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Koopman analysis of nonlinear systems with a neural network representation

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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.
出处 《Communications in Theoretical Physics》 SCIE CAS CSCD 2022年第9期183-193,共11页 理论物理通讯(英文版)
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)
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