Koopman analysis of nonlinear systems with a neural network representation

作     者：Chufan Li Yueheng Lan Chufan Li;Yueheng Lan

作者机构：School of ScienceBeijing University of Posts and TelecommunicationsBeijing 100876China State Key Lab of Information Photonics and Optical CommunicationsBeijing University of Posts and TelecommunicationsBeijing 100876China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2022年第74卷第9期

页      面：183-193页

核心收录：

学科分类：0711[理学-系统科学] 12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 0835[工学-软件工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China under Grant No.11775035 the Fundamental Research Funds for the Central Universities with contract number 2019XD-A10 the Key Program of National Natural Science Foundation of China(No.92067202) 

主　　题：deep learning autoencoder Koopman operator Van der Pol equation coupled oscillator 

摘      要：The observation and study of nonlinear dynamical systems has been gaining popularity over years in different *** intrinsic complexity of their dynamics defies many existing tools based on individual orbits,while the Koopman operator governs evolution of functions defined in phase space and is thus focused on ensembles of orbits,which provides an alternative approach to investigate global features of system dynamics prescribed by spectral properties of the ***,it is difficult to identify and represent the most relevant eigenfunctions in ***,combined with the Koopman analysis,a neural network is designed to achieve the reconstruction and evolution of complex dynamical *** invoking the error minimization,a fundamental set of Koopman eigenfunctions are derived,which may reproduce the input dynamics through a nonlinear transformation provided by the neural *** corresponding eigenvalues are also directly extracted by the specific evolutionary structure built in.