Koopman analysis of nonlinear systems with a neural network representation |
| |
Authors: | Chufan Li Yueheng Lan |
| |
Institution: | 1.School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;2.State Key Lab of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China |
| |
Abstract: | 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. |
| |
Keywords: | deep learning autoencoder Koopman operator Van der Pol equation coupled oscillator |
|
| 点击此处可从《理论物理通讯》浏览原始摘要信息 |
| 点击此处可从《理论物理通讯》下载免费的PDF全文 |
|