms a stool on which the foundation to complexity science might comfortably sit for a wide range of future research topics.
YangQuan Chen教授简介：YangQuan Chen earned his Ph.D. from Nanyang Technological University, Singapore, in 1998. He had been a faculty of Electrical Engineering at Utah State University (USU) from 2000-12. He joined the School of Engineering, University of California, Merced (UCM) in summer 2012 teaching “Mechatronics”, “Engineering Service Learning” and “Unmanned Aerial Systems” for undergraduates; “Fractional Order Mechanics”, “Linear Multivariable Control”, “Nonlinear Controls” and “Advanced Controls: Optimality and Robustness” for graduates. His research interests include mechatronics for sustainability, cognitive process control (smart control engineering enabled by digital twins), small multi-UAV based cooperative multi-spectral “personal remote sensing”, applied fractional calculus in controls, modeling and complex signal processing; distributed measurement and control of distributed parameter systems with mobile actuator and sensor networks. He received Research of the Year awards from USU (2012) and UCM (2020). He was listed in Highly Cited Researchers by Clarivate Analytics in 2018, 2019, 2020 and 2021. His lab website is http://mechatronics.ucmerced.edu/
