典型文献
Koopman analysis of nonlinear systems with a neural network representation
文献摘要：
The observation and study of nonlinear dynamical systems has been gaining popularity over years in different fields.The 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 operator.However,it is difficult to identify and represent the most relevant eigenfunctions in practice.Here,combined with the Koopman analysis,a neural network is designed to achieve the reconstruction and evolution of complex dynamical systems.By 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 network.The corresponding eigenvalues are also directly extracted by the specific evolutionary structure built in.
文献关键词：
中图分类号：
作者姓名：
Chufan Li;Yueheng Lan
作者机构：
School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China;State Key Lab of Information Photonics and Optical Communications,Beijing University of Posts and Telecommunications,Beijing 100876,China
文献出处：
引用格式：
[1]Chufan Li;Yueheng Lan-.Koopman analysis of nonlinear systems with a neural network representation)[J].理论物理,2022(09):179-189
A类：
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B类：
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AB值：
0.601292
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